Quantum Physics Paper Analysis

Fault-tolerant logical operations are fundamental for scalable quantum computation. Here, we report the experimental realization of lattice-surgery operations between a pair of distance-three surface-code logical qubits on a planar superconducting processor. During repeated syndrome extraction cycles, the logical qubits exhibit per-cycle error rates of $0.0365(2)$ and $0.0282(1)$, respectively, after leakage events are rejected. By leveraging joint initialization and lattice splitting, we deterministically prepare a logical Bell state, confirming genuine bipartite entanglement via the error-corrected logical state fidelity. We further execute a two-qubit Deutsch-Jozsa algorithm at the logical level to demonstrate algorithmic utility in a fault-tolerant framework. Finally, to achieve universal control, we implement magic-state injection and gate teleportation to realize continuous non-Clifford rotations about the logical $X$ axis. For the logical $R_{X}(π/4)$ gate, we achieve a logical gate fidelity of $0.943_{-9}^{+10}$ conditioned on the absence of detected errors. These results establish lattice surgery as a practical and versatile paradigm for logical computation in near-term surface-code architectures, representing a critical milestone toward scalable fault-tolerant quantum advantage in superconducting circuits.

Quantum Darwinism extends the decoherence formalism to explain how classicality and objectivity emerge from quantum mechanics. However, existing approaches often capture only partial aspects of objectivity, leading to its mischaracterization and making it difficult to pin down precisely. By connecting quantum Darwinism to operator algebra quantum error correction, we show that the emergence of objectivity can be identified with the algebraic local recoverability of quantum codes. Applying this algebraic framework to stabilizer codes, we show that it yields a far more precise characterization of classicality and redundancy, unifies the traditional measures of objectivity, enables efficient classification via coding-theoretic tools, and supports large-scale Clifford simulations of decoherence dynamics.

High-rate quantum low-density parity-check (qLDPC) codes are a leading candidate for fault-tolerant quantum computing. They feature higher encoding rates than planar alternatives such as the surface code, but their implementation often entails significant hardware hurdles like the need for long-range couplers. We leverage the flexibility of a trapped-ion quantum computer to demonstrate nine quantum error-correcting codes with starkly different qubit connectivity requirements on a single device without any hardware reconfiguration. These experiments span three families of quantum error-correcting codes: qLDPC codes, topological codes, and concatenated codes. With a qLDPC code encoding 4 logical qubits into 18 physical qubits, we achieve a logical error rate up to $9\times$ better than a previous demonstration of a similar code on superconducting solid-state qubits. Moreover, our implementation exhibits breakeven performance, with some instances achieving qubit lifetimes comparable to or slightly exceeding that of our trapped-ion qubits. We use a novel implementation of the optical-metastable-ground (OMG) architecture for addressable mid-circuit measurement and reset, which enables us to perform these experiments without any ion transport or dedicated coolant ions, requirements that typically consume a large fraction of the runtime or ion count of trapped-ion quantum computers.

Fault-tolerant quantum computation is inherently a spacetime problem, requiring not merely good static quantum error-correcting codes but also low-overhead protocols for protecting and manipulating encoded quantum information over time. Fault complexes provide a homological framework for treating such protocols as single spacetime objects. In this work, we initiate the study of low-overhead fault complexes by introducing {spacetime lifting}, a method that constructs fault complexes from symmetry-reduced product structures beyond standard foliation. We show that spacetime lifting yields fault complexes and in particular {spacetime-lifted} memory experiments with almost-linear fault distance in the total spacetime cost, which substantially outperforms existing constructions. We further interpret fault complexes as measurement-based cluster-state protocols and identify general conditions under which they realize fault-tolerant logical teleportation, showing that spacetime-lifted constructions combine favorable scaling with operational schemes. Our study opens a path toward more efficient quantum fault tolerance through general complex constructions.

The major challenge on the way to fault-tolerant quantum computing comes from the insufficient quality of hardware components and the difficulty of scaling their number without further compromising fidelity. Quantum Low-Density Parity-Check (qLDPC) codes offer a promising solution by encoding logical qubits with low overhead and at a comparatively high code distance. However, it remains an open question how to scalably implement efficient qLDPC codes on fixed-connectivity quantum chips without increasing hardware complexity to enable the non-local interactions in their underlying QEC cycles. We resolve this challenge for the first time by introducing a family of qLDPC "barbell" codes accompanied by a realistic chip layout that natively supports all required two-qubit interactions. Crucially, the hardware complexity required to implement barbell codes remains constant as code distance increases. We provide a detailed investigation into the feasibility of all required hardware components and simulate a specific family of barbell codes against circuit-level noise. We find that, with a modest overhead of $<30$ data qubits per logical qubit, barbell codes can preserve information at a physical noise strength of $10^{-4}$ for several trillion QEC cycles. Simulations of logical multi-Pauli measurements, performed with circuits tailored to the chip, yield similar logical performance per QEC round, indicating that entangling gates between logical qubits in barbell codes can be realized fault-tolerantly.

Gottesman-Kitaev-Preskill (GKP) states are essential non-Gaussian resources for fault-tolerant photonic quantum computing, enabling logical qubit encoding with intrinsic robustness against errors. Several approaches to GKP state preparation have been explored, including measurement-based protocols in circuit QED and trapped-ion systems, cat-state breeding, and photon-subtraction schemes. However, these methods are either restricted to specific platforms or require deep non-Gaussian resource chains with exponentially low success probabilities. Gaussian Boson Sampling (GBS) offers a compelling all-photonic alternative by generating non-Gaussian states through measurement-induced nonlinearity, without the need for matter-based ancilla or active feedforward. Nevertheless, its practical implementation is limited by the exponential computational cost of evaluating matrix hafnians-#P-complete functions that govern photon-number probabilities. To address this challenge, we introduce a two-stage Histogram Gradient Boosting surrogate pipeline that predicts, without any hafnian computation, the optimal heralding pattern, circuit fidelity, and post-selection probability for candidate GBS circuits, while reserving exact quantum simulation exclusively for surrogate-selected candidates. Trained on circuit configurations across 3-5 optical modes, the surrogate achieves 90.0% GKP-detection accuracy on a held-out set, representing a 23.7 percentage-point improvement over the baseline, with a fidelity mean absolute error of 0.032 and a log-scale post-selection probability $R^2 = 0.837$, reducing the total simulation burden by approximately 90%.

In recent years, the spacetime code has arisen as a candidate for a unifying view of fault tolerance in space and time. On the other hand, the recent study of dynamical phases has increasingly turned its attention to fault tolerance as a notion of a dynamically stable process. In this work, I explore one pathway between the two, achieved by gauging the spacetime code. This gives rise to a lattice gauge theory that inherits the elements of fault tolerance associated with a circuit, with Gauss laws corresponding to equivalence relations between configurations of spacetime errors and Wilson loops corresponding to detectors. The obtained gauge theory finds a surprisingly wide array of applications, from quantum error correction to condensed matter physics, and even learning theory: (1) It contains in its description foliated computation, and hence gives rise to one version of a gauge theory for measurement-based quantum computation. (2) For a class of topologically ordered mixed states, it gives us a gauge-theoretic language to describe the classical memory associated with the state. (3) The gauge-invariant observables of the theory which describe detectors also coincide with the learnable degrees of freedom of circuit Pauli noise.

Classically testing for the presence of anti-commuting operators on a quantum device is a critical tool underpinning recent progress in classical verification of quantum computation. While such tests can be based on cryptographic assumptions, known constructions rely on highly structured assumptions, e.g. trapdoor claw-free functions. In this work, we seek to explain this state of affairs by constructing strong cryptography from (certain forms of) classical tests of anti-commutation. In particular, we formulate the notion of a test of non-commutation (ToNC), an interactive protocol between a quantum prover and classical verifier in which the prover's final-round response is obtained by measuring one of two binary observables $P_0,P_1$ depending on the verifier's challenge bit $c$. We prove that, for a broad range of parameters, ToNC implies classical-communication key agreement (KA), and ToNC combined with one-way functions implies oblivious transfer (OT). Along the way, we develop tools for and provide the first known results on hardness amplification for post-quantum KA and OT, where communication is classical but adversaries may be quantum. In particular, we prove the following results of independent interest. - Post-quantum hard-core measure theorem: For any efficiently sampleable high-min-entropy distribution $D$ over pairs $(x,b)$ such that quantum circuits have advantage at most $δ$ in predicting $b$ from $x$, there exists a sub-distribution $M\preceq D$ of density $(1-δ)$ on which $b$ is nearly optimally quantum-hard to predict. - Post-quantum interactive XOR lemma: Given any classically-interactive protocol, if quantum adversaries have advantage at most $δ$ in guessing a private challenger bit $b$, then two sequential repetitions reduce the advantage for predicting the XOR of the challenger bits $b_1\oplus b_2$ to at most $δ^2+\rm{negl}(λ)$.

Quantum error correction protocols protect against local errors by storing logical information non-locally. This poses a challenge: how to design efficient logical gates on the non-local ``hidden'' logical information, and how to implement these gates using the local physical operations. We develop a general description of planar Pauli stabilizer codes and protocols for logical operations in terms of point-like particles called Majorana fermions. Information is stored in the pairwise fermion parities of spatially separated Majorana fermions. The description in terms of Majorana fermions captures not only large distance asymptotics, but also all scales down to the lattice constants. We exploit this locality to densely pack logical information in spacetime. The simplest application is to a static case: dense memory. More importantly, we implement fault-tolerant Majorana motion and leverage this primitive to design braiding-based logical gates. This approach reduces space overhead of logical operations resulting in an improved logical error rate given fixed number of physical qubits. We illustrate a practical use of our approach by designing and benchmarking of 2-qubit Clifford gates. We find numerically that our protocol outperforms lattice surgery in this setting for near-term error rates and realistic device constraints. More generally, introduction of compact motion of Majorana fermions as an efficient computational primitive opens a promising new route for the design of low overhead error correction protocols.

Quantum circuit ensembles that have the properties of unitary k-designs represent applications where there is no obvious bias toward any particular Pauli support, as is the case in simulating systems exhibiting ''quantum chaos,'' which range from quantum dynamics near black holes to gapless spin fluid analysis. However, noisy hardware makes quantum circuits prone to a myriad of error sources, of which depolarizing and coherent error can be particularly destructive. To combat depolarizing error, popular techniques typically involve circuit or gate folding, which can be time-intensive procedures due to increased circuit depth and shot overhead. Other tensor-network-based mitigation techniques suffer from intractability in high-entanglement regimes. In this work, we leverage the structure of unitary k-design Pauli support distributions by introducing a technique we name ''circuit balancing,'' along with gate benchmarking data, in order to estimate circuit-wide depolarization. We describe how to invert the diagnosed circuit depolarization even in the presence of coherent error, via Pauli twirling. We provide asymptotics to estimate the number of twirls needed to maintain a desired output fidelity. We test our method numerically in a variety of simulation settings and find that it can significantly reduce average random circuit infidelity. Further, we employ our methods to find significant infidelity reductions when running a random circuit ensemble on a contemporary superconducting quantum computer, IBM Fez. Overall, we show that the method effectively reduces gate-based error for unitary k-designs without incurring any two-qubit gate overhead.

A central promise of topological quantum computing is that increasing the excitation gap improves device performance significantly. Here, we experimentally validate this principle in an InAs--Pb tetron device via interferometric single-shot parity measurements. By replacing aluminum with the higher-gap superconductor lead in our superconductor-semiconductor hybrid devices, we have improved the robustness of our topological phase. In addition, to enable fast and precise bring-up at scale, we have developed an rf measurement technique that resolves low-energy wire-end states and directly measures their energy splitting with $μ\text{eV}$ precision. We employ this technique to bring up a device in a multi-tetron array and perform parity measurements of one of the tetron's hybrid nanowires (NWs). By controllably switching the wire parity, we observe $h/2e$-periodic bimodal shifts in the quantum capacitance of a quantum dot coupled to the hybrid nanowire in an interference loop. Further time-resolved measurements reveal a characteristic parity switching time of $\sim 20$ s with some instances reaching minute-scale. Such extremely long parity lifetimes are orders of magnitude longer than typical qubit operation times, which are on the order of $μ\text{s}$. Finally, we discuss potential implications for the fidelity of Pauli measurements.

Quantum low-density parity-check (QLDPC) codes are promising candidates for practical low-overhead quantum memories. For large-scale fault-tolerant quantum computation, we further need logical processing methods for QLDPC codes. In this work, we construct full extractors -- surgery systems capable of measuring arbitrary logical Pauli operators on a code block -- for several hypergraph product (HGP) codes. These extractors enable logical processing via Pauli-based computation (PBC) without the compilation overhead observed in prior works. Moreover, our extractors have sizes between 50% and 80% of the base HGP codes, and the extractor-augmented codes can be supported on fixed connectivity hardware with maximum qubit degree ten. Our approach involves assembling many partial extractors with verifiable fault-tolerance into a single full extractor. For a distance 10 HGP code, circuit-level noise simulations yield logical measurement error rates of approximately $10^{-6}$ at a physical error rate of 0.1%. These results demonstrate that extractor architectures, when designed in the fixed-connectivity setting, can achieve the space efficiency of QLDPC codes without introducing compilation overhead compared to surface code PBC architectures.

Noise remains the primary obstacle to realizing quantum advantage, continuously degrading the resources that enable quantum technologies. Purification aims to reverse this degradation by extracting high-fidelity resources from noisy ensembles, yet its conventional formulation is intrinsically static, acting only after noise has taken effect. Here we instead recast purification as a dynamical task, introducing a spatiotemporal framework that distributes interventions across the noise process. This formulation reveals operational capabilities inaccessible to existing approaches and gives rise to forward-assisted purifications that extend achievable performance. In certain regimes, a single-copy protocol already exceeds what can be achieved with up to 50 copies under conventional purification, demonstrating a significant overhead in required resources. Beyond these gains, our framework circumvents no-purification theorems within conventional protocols, including for Bell-state ensembles, thereby enabling purification previously considered impossible and pointing toward an efficient route to mitigating noise in quantum systems.

The ZX-calculus is a powerful graphical language for manipulating quantum circuits, which has recently found many applications in quantum error correction. We extend this language to handle Floquet and other dynamical stabilizer codes via the connection between measurement-based code switching and gauge fixing (arXiv:1810.10037). We combine gauge-fixing steps to implement a closed loop in the space of stabilizer codes, returning to the original codespace up to a logical Clifford gate. These measurement-based paths in the space of stabilizer codes can be viewed as shortcuts, or "chutes and ladders", relative to single-qubit Clifford operations and qubit permutations. This yields a machine-interpretable method for constructing dynamical automorphisms and facilitates the search for implementations of desired logical gates. As an example, we implement a logical phase gate via distance-preserving code switching for the seven-qubit code bare code (arXiv:1702.01155), which has no non-trivial logical Clifford gates based on single-qubit Clifford operations and qubit permutations (arXiv:2409.18175).

Clifford codes are a natural generalization of quantum stabilizer codes based primarily on representation theory. This class of codes has previously been extended to the setting of quantum subsystem codes. We formulate a two-fold generalization of Clifford codes, for both the hybrid classical and quantum information and projective representation theory settings. This leads to new classes of hybrid subspace and subsystem Clifford codes. We extend the fundamental representation theoretic quantum error correction theorem to include these codes, based on the operator algebra quantum error correction framework. We also discuss several examples throughout the presentation, of both stabilizer and non-stabilizer type.

Microwave crosstalk poses a major challenge to scaling superconducting quantum devices as it introduces excess control errors. Although its magnitude and impact have been explored in various experimental settings, quantitative physical models capable of explaining measured crosstalk for a given device geometry remain scarce. Here, we address this gap by investigating microwave crosstalk in planar superconducting devices with crossovers. We identify two structures that can lead to strong crosstalk: a drive line routed in close proximity to another qubit, and a drive line crossing a qubit-qubit coupler using an air bridge. We design and characterize devices involving these structures and develop physical models that quantitatively explain the experimentally observed crosstalk. Based on these models, we discuss the design considerations for reducing microwave crosstalk. Our results provide practical guidance for low-crosstalk device layouts and establish a basis for the systematic investigation of weaker crosstalk mechanisms.

Quantum LDPC code discovery requires searching large algebraic design spaces while reliably certifying the parameters and equivalence classes of any candidates found. We introduce an LLM-guided evolutionary workflow in which language models mutate Python programs that generate bivariate-bicycle and perturbed bivariate-bicycle code ansätze. Across five campaigns, the system performed approximately 1{,}650 evolutionary iterations, screened about $2 \times 10^5$ candidate codes, and required ${\sim}140$ hours of computation and ${\sim}$US\$400 in LLM inference cost. Candidate codes are evaluated through a staged validation pipeline combining $\mathrm{GF}(2)$ rank computation, distance estimation and certification, mixed-integer linear programming, BLISS Tanner-graph deduplication, decomposability analysis, and local-Clifford equivalence checks. At block length $n \leq 360$, the workflow identifies 465 distinct candidate codes: 97 CSS bivariate-bicycle codes and 368 non-CSS perturbed variants. The CSS search recovers known high-performing codes and finds new finite-length representatives, including an indecomposable [[288,16,12]] code and higher-weight codes with up to $k = 50$ at distance $d = 8$. The non-CSS search produces perturbed codes matching the gross-code figure of merit at [[144,12,12]], along with additional high-distance candidates reported as certified values or upper bounds according to MILP status. Overall, these results show that LLM-guided program evolution can serve as a practical tool for structured quantum-code discovery when paired with independent evaluation.

Shor's algorithm represents the main threat of quantum computers to cryptography. In order to precisely understand its feasibility, many authors have worked towards reducing its costs, either at the logical level (assuming a fault-tolerant architecture), or at the physical level (taking into account the constraints of envisioned hardware). In particular, recent works by Chevignard et al. (CRYPTO 2024) and Gidney (arXiv 2025) used improved arithmetic to significantly reduce the qubit cost of factoring RSA public keys. Even more recently, Babbush et al. (arXiv 2026) improved the cost of computing elliptic curve discrete logarithms, with a reduction of a factor 2 to 3 in gate count and qubit count compared to a previous work by Litinski (arXiv 2023). Their result relies on optimized point addition circuits on elliptic curves over prime fields. However they did not reveal their logical quantum circuits, relying instead on a zero-knowledge proof. In this paper, we detail a quantum logical circuit architecture which gives similar results as Babbush et al., with a slightly higher number of qubits (around 1.5% increase) and a slightly smaller Toffoli gate count (between 6.5% and 10% reduction) for the curve secp256k1. We also give gate counts for a generic variant of the circuit, which is valid for any prime field.

We apply the single-equation duality criterion to the square-octagonal random-bond Ising model recently obtained from an exact error-edge map for a surface code with nearest-neighbor correlated errors. The calculation is performed for the minimal cell after the error-edge reduction. For the symmetric case \(p_1=p_2=p_3=p\), this gives \(p_c=0.0288427147\), in close agreement with the reported numerical threshold of about \(3\%\).

Compile-time optimization is important for improving the efficiency and reliability of quantum circuits on current noisy hardware. While many existing methods simplify circuits using structural patterns or quantum-state information, most of them target only unitary circuits and do not support dynamic circuits with mid-circuit measurements and classical feedforward. In this work, we present Branch-Aware Quantum Constant Propagation (BQCP), a compile-time analysis for dynamic circuits. BQCP extends Quantum Constant Propagation (QCP) by tracking the classical information produced by mid-circuit measurements together with the corresponding post-measurement quantum states across different execution branches. This enables path-sensitive reasoning inside conditional blocks and more precise information propagation than QCP. To keep the analysis scalable, we bound both the size of the quantum-state representation and the number of tracked branches. Using the information inferred by the analysis, we apply semantics-preserving simplifications to circuit operations. We prove the soundness of both the analysis and the simplifications. Experimental results on both application-driven and synthetic benchmarks show that, on dynamic circuits, our method consistently achieves larger reductions than other existing passes including QCP.

Classical simulation of quantum circuits is expensive for two distinct reasons. The obvious one is state-space size: an n-qubit system requires exponentially many amplitudes. The less obvious one is interference: useful output distributions emerge only after many computational histories have been coherently combined at common endpoints, and this aggregation step is itself a substantial source of cost. We introduce statistical interference sampling, a framework that makes this second bottleneck explicit by treating endpoint interference as a separately schedulable computation. Using the Chemical Abstract Machine (ChAM) as our model, weighted path contributions evolve as concurrent molecular species, and interference reactions combine contributions that share a common output state. A threshold rule terminates the process once an endpoint accumulates sufficient amplitude, discarding the remaining reactions. The method does not improve worst-case complexity and is not intended as a general-purpose simulator. Its purpose is to ask a more targeted question: how much of the interference calculation can be skipped while still recovering a useful output distribution? On benchmark circuits for Deutsch-Jozsa, Grover search, Simon's problem, and small Shor period-finding instances, we find that nearly 50% of endpoint interference reactions can be omitted while maintaining over 90% output accuracy for most algorithms tested. These results suggest that interference arithmetic is a structured resource that admits meaningful approximation, and that exposing it explicitly opens new opportunities for pruning strategies across path-sum, Pauli-path, and tensor-network simulation methods.

Exact tensor network contraction underpins quantum circuit simulation, quantum error correction, combinatorial optimization, and many-body dynamics. The dominant parallelization strategy, slicing, scales exponentially and incurs redundant computation. We present a multi-GPU framework that instead distributes intermediate tensors across devices with explicit communication, converting a fixed contraction path into a communication-efficient schedule via GEMM-oriented mode reordering and communication-aware mode distribution planning. Within a single DGX H100 node (8 GPUs, NVLink), distribution delivers $7$--$173\times$ extra speedup beyond embarrassingly parallel slicing, capturing nearly all of the available compute reduction (87--101%) because NVLink's high bandwidth keeps communication small relative to compute. Scaling the same four workloads to 1024 H100 GPUs over InfiniBand, the extra speedup beyond slicing ranges from $42\times$ to $67{,}869\times$, demonstrating that communication-aware distributed contraction far surpasses slicing-based scaling limits for frontier tensor networks.

Fluxonium qubits have demonstrated high-fidelity operations and long coherence times in small-scale systems, highlighting their promise for quantum computing. However, large-scale integration into a high-performance two-dimensional (2D) qubit array remains the central challenge for practical applications. In this work, we introduce an extensible architecture for scaling up fluxonium qubits in 2D grids. To address the key challenges, namely achieving controllable strong interaction and high connectivity for qubits featuring small shunting capacitors (footprints), we propose using low-shunt-capacitance couplers to enable tunable interactions between fluxonium qubits. When embedded into 2D square lattices, large couplings can be achieved even with relatively small coupling capacitances, thus enabling multiple connections with sufficient capacitance budget. We further propose coupler realizations based on generalized flux qubit circuits, specifically the quarton and the fluxonium, and demonstrate that both enable fast, high-fidelity gates with low spectator errors, while supporting multiple connections on 2D grids.

The quantum speed limit establishes a bound on the minimal time required for a quantum system to evolve from a given initial state to a final state. When the mean energy variance is fixed this limitation is captured by the Mandelstam--Tamm bound. The fastest quantum evolution saturating this bound follows a geodesic arc connecting the two states. Such geodesics in the manifold of quantum states are explicitly known when the states are pure (Fubini-Study geodesics) and when they are mixed and given by faithful density matrices (Bures geodesics). In this article we obtain the explicit form of the Bures geodesic arcs joining two non-faithful density matrices, which may have different ranks. For pure states one recovers the Fubini-Study geodesics. A necessary and sufficient condition for the uniqueness of the shortest geodesic arc is given. When the condition is not fulfilled there are infinitely many such arcs, all having length equal to the arccos Bures distance between the two states, in analogy with the arcs of great circles connecting the two poles of a sphere. We discuss the implications of our results for the quantum speed limit.

A linear optical medium can delay, mix, and superpose light, but never make two pulses multiply: multiplication is nonlinear, and a linear system has no such operation. This roots a sharp limit on continuous-variable quantum reservoir computers (QRCs) built from Gaussian optics. Within the reservoir they cannot form genuine products of the input at different past times, the cross-time nonlinear correlations many temporal computations require; they can only fake them by storing each past input separately and multiplying in the readout, forcing an exponentially harder high-order measurement. We show that a single Kerr (intensity-dependent phase) element in a time-delayed feedback loop removes this limit. The Kerr effect makes phase depend on intensity, a true multiplication inside the medium; feedback makes the light revisit that element repeatedly, so one mode mixes its own history against itself once per round-trip. Feedback turns time into space: D passes through one nonlinear mode replace D parallel linear modes. We prove an unbounded resource separation (Theorem 3, Corollary 2): an N-mode Gaussian reservoir reaches cross-time nonlinear rank at most 2N, a hardware ceiling, while a single Kerr mode reaches rank equal to its feedback depth D, costing no extra modes. For every N, one Kerr mode performs a computation no N-mode linear reservoir can. Loss is the counterintuitive ingredient: each round-trip dims the light, so the nonlinear phase differs pass to pass, giving every echo its own fingerprint; without loss the passes would be redundant. We confirm activation on an exact open-system simulation and ground the separation in nonlinear channel equalization. Achievable D is 30 to 230 on integrated platforms, so one nonlinear mode replaces up to about 100 linear ones, at the price of measurement time.

We introduce and study a unified framework for density-functional theory and its variants for quantum systems on finite-dimensional Hilbert spaces. These theories seek to reduce the complexity inherent in the many-body quantum problem by describing ground states through reduced variables. The central ingredients of our unified framework are a generalized choice of basic observables, whose expectation values define precisely those reduced variables, and a fixed part of the Hamiltonian characterizing the class of quantum systems under consideration. It is this minimal structure, which we call the scope of a functional theory, that is necessary and sufficient for the formulation of a functional theory. In particular, it allows one to define the universal functionals, establish their convexity and differentiability properties, address representability questions, and prove a Hohenberg-Kohn-type uniqueness result. A purification construction also relates ensemble and weighted-ensemble functionals to the pure-state variant. Particular emphasis is placed on functional theories with Lie-algebra observable structures, connecting the variational framework to symplectic geometry. The result of this work is a systematic mathematical formulation in which structural results can be proved once and applied across a broad class of finite-dimensional functional theories.

A quantum system can restore a broken symmetry faster the more strongly it initially breaks it, an anomaly known as the quantum Mpemba effect. Whether this effect survives once conservation laws fragment the Hilbert space into exponentially many disconnected Krylov sectors has remained open. We address this question for circuits and Hamiltonians with simultaneous charge and dipole conservation, the paradigmatic setting for strong Hilbert-space fragmentation. Combining a replica tensor-network formulation for charge and dipole-conserving gates, which reaches the annealed Rényi-2 entanglement asymmetry up to $L=128$, with Hamiltonian simulations and an exactly solvable dissipative model, we uncover a higher-order symmetric quantum Mpemba effect: the charge and dipole asymmetries each display Mpemba-like crossings on parametrically distinct timescales. Resolving the state into frozen and active Krylov sectors reveals the mechanism: frozen fragments retain a finite asymmetry that obstructs full restoration, while active fragments host the relaxation responsible for the crossings. Fragmentation thus does not preclude the quantum Mpemba effect but reshapes it into frozen memory and active-fragment relaxation, providing a framework for the Mpemba phenomenology of higher-moment symmetries.

Non-Hermitian topological phases are usually engineered through gain, loss, asymmetric couplings, or explicit environmental channels. Here we show that non-Hermitian crystalline braid topology can instead emerge from projection alone, starting from a fully Hermitian and topologically trivial parent lattice. The mechanism is zero-mode-resonant projection. When the eliminated complement is zero-mode free, projection has a smooth low-frequency limit and reduces to a static Schur complement, yielding conventional SSH-type descendants. When a complement zero mode couples to the retained subsystem, the embedding self-energy develops a pole, the zero-frequency limit becomes singular, and topology is carried by the finite-frequency projected Green's function-where frequency is a tunable parameter, the drive frequency in a circuit realization, for instance. We demonstrate this mechanism in an exactly solvable model, a trivial nearest-neighbor square lattice with an embedded one-dimensional zig-zag brane. Odd-parity periodic sectors are resonant: a sublattice-imbalance zero mode generates the singular self-energy, and the complex spectrum forms an abelian two-band braid whose transitions occur only at isolated finite frequencies. Although the internal class is $\text{AI}^†$ featuring only trivial phases, embedding parity induces conjugated pseudo-Hermiticity (CPH), quantizes the complex Berry phase, and identifies it with the braid count. The model is free of the non-Hermitian skin effect, making the invariant a genuine Bloch bulk quantity. In topolectrical realizations, the same finite-frequency braid transitions appear as transmission zeros and admittance features at the predicted drive frequencies.

We study a bosonic analog of the paradigmatic Dicke model of superradiance, comprising interacting bosonic modes subject to fully symmetric collective decay. Depending on the interaction strength, we uncover qualitatively distinct regimes of emission. For strong interactions, the emission closely resembles Dicke superradiance, with perturbative corrections arising from the presence of additional levels. For weaker interactions, the bosonic statistics qualitatively changes the dynamics, leading to a crossover to subradiant emission. Remarkably, we show that the dynamics in this regime can be described by rate equations analogous to those of the Dicke model despite the large accessible bosonic Hilbert space. Our findings are based on a combination of analytical arguments and large-scale numerics enabled by the permutational symmetry of the problem and may be probed in circuit QED experiments.

Quantum many-body scars (MBS) exhibit weak ergodicity breaking and long-lived coherent dynamics within an otherwise thermal spectrum. We investigate their metrological properties using the quantum Fisher information (QFI), focusing on estimating the amplitude of a weak AC field in the PXP model. We show that the approximately uniform energy spacing of the scar tower enables collective resonant processes when the driving frequency matches integer multiples of the scar gap, resulting in a quadratic-in-time growth of the QFI over an extended time window. We analyze how the connectivity induced by different probe operators shapes sensing performance and demonstrate that staggered magnetization leads to a more favorable growth of the QFI with system size than homogeneous magnetization. Through frequency scanning and finite-size analysis, we characterize the scaling of the QFI with the number of particles. Finally, we develop a single-tower approximation under resonant driving, deriving a compact analytical expression that captures the time dependence and system-size scaling of the QFI. Our results establish how to leverage structured non-ergodic dynamics in quantum sensing protocols.

We introduce the quantum vector Hopfield network, in which patterns are formed by orientations of quantum vector spins; quantum dynamics arise intrinsically from the non-commutativity of the spin operators. We derive the equations of state and the phase diagrams for this network as well as its classical counterpart. We find that quantum fluctuations, surprisingly, stabilize the stored patterns. Both the critical retrieval temperature and the target pattern overlap are enhanced relative to the classical network. Additionally, we find that this enhancement grows with pattern loading up to network capacity. We interpret this effect as an analog of quantum order-by-disorder, a mechanism by which quantum fluctuations promote the formation of ordered phases. These findings offer a new route to quantum-enhanced associative memory.

We study inner products and partial amplitudes of graph states--a commonly employed class of quantum states, which are specified by graphs. We find that the magnitudes of these quantities are simply related to the rank of the adjacency matrix of the graph over F_2 while the phase is determined by the Arf invariant of its quadratic refinement. These facts motivate a nonlocal tensor factorization of the Hilbert space, with respect to which all graph states are products of Bell pairs with unentangled ancillae. These results may illuminate the quantum advantage in the framework of Measurement-Based Quantum Computation and suggest that graph states can be usefully visualized in the language of algebraic topology. In addition, we develop a specialized technique for computing expectation values of qubit-wise permutations in graph states, which is useful for calculating multi-invariants.

Plasmonic nanocavities enable the synchronization of spatially distant emissive dipoles through strong near-field coupling in sub-nm gaps. We report formation of a room-temperature synchronized dipole state in locally-ordered plasmonic nanogap 2D arrays under non-resonant continuous-wave pumping. Unlike lasers, photonic Bose-Einstein condensates, or exciton-polariton condensates, this system exhibits spatial coherence across the dipoles, while rapid radiative and non-radiative emission suppresses temporal photon coherence. A change of behaviour is observed with increasing pumping, marked by the spatial spread of g(1) coherence, but without spectral narrowing or directional emission. This driven-dissipative system exhibits fast temporal coherence decay and complex spatial correlations, offering a new platform for studying synchronization at room temperature. Combining ultralow mode volumes, high Purcell enhancement, and scalable ambient operation, it opens pathways for novel photonic and quantum technologies.

We investigate the interacting non-Hermitian Su-Schrieffer-Heeger (SSH) model, focusing on the interplay between topology and charge ordering. Using a real-space topological marker, charge correlations, and the complex many-body spectrum, we map out the phase diagram under periodic and open boundary conditions. We show that the topological marker remains a robust diagnostic of non-Hermitian topological phases in the presence of interactions and consistently signals their breakdown at the onset of a charge density wave (CDW). We further demonstrate that non-Hermiticity enhances interaction effects: While moderate changes occur under periodic boundary conditions, open boundary conditions lead to a pronounced amplification of staggered charge correlations near exceptional points. This enhancement arises from the accumulation of low-energy states near exceptional points, which promotes electronic instabilities and strengthens CDW tendencies.

Quantum algorithms for basic numerical linear algebraic tasks have proven essential for translating diverse problems to a unified quantum computational context. Many of these tasks -- e.g., applying a polynomial function to the spectrum of a matrix embedded in a unitary process (a so-called block encoding), or taking linear combinations of block encodings -- are well-addressed by techniques like quantum singular value transformation (QSVT) or linear combination of unitaries (LCU). However, there exist useful matrix transforms whose realization by existing quantum algorithms is unclear or inefficient. In this work we construct improved quantum algorithms for some of these transforms, the simplest of which is a polynomial function applied element-wise. We show the space required to compute quantum element-wise transforms can be reduced exponentially in the degree of the applied function compared to prior work, and raise and rectify errors in previous constructions. We present our algorithms alongside applications to machine learning, simulation, and signal processing.

We present a rigorous theoretical framework for symmetry breaking and quantum irreversibility arising from stochastic Ito field reversal within a cubic-quintic nonlinear Schrodinger equation (CQ-NLSE) formalism. Starting from three physically motivated considerations, forward and backward nonlinear stochastic differential equations are derived via the Ito calculus. Kinematic time-reversal is shown to be fundamentally incompatible with the Ito stochastic structure, yielding the universal asymmetry-coupling parameter of 2/3. An energy-driven collapse operator proportional to the product of noise strength, local probability density, and excitation energy squared is introduced, amplifying the collapse in high-density, high-excitation regions. Exactly bright soliton solutions are obtained for a quasi-one-dimensional BEC of attractive Li-7 atoms, with forward and backward amplitude ratio of 1.870. Heat map analysis of the parameter planes reveals that the forward collapse operator grows monotonically in time while the backward counterpart decays, achieving a ratio approximately 1030, sharply distinguishing this framework from conventional symmetric collapse models.

In celebration of the 2025 UN International Year of Quantum Science and Technology, this Resource Letter surveys the rapidly-growing field of scholarship in quantum information science and engineering (QISE) education. It is primarily written as a guide for educators wishing to get started teaching QISE using research-based teaching methods, as well as for discipline-based education research (DBER) practitioners looking to get started in this field. Topics covered include scoping the field of QISE education, research into student reasoning in QISE, research-based and research-inspired curricular materials from the high school to graduate level, research-based assessments, simulation and gamification tools, and tools for incorporating discussion of the societal and ethical implications of quantum technologies into the classroom.

Semiconductor nanostructures are central to many developing technologies. Notably, double quantum dots are especially important for semiconductor spin-qubit architectures, quantum sensing applications, and quantum-dot solar cells. Accurate modelling is highly desirable but conventional methods can struggle when dynamics involve more than two interacting electrons. In this work, we present a quantum simulation framework capable of addressing multi-electron double quantum dots. We adopt an efficiently scaling 1$^\text{st}$ quantised representation of the system and develop algorithms based on both Trotterisation and qubitisation. Incorporating insights from classical simulations enables us to produce resource estimates that are more realistic than those obtained from theoretical error bounds. Using a standard surface code model with physical noise at $10^{-3}$, our results indicate that the ground-state energy of four electrons in a double quantum dot can be estimated in approximately 24 hours using 226k physical qubits, or an eight-electron system in 3.4 days with 314k qubits (with runtimes falling dramatically when more qubits are available). We anticipate that incorporating very recent advances including dense surface code architectures (Low et al. arXiv:2605.30455) may reduce these costs significantly further. We conclude that early fault tolerant computers may prove to be valuable tools for designing mature-era quantum technologies.

We propose a new concept for quantum thermal logic gates -- analogous to classical electronic logic gates -- that exploit the heat current in a coupled quantum-dot system tunnel-coupled to metallic thermal reservoirs for logic operations in quantum circuits. We obtained a remarkable one-to-one correspondence with the structure of classical electronic logic gate circuits. An experimental setup is presented that demonstrates a realizable nano-electronic quantum circuit architecture for implementing such quantum thermal logic operations.

We formulate stationary-density-preserving nonreversible perturbations of Fokker--Planck dynamics as gauge fields that deform relaxation spectra while leaving the invariant state fixed. When detailed balance holds, a similarity transformation maps the reversible Fokker--Planck operator to a Witten-Laplacian-type supersymmetric Hamiltonian; nonreversible gauges then appear as non-Hermitian perturbations that preserve the zero mode but modify the excited spectrum. This operator viewpoint gives a common language for relaxation gaps, circulating probability currents, hypocoercive acceleration, and finite control costs. We represent admissible gauge currents by antisymmetric tensor fields and identify the detailed-balance-violating Ohzeki--Ichiki force as a constant symplectic example whose infinite-strength limit is Hamiltonian dynamics. The continuous-time spectral gap alone does not select a finite gauge strength, so we introduce a finite-time regularized objective and an actor--critic procedure for learning the gauge. An exactly solvable anisotropic Gaussian Ornstein--Uhlenbeck benchmark separates the spectral transition from the finite-time optimum and shows that the learned gauge recovers the Lyapunov-equation optimum. A double-well benchmark then illustrates the same constrained selection in a nonconvex metastable landscape. Stochastic gradient methods enter this framework as physically relevant Fokker--Planck systems: mini-batch noise acts as an effective diffusion tensor, and adaptive methods such as Adam correspond to metric choices with possible nonequilibrium currents.

We study the robustness of asymptotic entanglement manipulation beyond the exact i.i.d. regime, focusing on Mazzola--Sutter--Renner (MSR) almost i.i.d. sources, which allow a sublinear number of deviations from a tensor-power structure. For pure MSR sources along a bipartite reference state $|φ\rangle_{AB}$, we prove that the entanglement concentration rate is robust: every rate below the entropy of entanglement $S(φ_A)$ remains achievable. Moreover, this can be done by a single Schur--Weyl concentration protocol that is universal within the MSR class, depending only on the reference state and not on the particular source sequence. For mixed MSR sources along a reference state $ρ_{AB}$, we prove a source-dependent entanglement-distillation achievability result: every rate below the coherent information $I(A\rangle B)_ρ$ of the reference state is achievable, although the entanglement distillation protocol may depend on the particular MSR source sequence. For the reverse task of entanglement dilution, we prove a rate-robustness theorem: the asymptotic entanglement cost of any MSR target sequence along $ρ_{AB}$ is at most $E_F^\infty(ρ_{AB})$, the regularized entanglement of formation of the reference state. To establish these results, we prove structural and entropic properties of MSR almost i.i.d. sequences which may be useful in other information-theoretic settings. Thus, for the achievability statements considered here, MSR almost i.i.d. perturbations exhibit the same asymptotic behaviour as their i.i.d. reference states, despite allowing sublinear deviations from a tensor-power structure.

We study thermalisation and the possible occurrence of the Mpemba effect in a closed quantum setting that mimics the interaction of a system with thermal reservoirs coupled only at its boundaries. Specifically, we consider a tripartite geometry in which a finite chain, initially prepared at a finite temperature, is suddenly connected on both sides to two semi-infinite chains of the same nature held at a different temperature. These outer chains act as thermal baths, while the full system evolves unitarily under a homogeneous Hamiltonian. This setup provides a simple quantum realisation of a temperature quench and closely resembles the original scenario in which the classical Mpemba effect was first observed. We focus on two paradigmatic free-fermion models, the XX chain and the transverse-field Ising chain, which respectively preserve and break the global $U(1)$ particle-number symmetry. As a probe of relaxation, we consider the Frobenius distance between the time-evolved reduced density matrix of the central subsystem and its stationary state, which is the thermal state at the bath temperature. Exploiting the free-fermionic structure of both models, the dynamics remains Gaussian and the Frobenius distance can be expressed exactly in terms of two-point correlation functions. Combining this representation with generalised hydrodynamics, we derive analytical predictions for the Frobenius distance in the hydrodynamic limit, providing a complete characterisation of the thermalisation process. Using these results, we investigate the possible occurrence of the Mpemba effect. We find that, despite the genuine non-equilibrium dynamics displayed by the system, no Mpemba effect arises in this setting. Our analysis identifies a broad class of boundary-driven thermalisation protocols in which relaxation is fully characterised analytically and exhibits no anomalous acceleration of equilibration.

The dynamics of open quantum systems is commonly described by quantum master equations derived under the assumption of weak system-bath coupling and a separation of timescales between system and bath. When the system is additionally subjected to a periodic driving, the validity of the resulting Floquet master equations is further restricted to regimes of weak or high-frequency driving. Here, we benchmark a set of commonly used Floquet master equations for a model of two locally driven spins coupled to a shared Ohmic reservoir at finite temperature. We systematically probe the accuracy of the equations as a function of the driving parameters, thus identifying limits of their applicability. Dynamical maps predicted by each master equation are compared against numerically exact non-Markovian simulations, tracking the full relaxation dynamics. We find that the accuracy of each master equation closely reflects the assumptions underlying its derivation. For the Floquet-Lindblad equation, errors can be strongly amplified near resonances where the secular approximation breaks down, while approaches that avoid the secular approximation perform better and exhibit a more systematic dependence of the error on driving frequency and amplitude.

Extracting work from quantum states is a fundamental task in quantum thermodynamics. Previous studies have primarily focused on determining the best achievable rate of work extraction, and remarkably, this characterization appeared to remain unchanged regardless of the choice of allowed processes: whether one considers the operationally motivated class of energy-conserving thermal operations, or the axiomatic class of Gibbs-preserving operations, the optimal extractable work is given by the Helmholtz free energy. Here, we challenge this perspective, showing that a more refined analysis of the asymptotic performance of work extraction reveals significant differences in the performance for the two different classes of free operations. Precisely, we focus on the trade-off between the extraction rate and its reliability, characterized by the optimal asymptotic speed at which the extraction error can be suppressed. We establish that the reliability of Gibbs-preserving operations and of thermal operations are respectively characterized by the Petz and the sandwiched Rényi relative entropies, demonstrating that the former in general strictly outperforms the latter, and providing new interpretations of several information-theoretic divergences. Our analysis reveals that operational constraints such as energy conservation impose stronger limitations on the achievable precision of quantum tasks than can be inferred from their asymptotic rates, thereby questioning the use of Gibbs-preserving operations as a mathematically convenient substitute for the physically realizable thermal processes.

Financial crashes, cascading failures in infrastructure, and critical errors in AI systems are frequently triggered by events that occur with extremely small probability. Efficiently discovering and sampling events with probability below a threshold is therefore of critical interest. Yet this task is highly non-trivial using existing classical or quantum methods. Being rare, such events require an immense sampling overhead to collect sufficient data samples. Moreover, because the rare events are not known in advance, they cannot be flagged for amplification using standard techniques. Here, we introduce a quantum algorithm for rare-event discovery and sampling without first learning which events are rare. The algorithm achieves the optimal quantum scaling with the rarity threshold. We further demonstrate that this can achieve a quadratic speedup for heavy-tailed systems whose tail has nonvanishing total mass, and translates into a robust polynomial speedup for stationary stochastic processes, with the exponent determined by its entropy-rate structure.

Triangles capture higher-order structures in graphs and are fundamental to applications such as clustering and network analysis. To enable efficient use of such structures at scale, we study the problem of \emph{triangle cut sparsification}, which aims to reduce the graph size while approximately preserving triangle counts across every cut. We investigate \emph{quantum algorithms} for this problem, using triangle listing as our main technical ingredient. In particular, we present a quantum algorithm for triangle listing that, for a graph with $n$ vertices, $m$ edges, and $t$ triangles, runs in time $T_{\mathrm{q\text{-}list}} =$ $\widetilde{O}\bigl(\min(n^{5/4}t^{7/12} + n^{7/6}t^{7/9}, m + m^{3/4}t^{1/2},$ $n^{3/2}t^{1/2})\bigr)$, improving upon the best known classical bounds over a broad range of parameters. Our algorithm is based on a heavy-light vertex partition and an extension of triangle detection via quantum walks and Grover search. Leveraging this result, we design a quantum algorithm for constructing $\varepsilon$-triangle cut sparsifiers of size $\widetilde{O}(n/\varepsilon^2)$ in time $\widetilde{O}(T_{\mathrm{q\text{-}list}} + \sqrt{mn}/\varepsilon)$. Finally, we demonstrate applications to clustering algorithms based on triangle-related measures and prove a lower bound of $Ω(n/\varepsilon^2)$ on the size of any $\varepsilon$-triangle cut sparsifiers.

Standard objective collapse models offer a unified approach to the quantum measurement problem but predict an unphysical, indefinite increase in the energy of the system. The dissipative Diósi-Penrose (dDP) model resolves this heating issue by introducing a linear friction mechanism. However, this modification induces complex, non-Gaussian phase-space dynamics. We rigorously establish the thermodynamic consistency of this friction mechanism -- extended to the CSL model -- across both weakly and strongly non-Gaussian regimes. Using the Wigner phase-space formalism, we go significantly beyond the quadratic approximation and, to bypass the failure of perturbative methods under strong dissipation, introduce a novel exact pseudo-spectral simulation approach. Our analysis reveals that the system subjected to the dDP mechanism does not thermalize, but rather settles into a non-equilibrium steady-state (NESS) where the asymptotic non-Gaussianity scales as the third power of the dissipation parameter $β$. By evaluating the Wigner entropy production, we confirm the thermodynamic validity of the model and demonstrate that highly sensitive information-theoretic quantities require exact numerical methods to accurately capture the key non-Gaussian tails of the distribution.

We consider Bayesian discrimination among multiple quantum states and establish a dimension-free one-shot upper bound on the minimum probability of error in terms of the sum of pairwise errors. This resolves a conjecture of Audenaert and Mosonyi [J. Math. Phys. 55 (2014)] and improves the multiple quantum Chernoff bound of Li [Ann. Statist. 44 (2016)] by removing its dimension-dependent prefactor. In the asymptotic many-copy regime, our bound proves the achievability of the multiple quantum Chernoff distance for arbitrary separable Hilbert spaces, thereby settling the previously open infinite-dimensional case, and further yields constant-factor sharp asymptotics for the optimal error probability. In binary quantum hypothesis testing, we prove that the minimum error probability is characterized, up to universal constants, by a trace harmonic-mean quantity. Consequently, the optimal binary quantum error probability is within a factor of two of the optimal classical error probability for the associated Nussbaum-Szkoła distributions, complementing the lower bound of Nussbaum and Szkoła [Ann. Statist. 37 (2009)].

Identifying whether a state family admits an irreducible quantum advantage is a fundamental task in quantum resource theory and quantum information processing. Here we study classically simulable state families, namely those residing within the convex hull of pairwise commuting families and therefore admitting a classical explanation. We develop a complete semidefinite-programming (SDP) hierarchy characterizing the set of classically simulable state families in arbitrary finite dimension. The key step is to reformulate classical simulability as a feasibility problem over deterministic response functions and auxiliary positive-operator-valued measures (POVMs) simulable by rank-one projective measurements. We establish a complete SDP hierarchy for rank-one projectively simulable POVMs and transfer the resulting characterization to state families, yielding both primal feasibility tests and dual affine witnesses certifying failure of classical simulability. Applying the hierarchy to state families mixed with depolarizing noise gives computable upper bounds on the critical classical visibility, which are matched by explicit classical simulations in several symmetric examples. These results provide a systematic convex-optimization framework for certifying classical simulability of quantum state families.

Charge conjugation violation (CCV) is a central concept in particle physics and appears also for quasiparticles in quantum many-body systems, which typically relies on an embedded external symmetry breaking to the underlying system. An open question is how an intrinsic CCV mechanism could emerge and what its macroscopic consequences would be. We establish sublattice kinks in bipartite fermionic lattices as a concrete setup showing intrinsic CCV. The intrinsic CCV of the sublattice kink is based on the graph-topological nature of the underlying Hamiltonian, with no explicit symmetry breaking taking place. It leads to a population asymmetry of different configurations and imprints a hidden leaf-like structure in the eigenenergy spectrum. The population asymmetry also leads to an imbalanced sublattice-kink production triggered by the vacuum-instability in the quench dynamics. Our work demonstrates the graph topology as the microscopic origin of intrinsic CCV, with the population asymmetry as the macroscopic consequence, of which the proposed setup is highly amenable to experimental implementation via cold-atom quantum simulators.

Long-lived dark excitons in monolayer WSe2 present promising candidates for carrying spin and valley information, but their optical access and spin manipulation have conventionally required the use of strong external magnetic fields. Here, using a ferroelectric hybrid perovskite heterostructure, we leverage the ferroelectric proximity effect to break the WSe2's in-plane rotational symmetry and brighten the spin-forbidden dark excitons under zero magnetic field conditions. Furthermore, we show that the twist angle between the WSe2 and perovskite crystals controls the ferroelectric coupling strength and valley-contrasting polarization. Our proposed mechanism, supported by a four-band tight-binding model, suggests that the ferroelectric proximity effect induces an asymmetric intersublattice interaction, generating an effective in-plane spin-orbit coupling (SOC) field that rotates spin/valley polarization and brightens dark excitons. Our work establishes ferroelectric proximity coupling as an electrically reconfigurable, magnetic-field-free strategy for spin exciton control in two-dimensional semiconductors.

Quantum key distribution (QKD) is increasingly considered for deployment in realistic communication networks, where long distances, heterogeneous fiber infrastructure, and coexistence with classical traffic present substantial challenges. Here, we demonstrate trusted-node QKD between Linköping University and the Stockholm hub of the Swedish national quantum communication infrastructure over 270 km of deployed single-mode fiber, extended by a 33 km multi-core fiber (MCF) segment emulating a metropolitan access link, for a total distance of 303 km. The two sub-links use commercial QKD systems whose receivers are interfaced with external superconducting nanowire single-photon detectors, enabling operation at losses beyond those supported by standard internal gated-mode detectors. We operate the link while actively switching the QKD channel between two MCF cores, with co-propagating Ethernet traffic and injected broadband optical noise in the other cores. The results demonstrate the integration of commercial QKD into demanding, dynamically reconfigurable fiber infrastructure relevant to future hybrid quantum-classical networks. Finally, using the generated secret keys, we illustrate how limited and time-varying QKD throughput affects one-time-pad-protected image transmission: image fidelity depends strongly on the available QKD-generated key budget and the choice of compression algorithm, highlighting application-level challenges for QKD-based encryption in realistic scenarios.

We establish the ultimate precision limit for estimating the optical spatial coherence radius (Fried parameter) within a quantum metrological framework. In the weak field regime, we show that spatial-mode decomposition -- originally introduced for superresolution imaging -- enables substantially more precise estimation than conventional direct imaging when the receiver aperture is smaller than the coherence radius.

Controlled time-evolution circuits select forward or backward Hamiltonian time evolution according to the state of an ancilla qubit. They are fundamental building blocks in quantum eigenvalue transformation of unitaries, Hamiltonian filtering, and related quantum algorithms. A direct realization adds ancilla control to the elementary gates of the time-evolution circuit and therefore increases the two-qubit gate count, compiled T depth and CX depth. We develop an efficient recursive algorithm that, for an arbitrary Pauli-sum Hamiltonian, partitions the input Pauli terms into groups and assigns to each group a sign-flip Pauli string that anti-commutes with the in-group terms, thereby removing ancilla control from the grouped time-evolution blocks. Numerical benchmarks on random Hamiltonians and structured spin Hamiltonians show reductions in compiled T depth and compiled CX depth. For a Kagome Hamiltonian with 24 spins under full connectivity, the proposed construction reduces the compiled T depth by 85.2% and the compiled CX depth by 68.9%, compared with a conventional implementation that decomposes the Hamiltonian into individual Pauli terms and implements the controlled time evolution of each term by directly adding the ancilla qubit to the corresponding Pauli-rotation circuit.

Artificial atoms built from Josephson junctions have become a powerful tool to explore the limits of quantum optics due to their strong coupling to electromagnetic fields and their sensitivity to changes at the single-photon level. This sensitivity to quantum fluctuations complements their metrological and computational use, which are based on the precise oscillating frequency of the underlying supercurrents. We present here a theory for Josephson junctions immersed in electromagnetic fields where focus is shifted from temporal correlations and towards spatial ones. Unlike the commonly used circuit and black-box descriptions, our work is based on a microscopic model that enables systematically accounting for the effect of the spatial and vectorial profile of an electromagnetic field over a junction. As an example of the interactions that emerge in such a setup, we investigate the possibility of driving a junction via a quadrupole transition, using typical experimental parameters in existing devices. With the transition being dependent on the gradient of the electric field -- rather than its intensity -- the junction can be excited in a region where the electric field vanishes.

"Polymer quantum mechanics" is the name given to a quantization scheme inspired by loop quantum gravity in which the configuration space of the theory is chosen to have a discrete topology. Polymer quantization yields a representation of the canonical commutation relations that is genuinely distinct from the conventional "Schrödinger" representation. In this paper, we summarize the main features of polymer quantum mechanics and investigate in detail the polymer quantization of systems with configuration spaces that are classically compact. We show explicitly how using the standard construction of polymer states leads to a Hilbert space of states defined on a finite graph of points. By way of example, we find the exact energy eigenvalues and eigenfunctions for a particle on a ring and a particle in a box defined on such lattices, and discuss similarities and differences from standard Schrödinger quantum mechanics. We also explore the continuum limit of states in these systems, and demonstrate in detail how the exact eigenfunctions in the position representation approach their continuum counterparts.

We present a multilevel embedding framework for quantum chemistry calculations on a quantum computer. In our framework, a quantum algorithm treats the strongly correlated active space, while a high-level wave-function method such as coupled cluster theory or multireference perturbation theory recovers the remaining correlation in the surrounding region. A sampling-based quantum algorithm, quantum-selected configuration interaction, bridges the quantum and classical treatments. The entire calculation is embedded in a low-cost density functional theory description of the surrounding environment using Manby's projection technique. We apply the framework to organic, metal-organic, and metallic systems, computing bond dissociation energies, adsorption energies, and reaction barriers using only the subset of qubits of a 144-qubit superconducting quantum computer at the University of Osaka and achieving $\sim$1 kcal/mol agreement with classical references for a Menshutkin $\mathrm{S_N2}$ reaction inside a carbon nanotube. Our results may open the way to quantitatively reliable quantum-classical hybrid calculations for large-scale chemical systems.

Fixed-ansatz Variational Quantum Eigensolvers (VQE), such as the Unitary Coupled Cluster with Singles and Doubles (UCCSD) framework, frequently suffer from severe initialization paralyzation and zero-gradient traps when evaluated using the non-local Bravyi-Kitaev (BK) fermion-to-qubit mapping. In this work, we systematically demonstrate how the Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT-VQE) framework shatters these structural limitations across three distinct electronic and geometric molecular pillars: Lithium Hydride ($\text{LiH}$), Hydrogen Fluoride ($\text{HF}$), and Water ($\text{H}_2\text{O}$), under heavily stretched or asymmetric multi-reference configurations. While conventional UCCSD-VQE flatlines completely at a zero energy shift ($0.000000$~Ha) due to global phase cancellations inherent to the BK tree structures, our dynamic ADAPT-VQE loop successfully isolates the dominant symmetry-breaking operators using analytical commutator gradients. To bypass the severe $\mathcal{O}(N^3)$ computational bottlenecks of dense matrix exponentiation and Singular Value Decomposition on larger registers, we implement a highly optimized, vector-based Taylor series expansion state-evolution engine. Our numerical results show that the accelerated ADAPT-VQE framework achieves instant, exact Full Configuration Interaction (FCI) convergence within the very first macro-cycle across all three molecular systems, maintaining absolute numerical stability up to a 12-qubit register space. This study establishes a robust, hardware-efficient path for simulating strongly correlated, highly polarized triatomic chemical environments on near-term local architectures.

In this paper, we re-examine the well-known question of why electric charges exist only in quantized portions. In this context, we revisit the motion of a charged particle in a field-free region around a current-carrying solenoid. Solving the corresponding Schrödinger equation leads to a simultaneous quantization condition for the magnetic flux and the electric charge. We also demonstrate the Lorentz invariance of this condition by showing that the magnetic flux behaves like a pseudoscalar under Lorentz transformations.

We propose quantum algorithms for preparing thermal states via the simulation of the thermofield double states. The key idea is to leverage double-bracket quantum algorithms to implement imaginary-time evolution on thermofield double states, whose reduced state realizes the Gibbs state. Our method, termed double-bracket thermofield double (DB-TFD), introduces two variants. The first, the vanilla DB-TFD algorithm, directly implements imaginary-time evolution using double-bracket quantum imaginary-time evolution. The second, poly DB-TFD, employs double-bracket quantum signal processing to approximate the imaginary-time evolution operator via a polynomial transformation. We demonstrate that the complexity of the poly DB-TFD algorithm scales exponentially with the inverse temperature in a broad practical regime. This scaling is consistent with existing methods, and numerical simulations support the corresponding theoretical bound. We further demonstrate the utility of DB-TFD in quantum Boltzmann machines for generative modeling, achieving improved performance compared with variational imaginary-time evolution approaches. These results establish DB-TFD as a promising route for thermal state preparation in the near-term and early-fault-tolerant regimes.

The nitrogen-vacancy (NV) center in diamond has attracted considerable attention as a highly sensitive quantum sensor that can operate at room temperature. In particular, continuous-wave optically detected magnetic resonance (CW-ODMR) is promising for a wide range of applications because of its simplicity. However, conventional AC magnetic-field sensing schemes based on CW-ODMR suffer from a limited detection bandwidth: the detectable frequency is either fixed by intrinsic physical parameters of the NV center or, even when tunable, restricted to a narrow range of only a few MHz. Here, we propose a broadband AC magnetometry scheme based on CW-ODMR with NV centers using microwave-driven dressed states.Through theoretical analysis and numerical simulations, we show that the proposed scheme enables the detection of AC magnetic fields with frequencies up to the order of 100 MHz, which has been difficult to achieve using conventional CW-ODMR-based methods.

We show the emergence of memory effects in the dynamics of a driven two-level system interacting with a composite environment, and analyze their influence on work, heat and entropy production. We further investigate how the interplay between driving, dissipation and memory effects, stemming from the finiteness of the environment, shapes the thermodynamic response of the system, thus providing insight into quantum thermodynamics beyond the Markovian approximation.

Uncertainty principle, one of the most iconic features of quantum mechanics, was originally viewed as a fundamental limitation. Since the inception of quantum information science, researchers began to use it to achieve quantum advantages. To better understand the origin of these advantages, an essential question is: To what extent can the uncertainty principle's signatures be simulated by a single measurement? As a single measurement clearly cannot demonstrate the uncertainty principle, such a simulation, if exists, implies the claimed advantages may either stem from other quantum features, or just be reproducible in a less resourceful way. In this work, we report a series of noise-robust no-go theorems, showing that strong enough signatures of uncertainty principle cannot be simulated by a single measurement, even when assisted by quantum pre- or post-processing. This signature is modelled by complementary instruments. We completely characterise complementary instruments by a numerically feasible measure and show that they are necessary and sufficient resources for the advantage in an operational task that aims to unambiguously send classical information.

We present a symmetry-adapted qubit encoding with complete active space (SAE-CAS) for quantum chemistry on fault-tolerant and near-term quantum processors. Building on exact-symmetry encodings, we extend symmetry-adapted mappings to approximate $Z$-symmetries corresponding to frozen-core and virtual orbitals, thereby reducing qubit requirements without significant loss of accuracy. We derive the mapping from the second-quantised Hamiltonian to active-space qubit Hamiltonians, prove its equivalence to the canonical CAS Hamiltonian with frozen-core and virtual-orbital projection, and integrate it with point-group and spin-parity symmetry encodings via affine Clifford transformations to maximise qubit reduction while preserving the target symmetry sector. The same framework also accommodates the Bravyi--Kitaev mapping, yielding an SAE-CAS-BK variant that is unitarily equivalent to SAE-CAS. Numerical benchmarking on nine small molecules using UCCSD and a hardware-efficient shifted-circular-alternating (HE-SCA) ansatz shows that SAE-CAS reduces qubit counts and Pauli-operator weight, yields shallower circuits with fewer parameters, and often accelerates VQE convergence; with HE-SCA it consistently reaches CAS reference energies in cases where JW-CAS does not converge within the tested budgets. We provide an open-source implementation in the Python package QuantumSymmetry. SAE-CAS offers a route to resource-efficient molecular simulations on fault-tolerant and near-term quantum processors.

Adiabatic state preparation is often slowed by nonadiabatic leakage near small spectral gaps. We propose an engineered dissipative protocol that uses a filtered reservoir to induce predominantly downward transitions in the instantaneous energy eigenbasis while leaving the instantaneous ground state dark. The leaked population generated by nonadiabatic driving is therefore continuously relaxed back toward the low-energy sector. An effective avoided-crossing analysis shows that in the regime where the engineered relaxation strength is much larger than the minimum gap, the runtime scaling can improve from the closed-system behavior $\mathcal{O}(Δ^{-2})$ to $\mathcal{O}(Δ^{-1})$ Finite-temperature upward transitions introduce a thermal error floor, but the enhancement survives when this heating rate remains below the target error tolerance. Numerical results show improved ground-state preparation over closed-system annealing. We also discuss a possible superconducting-circuit implementation using structured bosonic reservoirs.

We extend the symmetry-adapted encoding (SAE) framework to periodic electronic structure, enabling qubit-efficient quantum simulation of crystalline materials. By constructing a $Γ$-point supercell Hamiltonian from a folded $k$-point calculation and systematically identifying all applicable space-group symmetry generators -- including spin-parity, point-group, and crystal translation symmetries -- we obtain qubit Hamiltonians with fewer qubits than the Jordan--Wigner starting point. We benchmark diamond, silicon, 3C-SiC, MgO, NaCl, CsCl, h-BN, wurtzite AlN, $α$-quartz SiO$_2$, and MgF$_2$ using active spaces chosen to preserve complete near-degenerate frontier manifolds across cubic, hexagonal, trigonal, and tetragonal space groups. Across the suite the periodic SAE removes 4--8 qubits. The B2 CsCl benchmark realises eight independent Boolean generators, i.e. a symmetry group isomorphic to $\mathbb{Z}_2^8$, reducing CAS(6,7) from 14 to 6 qubits. This exceeds the $\mathbb{Z}_2^5$ maximum of molecular SAE, where only two spin parities and at most three independent Boolean point-group generators are available, because the folded crystal supplies three additional half-translation symmetries. Noiseless UCCSD-VQE benchmarks against exact diagonalisation in the active-space sector show that the reduced encodings preserve the target energies to well below chemical accuracy while reducing variational parameter counts by $3$--$8\times$ and CNOT counts by up to $309\times$. The largest circuit savings occur when translation and point-group generators act independently in the active space, demonstrating that periodic symmetry can be converted directly into both qubit and ansatz compression. The method is implemented in the open-source QuantumSymmetry package and requires no manual specification of symmetry generators.

The dynamics of quantum measurements defines a precise relation between the information gained about one physical property of a system and the observable changes in another physical property of the same system. Here, we express this relation in terms of the Hilbert space superpositions of the corresponding eigenstates and show how the probability of an observable physical change can be obtained from the Bayesian update of the probabilities associated with the information obtained in the measurement. Our analysis demonstrates that the superposition principle provides the tightest possible expression of the trade-off between information and back action in a quantum measurement.

Determining the minimal distance between a target channel and a convex hull of predefined set of implementable channels is a fundamental problem in quantum resource theory, and provides key guidance for experimental implementations. In this work, we develop a unified analytical framework for optimal convex approximation of quantum channels based on the quantum $α$-affinity measure. We construct a channel distance metric induced by the α-affinity and the ChoiJamiolkowski isomorphism, which satisfies the required properties of a well-defined channel distance. Subsequently, we present an optimization framework for the convex approximation of quantum channels, and derive analytical solutions for the optimal convex approximation of single-qubit unitary channels over both the SU(2)-covariant and Pauli channel families, obtaining closed-form expressions for the optimal parameters and the minimal approximation distance. This framework is further applied to the amplitude-damping channel, yielding the explicit form of its optimal approximation and the associated minimal α-affinity distance. In contrast to conventional approaches based on the diamond norm, our framework provides a systematic and analytically tractable approach to quantum channel approximation under realistic constraints.

We perform detailed studies of five Hamiltonian variational ansatzes (HVA) based on the Hamiltonian of the $(1+1)$d $\mathbb{Z}_2$ lattice gauge theory. The ansatzes are designed to respect local and global symmetries of the original Hamiltonian and therefore act on a finely segmented state Hilbert space. Following Larocca et al. (2023), we numerically study the dimension of the dynamical Lie algebra (DLA) and the rank of the quantum Fisher information matrix (QFIM) of the ansatzes within specific invariant subspaces. The ansatzes all involve sums of weight-three Paulis in their generators, which is a feature that have so far been underexplored in this context. We also perform numerical experiments to determine the ground state energy of the original Hamiltonian via variational quantum eigensolver (VQE), and observe that overparametrization of the ansatzes coincides with the apparent disappearance of local minima in the loss function, in line with the finding in the reference. Finally, the decay rate of the VQE loss function under gradient descent optimization is revealed to scale linearly with the number of parameters in the ansatz. These results help to enrich the theory of overparameterization of quantum circuits and inform the design of scalable variational ansatzes.

Entanglement generation is a central resource for quantum information processing, quantum networking, and quantum sensing. In practical implementations, however, entangling interactions are inevitably subject to uncertainty and fluctuations in the interaction strength. We investigate the robustness of entanglement generation in the presence of such imperfections and establish a direct connection between the robustness of entanglement generation and quantum Fisher information (QFI). For two interacting qubits, we show that the reduction in concurrence caused by fluctuations in the interaction parameter is bounded by the QFI with respect to the interaction strength.

We study the problem of learning an unknown $n$-qubit Hamiltonian $H$ from $U = e^{-iHt}$ for a single time $t$, where $t$ may be arbitrarily large. For broad families of local Hamiltonians, we prove that, with high probability over $H$ and $t$, any sum of local observables $A$ that is normalized and orthogonal to $H$ satisfies $\tfrac{1}{2^n}\|[U(t),A]\|_F^2 \geq 1/\text{poly}(n)$. The Hamiltonian is therefore the unique approximately conserved local observable, and we can efficiently recover $H$, up to scale, as the approximate null vector of a data matrix built from random product-state inputs and classical shadows. As a corollary, we obtain a weak equilibration statement: the infinite-temperature autocorrelation of every sum of local observables orthogonal to $H$ decays by at least an inverse-polynomial amount.

In compression-based quantum relaxations like QRAO, classical variables are encoded into qubits and decoded after optimization. We formalize that the choice of the quantum Hamiltonian is fundamentally determined by this decoder. By representing the decoder as a POVM, we define a unique decoder-consistent Hamiltonian via the pullback of the post-decoding expected objective value. Using this framework, we reveal that standard QRAO Hamiltonians are inconsistent for certain mixed-degree quadratic functions, and we provide new approximation guarantees for the MaxCut problem based directly on POVM decoder design.

We study two-photon entangled states for quantum radar cross section (QRCS), which is an extension of a single-photon QRCS formula. Since signal-idler entanglement does not provide any enhancement of the QRCS [Brandsema's PhD Thesis (2017)], we focus on signal-signal entanglement and derive the corresponding biphoton QRCS. We show that it can provide an enhancement over the single-photon QRCS and two-photon separable QRCS, where the performance is evaluated for various two-dimensional target geometries in monostatic/bistatic configurations. Furthermore, using the double-Gaussian approximation, we derive QRCS formula for biphoton states with arbitrary degree of entanglement and compute the resulting scattering patterns.

We introduce Transition states (T states), denoted by $\ket{T_k^n}$, as a class of multipartite entangled states characterized by a fixed number of state transitions between adjacent qubits. These states form equal-amplitude superpositions over all states with a specified transition count. Unlike Bell states based on two-qubit correlations, GHZ states characterized by global correlations among all qubits, and W and Dicke states based on fixed numbers of qubit excitations, T states are defined by transition counts along an ordered sequence of qubits. We prove that T states are unitarily equivalent to Dicke states through a chain of CX (controlled-X) operations, thereby establishing a direct correspondence between transition-based and excitation-based representations of multipartite entanglement.

We study the long-time dynamics of many-body bosonic lattice systems under translation-invariant Gaussian quantum cellular automata. We formulate two sets of conditions on GQCAs which separately guarantee thermalization of any state on the local Weyl algebra to the infinite temperature state, whenever the state is locally normal and has uniformly bounded particle density. Our main intermediate result is a quantum many-body generalization of the classic Riemann-Lebesgue lemma which is a bound on expectation values of local Weyl operators involving their support and the state's particle density.

We present a universal framework to harness fermionic ultracold atom platforms for quantum simulation, showing how variational algorithms on existing hardware can simulate many-body systems well beyond the hardware's native Hamiltonian. Our analysis provides evidence that one can quantum simulate the ground-state properties of a broad class of gapless target Hamiltonians of local observables in a quantum evolution time that grows polynomially with the inverse relative error, $T\sim O(\mathrm{poly}(1/ε))$ up to logarithmic corrections, offering an exponential speedup over na{ï}ve classical algorithms such as exact diagonalization. We provide numerical evidence and theoretical argument that this holds for energy density, density-density, and spin-spin correlations in three qualitatively distinct models -- the repulsive Hubbard model; a Hubbard model augmented with nearest-neighbor attractive interactions, which introduces the phenomenon of pairing; and the Hofstadter-Hubbard model, which introduces a gauge field and fractional quantum Hall physics. This work demonstrates quantum simulation using current fermionic platforms far beyond the models natively implemented in the hardware.

It is proposed that spatial subregions in quantum gravity can be assigned pure states, rather than mixed reduced density matrices. The state is prepared by a partially frozen gravitational path integral, in which a spacetime subregion containing the spatial subregion is fixed while the field configurations and ambient geometry are summed over. In the semiclassical regime, we further propose a holographic prescription for the entanglement entropy of bipartitions of this state, with a frozen-region analogue of the homology constraint. The prescription satisfies nontrivial self-consistency conditions, including strong subadditivity, complementarity, and entanglement wedge nesting, and reproduces several known entropy formulas in holography and gravity as special cases. The construction suggests an observer-dependent entanglement wedge labeled by the frozen subregion.

Informationally complete (IC) measurements are a useful class of measurements, as their outcome statistics uniquely determine an unknown quantum state. Hence, they are important for certain tasks such as quantum state tomography, quantum process tomography, etc. In this work, we study the quantification of informational completeness for arbitrary quantum measurements by introducing and characterizing a faithful measure for it. We explicitly evaluate the informational completeness of qubit symmetric informationally complete (SIC) measurements and show that it is an upper bound for all qubit minimal informationally complete measurements. Furthermore, by introducing a faithful measure, we try to quantify and characterize the ability of an arbitrary quantum channel to preserve informational completeness of any IC measurement when the channel acts on it in the Heisenberg picture. We call this measure informational completeness-preservability (IC preservability) of quantum channels. After studying its properties, we finally establish its relation to another quantity, namely, the absolute output coherence of a quantum channel, which quantifies the minimum amount of coherence (w.r.t. an arbitrary incoherent basis) that can always be obtained from the output of that channel. Thus, in this work, not only do we try to provide a quantitative framework for studying both the informational completeness of quantum measurements and the ability of quantum channels to preserve it, but we also try to offer key insight into the conceptual relation between informational completeness and quantum coherence.

We investigate operator spreading in random quantum circuits with gates drawn from orthogonal-invariant or symplectic-invariant ensembles, revealing several key distinctions from the well-studied unitary-invariant case. We find that the ensemble-averaged Pauli-string weights relax to a ternary-valued structure, instead of the binary structure of unitary-invariant circuits. For orthogonal- or symplectic-invariant circuits, the domain wall separating trivial and scrambled regions has a finite width even for Haar-random gates, whereas domain walls are sharp for Haar-distributed random unitary circuits. We further find a fundamental dichotomy between random circuits with two-qubit gates from the two disconnected components of the orthogonal group: While the butterfly velocity for the special orthogonal ensemble lies between zero and the Haar value, the negative-determinant sector exhibits a non-zero lower bound for any gate distribution. Moreover, for qudit size $q=2$, the butterfly velocity can exceed that of the Haar-random ensemble.

Two-dimensional higher-order topological insulators are typically classified either as dipolar or quadrupolar depending on the relevant invariant. These two classes were previously considered non-overlapping. Here we put forward an example system exhibiting dipolar and quadrupolar higher-order topology simultaneously, suggest its implementation using the arrays of laser-written evanescently coupled optical waveguides and support our conclusions by the full-wave numerical simulations.

Continuously replenished optical tweezer arrays will unlock unlimited-depth quantum circuits with neutral atom qubits. A key bottleneck limiting the cycle time of these systems is removing atoms from tweezers initially loaded with more than one atom. In the conventional technique of light-assisted collisions, slow collisional dynamics limit the timescale for removing excess atoms to several milliseconds. Here, we propose and demonstrate a scheme for selectively removing one atom at a time from multiply occupied tweezers on a microsecond timescale, using intra-tweezer Rydberg blockade and autoionization. We demonstrate the protocol in $^{171}$Yb in two complementary regimes. With two-photon Rydberg excitation from the ground state, we reduce multi-atom probability to 1% in 64.8 $μ$s, while retaining single atoms in 58.2(2)% of the tweezers, which is comparable to the filling fraction achieved with light-assisted collisions under the same experimental conditions, but over two orders of magnitude faster. With single-photon excitation from the metastable state $^3P_0$, reduced single-atom loss enables a higher filling fraction of 74.8(3)%, at the cost of additional temporal overhead to prepare the atoms in $^3P_0$. The final filling fraction is limited by an unexplained two-body loss mechanism, which, if solved, could enable fast, quasi-deterministic loading.

Quantum Erasure Imaging (QEI) turns delayed-choice erasure into a practical imaging protocol. Entangled photon pairs encode two classical modalities, absorption $T(x,y)$ and a phase-sensitive cosine quadrature of $φ(x,y)$, reconstructed from a single run of time-tagged coincidences by retrospective sorting on a remote ancilla. Measuring the ancilla in H/V yields $T$ via which-path information; D/A yields interference visibility $\propto \frac{2\sqrt{T}}{T+1}\cosφ$; and a rotated orthonormal analyzer continuously trades between them. We derive balanced two-port estimators whose denominators are analyzer independent (completeness / no signaling), together with Fisher information (FI) and Cramér--Rao bounds (CRBs) that establish an equivalence to time division under labeled randomization. The advantages of QEI are operational: single-run acquisition, perfect co-registration, and remote / delayed mode choice. We illustrate the protocol with Monte-Carlo simulations and open source our code.

This paper investigates semi-device-independent quantum randomness generation with a trusted binary pure-state source and an untrusted binary detector whose side information is classical. We derive a closed-form Shannon-rate expression for this setting, depending only on the trusted Gram overlap of the two source states and the observed symmetric error probability. The key point is that the full binary-qubit POVM optimisation must include the two deterministic extreme points omitted by the projective-only treatment; including them gives a substantially lower, and correct, certified rate. The closed form is an unconditional upper bound on the certified asymptotic i.i.d.\ Shannon rate, and becomes tight on a numerically verified dual-feasibility region containing all operating points used in the paper. Outside this region the same expression remains an upper bound. We then apply the result to squeezed-coherent BPSK sources, showing how squeezing changes the trade-off between state distinguishability and certified randomness in the lossless and lossy regimes. Finally, we clarify the adversary model if the adversary is allowed to hold a detector-purification register that tags the outcome.

Efficient quantum state transfer between superconducting circuits and solid-state spins would unlock high-coherence quantum memories for superconducting quantum processors. We demonstrate dynamically controlled strong coupling between a Josephson circuit and a rare-earth spin ensemble. Using a parametric pump, we realize on-demand coupling of several MHz, which will enable faithful state transfer between quantum circuits and spins. Our architecture enables quantum control of spin ensembles, and paves the way for hybrid memories with coherence far beyond those of superconducting circuits alone.

The quantum-computing speedup theory considers the symmetric structures and properties of quantum systems as the fundamental Quantum-Computing-Speedup (QCS) resources which are responsible for exponentially speeding up quantum computing and simulating. At present a large and important problem is how to make use of the fundamental QCS resources to speed up essentially quantum computing and simulating. Here the author makes a great effort toward solving this important problem. The theoretical research work in this paper is mainly divided into the two Parts I and II. The Part I investigates mainly the multiple-quantum operator algebra spaces. And the relationships are analyzed among the multiple-quantum operator algebra spaces, quantum simulating for the unitary time-evolutional processes, and the fundamental QCS resources which exist in the different kinds of basic quantum spaces: the multiple-quantum operator algebra space, the density operator space, and the Hilbert space. It concludes that the multiple-quantum operator algebra space must be positioned as the central place where the QCS resources are exploited to speed up quantum computing and simulating. The Part II investigates mainly the subspace-selective unitary manipulation based on the Hilbert-space symmetric structures. Recognize that the multiple-quantum operator algebra space is the central place. Then those QCS resources original from the Hilbert space (a quantum-state space) must be explicitly taken into account in the multiple-quantum operator algebra space (a linear operator space). This is an important problem. The subspace-selective unitary manipulation is able to solve this problem. It aims to harness the fundamental QCS resources original from the Hilbert space to speed up quantum computing and simulating in the multiple-quantum operator algebra space.

We establish a reverse-time denoising theory for quantum diffusions of continuously measured quantum systems. Starting from the stochastic Schrödinger equation of a forward noising dynamics, we derive the exact reverse-time dynamics for quantum trajectories, whose law coincides with the time-reversal of the original process. We prove that the denoising dynamics is a physically admissible quantum diffusion, with the same measurement-induced noise but a state-dependent feedback Hamiltonian, a direct analogue of the "score function" of generative classical diffusion models. This provides a principled framework for converting samples of a simple distribution into those of a more complex ensemble of quantum states. We show how the denoising dynamics can be directly learnt from forward trajectory data, and how to exploit purification to initialise the denoising process.

Determining spectral gaps in the thermodynamic limit is a central challenge in quantum many-body physics. Existing rigorous methods are largely limited to special settings, while variational numerical approaches typically provide estimates rather than certified bounds. Here we introduce a complete family of certified upper bounds on the bulk spectral gap of quantum many-body systems. These upper bounds are obtained by solving a series of semidefinite programs and they become arbitrarily tight at the cost of more computational resources. This shows that the bulk spectral gap is semi-decidable, in contrast to undecidability results for alternative notions of spectral gap based on sequences of finite systems with prescribed boundary conditions. As a proof of principle, we apply our algorithm to the spin-$\frac{1}{2}$ kagome lattice Heisenberg antiferromagnet and obtain, to our knowledge, the first nontrivial certified upper bounds on its bulk spectral gap.

Superconducting transmon qubits are a leading technology for quantum information processing, yet their reliable operation rests on meticulous calibration and characterization routines. These processes have been fine-tuned and are relatively well understood by the quantum computing community. Nevertheless, it is often challenging for newcomers to compile all the available information into a practical experimental flow. In this tutorial, we present a comprehensive walkthrough for the characterization and optimization of tunable transmon qubits, demonstrated on a commercial five-qubit processor. Moving beyond theoretical description, we detail in a straightforward manner the complete workflow, from cryogenic setup and wiring to parametric amplifier optimum operation, flux sweet-spot identification, pulse calibration, and readout optimization. We also demonstrate the characterization of qubit-qubit coupling, covering all steps before multiqubit operations. This guide serves as a reference for experimentalists seeking to efficiently bring up transmon-based quantum devices.

A fermionic three-site generalization of the popular bosonic Swanson model is studied as providing an exactly solvable five-parametric example of the quantum-mechanical unitary-evolution process leading to an ultimate loss of the observability and fall in an exceptional-point singularity (EP3). The instant of degeneracy is found to have an explicit one-parametric form. Its unitarity-compatible vicinity (i.e., the corridor of access to EP3) is also specified in closed form. The exact, numerical-error-independent solvability is found essential due to another, avoided, false energy-level crossing which is found to occur not too far from the true EP3 singularity.

The Hubbard model on the honeycomb lattice is a pristine realisation of a semimetal-to-insulator Mott transition belonging to the Gross-Neveu O(3) universality class. We couple this system to a single linearly polarised cavity photon mode. The light-matter coupling is such that the photon number remains an intensive quantity as is the case for an empty cavity. For this interacting light-matter model, we formulate a negative-sign-free fermion quantum Monte Carlo algorithm that allows for bias-free results on finite system sizes. Our numerical results show that the coupling to the cavity is irrelevant at criticality, even at strong electron-photon coupling. On the other hand, we observe, and show analytically, that the photon spectral function couples to the optical conductivity of the electronic system. The cavity photons thereby undergo a Mott transition, and the photon spectral function acts as a contact-free non-invasive probe for Mott criticality.

We investigate the quantum dynamics of a particle confined to a space curve within the thin-layer quantization framework. For a nondegenerate scalar transverse mode, torsion does not enter the local effective Hamiltonian, which contains only the curvature-induced scalar geometric potential. In contrast, when a degenerate transverse subspace is retained, the rotation of the Frenet normal frame becomes dynamically relevant and generates a matrix-valued Abelian gauge potential. Using a projection-based derivation in a co-rotating Frenet-frame basis, we show that this effective gauge potential is directly determined by the local torsion of the curve. The resulting effective Hamiltonian takes a gauge-covariant form and produces two transverse-mode branches whose parabolic dispersions are shifted in opposite directions in momentum space. For closed curves, the associated holonomy is controlled by the integrated torsion and leads to geometric interference. These results provide a direct realization of a Wilczek--Zee-type connection induced purely by spatial geometry in curved quantum waveguides. We further construct a classical-wave analogue using the degenerate bending modes of an isotropic elastic rod, demonstrating that the same torsion-induced gauge structure appears in continuum wave physics.

We develop systematic frameworks for characterizing the entanglement properties of two-qubit channels beyond unitary settings. We introduce averaged local-unitary invariants, referred to as moments, obtained from Haar integrals over input states or unitaries. These moments provide computable descriptions of how a quantum channel can create, preserve, or destroy bipartite entanglement. We first show that second-order moments yield criteria for non-entangling and entanglement-breaking channels, which allow us to detect entanglement-creating and entanglement-preserving channels. We then demonstrate that higher-order moments can capture additional information and distinguish channels beyond second-order moments alone. Finally, we show that combinations of moments associated with different channel families improve the discrimination of locally inequivalent two-qubit unitaries.

Quantum states that do not commute exhibit coherence, but only when the device preparing them is assumed to be unaffected by classical parameters inaccessible to the experimenter. Such hidden classical control arises both in fundamental tests of quantum phenomena and in quantum information protocols that operate under limited control assumptions. Here, we address the problem of coherence certification by developing complete and practically efficient methods. First, we prove that coherence can be fully characterised through a hierarchy of semidefinite programs. Second, we introduce a practical semidefinite programming approach that achieves useful accuracy while remaining computationally efficient even for preparation devices generating many, potentially high-dimensional, quantum states. For the important special case of qubits, we further exploit conceptual connections with the theory of joint measurability to obtain highly accurate coherence characterisation that scales to more than one thousand qubits. Finally, we apply these methods to determine whether quantum channels are able to preserve coherence or are inherently coherence-breaking. Together, these results provide a powerful toolbox for analysing quantum superposition in the presence of hidden classical control.

Gravity is the most apparent force in our everyday existence. Yet its fundamental nature remains the most opaque of the known interactions. This gap in our understanding is, in large part, due to the weakness of the gravitational interaction, which makes its empirical probing exceedingly hard. Nevertheless, on the backdrop of rapid advances in quantum technologies, hope has mounted that tests of the quantum nature of gravity could be realized in tabletop experiments. In this essay, we frame these recently proposed tests as quantum-gravitational imitation games. In particular, we examine how gravitational interactions among mechanical oscillators enable the teleportation of arbitrary quantum states and how this can inform fundamental tests of gravity.

The generation of macroscopic quantum states can drive both fundamental physics and quantum technologies. This work proposes a top-down approach to the generation of macroscopic spin GHZ states using a levitated ferromagnet, where a strong locking between the collective spin and the lattice rotation enables mechanical control of the collective spin. We quantify the metrological advantage of the resulting macrospin superposition state by showing that Heisenberg scaling of the quantum Fisher information is achievable. Roles of symmetry and geometry are analyzed in terms of decoherence due to gas collisions, identifying accessible conditions for experimental realization. The usefulness of a macrospin superposition state of a levitated cylindrical ferromagnet in testing spin-dependent wavefunction collapse models is also discussed.

In gravitational physics, matter does not merely move within spacetime; it also determines the light cones that define causal relations. What happens when the matter that determines these light cones is itself in a quantum state? We address this question in a controlled low-energy setting: a massless scalar field propagating in the spacetime with the Newtonian gravitational potential sourced by a non-relativistic quantum particle. We show that the light cones are affected by an operator-valued Shapiro delay, with the three consequences: (i) causal-boundary shifts are promoted to noncommuting observables, giving the causal structure an irreducible quantum uncertainty; (ii) the causal relation between two fixed spacetime points can become a superposition of timelike and spacelike configurations; and (iii) tracing out the source smears the Wightman light-cone singularity, producing an effective UV cutoff. Thus, quantum matter does not merely fluctuate within spacetime; it makes the causal structure itself quantum, even without quantized gravitons.

We derive a necessary condition of the local equivalence between two-qudit gates in terms of singular values of transformed gate matrices. This condition is valid for arbitrary qudit dimensions $d$ and is thus a relatively simple general way of checking whether two gates can be reduced to one another with single-qudit (local) gates. We use this condition to investigate the local equivalence of two widely used trapped-ion two-qubit gates in qudit space: the Molmer-Sorensen (MS) gate and a special case of the Light-Shift (LS) gate, both of which we studied in one of our previous works.

A spherical Penning trap has well-separated, clean microwave resonances, making it attractive for precision measurements of the electron magnetic moment and for dark-photon and axion searches with trapped electrons. We demonstrate single-electron trapping in a spherical Penning trap and characterize its microwave resonance structure. The design, single-electron detection, microwave mode characterization, and advantages of this geometry are presented.

We propose an efficient quantum algorithm for preparing the Hadamard product state of two quantum states whose amplitudes are generated by functions on a uniform grid with grid number $N$. As the Hadamard product operation is non-unitary, the conventional approach generally suffer from a success probability that scales as $O(1/N)$, leading to an $O(\sqrt{N})$ query complexity even with quantum amplitude amplification. Our method exploits the Fourier-space representation of the input functions, where the Hadamard product can be treated through a convolution structure and approximated using localized Fourier coefficients. The resulting quantum circuit has complexity governed by the Fourier regularity of the underlying functions rather than directly by the grid number. In particular, when either of the input functions has finitely many non-zero Fourier coefficients, the algorithm prepares the exact quantum Hadamard product state under $N$-independent query complexity. Moreover, we also propose a novel quantum circuit for the partial inner product as one of its applications.

Topological holography (TH), or SymTFT, realizes symmetries and dualities of a quantum system as boundary data of a topological bulk in one higher dimension. We formulate fracton topological holography (FTH), extending this mechanism from liquid topological orders to fracton stabilizer codes. The construction is organized as a general four-stage framework: prepare the bulk model and compute its excitations, determine boundary data and admissible gapped top boundaries, identify the low-energy preserving operator algebra together with its symmetry, relation, and twist data, and then switch among top boundaries to compare the induced boundary descriptions. As a type-I example, we develop FTH for the X-cube model with smooth and rough top boundaries; for a minimal effective Hamiltonian, both yield transverse-field plaquette Ising models, with exchanged subsystem symmetry and twist data, and the boundary switch is implemented by a linear-depth local unitary sequential quantum circuit (SQC). As a type-II example, we formulate FTH for Haah's cubic code in the Laurent-polynomial stabilizer formalism and analyze the natural $(Z)$ and $(X)$ top boundaries, which induce two two-dimensional qubit systems related locally by exchanging generalized plaquette Ising and transverse-field terms and nonlocally by a symmetry--relation duality. These results show that FTH is a genuine extension of TH to both type-I and type-II fracton orders. FTH therefore provides a concrete framework for organizing and understanding duality, with the prospect of offering a systematic route to new dualities.

The distillability conjecture for two-copy four-by-four Werner states has been an open problem in quantum information for years. We investigate the conditions under which the conjectured inequality becomes an equality. For all known cases where the conjecture has been verified, we characterize the saturation conditions and show that equality forces the matrices $A$ and $B$ to be two-by-two block-diagonal. In particular, several previously obtained partial results, including the cases of one normal matrix, unitary similarity between $B$ and $-A$ or $-A^T$, and anti-diagonal block structures, are reduced to this common block-diagonal structure. We also employ a manifold optimization method, which provides numerical evidence that the two-by-two block-diagonal structure is essential for saturating the inequality. Furthermore, we prove that the identified saturation points are critical points of the objective function on the constraint manifold.

Training quantum neural networks (QNNs) on quantum hardware is currently bottlenecked by the cost of gradient estimation: standard parameter-shift methods require a number of circuit evaluations that grows quadratically with the number of trainable parameters, making hardware-based optimisation impractical beyond small system sizes. In this work, we introduce a training framework that reduces this cost to logarithmic in the number of qubits, making gradient-based QNN optimisation feasible on near-term hardware at increasing scales. Our framework combines three co-designed ingredients: (i) a structured, subspace-preserving Butterfly circuit architecture with $O(n \log n)$ parameters and logarithmic depth; (ii) a layer-wise training strategy that confines on-hardware optimisation to one small, well-structured layer at a time; and (iii) a parallelised parameter-shift rule that exploits the commuting structure within each Butterfly layer to extract all gradients in a constant number of circuit executions. Together these reduce the number of distinct circuit evaluations per optimisation step from $O(n^2)$ to $O(\log n)$. We validate the framework on clinical data imputation using the MIMIC-III electronic health record dataset, a demanding benchmark sensitive to optimisation instability and model variance. Hybrid classical-quantum models are trained directly on IonQ Forte Enterprise trapped-ion hardware at 16 qubits without performance degradation relative to ideal or noisy simulation and via tensor-network simulation at 32 qubits, with 32-qubit inference executed on hardware. The resulting models match or exceed strong classical neural baselines in downstream patient survival prediction while exhibiting reduced variance across runs, demonstrating that the proposed framework enables practical, scalable QNN training under realistic hardware constraints.

Quantum computing presents a promising method to overcome the efficiency and memory constraints in large-scale mechanical problems, with numerous successful applications demonstrated in fluid mechanics. However, solid mechanics problems usually require irregular grids for spatial discretization, due to the Lagrange formulations and complex boundaries, which makes the quantum simulation of the system matrix, e.g., the mass or stiffness matrix which is often referred to as the Hamiltonian in quantum computing, difficult to be effectively conducted. This study proposes a voxel-based quantum computing method (VBQC) for the quantum simulation of Hamiltonians in solid mechanics. VBQC applies voxel grids to discretize the spatial domain, thereby enabling the system matrix to exhibit the tridiagonal fractal property. Based on this property, the system matrix can be decomposed into three groups of fundamental matrices, $\mathbf{k}_{n}$, $\mathbf{c}_{n}$, and $\mathbf{q}_{n}$. This decomposition process is referred to as the KCQ decomposition. By integrating the KCQ decomposition with the quantum Fourier transform and the quantum multiplexer, VBQC enables efficient quantum simulation of Hamiltonians in solid mechanics. Three specific solid problems with different dimensions and numbers of variables are applied to preliminarily verify the correctness of the proposed VBQC for solid mechanics problems.

Field-programmable gate arrays provide a high-performance solution for real-time signal processing in emerging quantum and photonic technologies. We present an FPGA-based fast feedforward system, that incorporates a high quantum efficiency fully fibre based homodyne detector, to enable low-latency signal processing critical for continuous variables (CV) measurement-based quantum information processing (MB-QIP) protocols. CV MB-QIP typically relies on adaptive measurements and/or displacements via feedforward to achieve scalability and universality, but existing implementations typically handle these operations in post-processing, limiting real-time applicability. Our system performs signal acquisition, conditioning, and logic operations in real-time, meeting the tight latency requirements of photonic quantum computing protocols. The detector exhibits a large clearance of 15 dB at 1 GHz with 4 mW linear oscillator and quantum efficiencies of >95% with a total system latency of 196 ns. This work highlights the role of FPGAs in bridging the gap between theoretical models and physical implementations in photonics-based technologies

We propose a scheme for piston control in a two-ion quantum device with motion confined to orthogonal axes. In this system, one ion plays the role of a ''classical'' piston driven by the Coulomb interaction with the other ion, whose quantum motion is controlled through modulation of its trapping potential. The stationary state is determined self-consistently, taking quantum effects into account. We identify a narrow quantum regime of the ground state connecting two broad classical regimes. We further design inverse-engineering protocols to control the motion of the ''classical'' ion. The proposed control scheme provides a useful route toward controlled piston dynamics in microscopic quantum devices.

Two-dimensional Chern insulators support topologically protected, chiral edge currents, and these can be detected in experiments with ultracold atoms in optical lattices. It has previously been shown that one can populate a selected group of edge states of a Chern insulator by transferring particles from a reservoir. Here, we numerically investigate the effect of performing an instantaneous, projective measurement on the reservoir before the reservoir is discarded. In this way, the final state of the system is pure and described by a wavefunction. We also show that quite likely measurement outcomes can help to increase the final number or percentage of particles in the chiral edge states through postselection. Without the measurement step, the physics can be described in terms of single-particle physics. The measurement significantly complicates the description. By appropriately rewriting the analytical expressions, we show that measurement probabilities, expectation values, averages of expectation values, and purity can nevertheless be computed from the state before the measurement in a way that scales only linearly with the number of lattice sites for a fixed number of particles. This enables us to investigate a setup with, for instance, 14 particles and 198 lattice sites numerically. The approach applies generally to noninteracting, fermionic models that conserve the number of particles.

Topological state transfer in Fock-state lattices has been demonstrated with high speed using sinusoidal profiles of coupling, yet the underlying reason has remained unclear. A global adiabatic criterion (GAC) is developed to bound the infidelity by the mean and variance of the nonadiabatic factor. The GAC reveals that the key to fast transfer is not a constant energy gap but the vanishing nonadiabaticity variance. For power-law coupling profiles, the variance vanishes only for the sinusoidal shape, which is thus globally optimal. Incorporating experimental decoherence parameters, it is predicted that the optimal transfer duration for a five-photon state is 161 ns, far shorter than 600 ns used in the experiment, reducing time by over 73% while increasing transferred photons by 29%. The optimal duration follow a simple linear scaling with photon number, providing a practical guideline. Through constructing an alternative constant-gap coupling family, it is confirmed that a constant gap alone is not sufficient for fast topological photon transfer. The essential condition is uniformity of nonadiabaticity. This work offers a rigorous explanation for the observed speed and a general framework for fast topological photonics engineering.

We give detailed analysis and circuit design of structure-preserving quantum algorithms for second-order linear evolutionary PDEs, including parabolic equations and hyperbolic equations with mixed Dirichlet, Neumann, and periodic boundary conditions and source terms. While prior quantum algorithms usually neglect the stability problem from the PDE-to-ODE reduction, our method-of-lines approach investigates the boundary lifting via Coons interpolation and boundary-aware discretization, so that the resulting semi-discrete systems are stable and compatible with efficient quantum ODE primitives. For the parabolic problem, we use a diagonal similarity transform to ensure the semi-discrete generator must have a positive semi-definite Hermitian part, and then solve the resulting ODE system by the optimal linear combination of Hamiltonian simulation (LCHS). For the hyperbolic problem, we rewrite the semi-discrete equation as an equivalent first-order system and solve it by Hamiltonian simulation. We implement our quantum algorithms with explicit block-encoding constructions and circuit implementations, as well as demonstrating the end-to-end complexity bounds together with spatial and quadrature error estimates. We conduct classical numerical experiments on the convection-diffusion equation, inhomogeneous heat equation, and Klein-Gordon equation to validate our structure-preserving analysis and algorithmic constructions.

The non-Hermitian skin effect (NHSE) represents one of the most distinctive phenomena in non-Hermitian physics. Here, we uncover a new drag-induced NHSE mechanism in interacting Bose--Fermi mixtures where only bosons and not fermions experience asymmetric hoppings. %While bosons exhibit intrinsic skin localization due to asymmetric hopping, fermions remain Hermitian in isolation and do not independently support NHSE. We show that strong Bose--Fermi interactions enable fermions to inherit boundary accumulation through correlated bound states. %In the few-body regime, The interplay of interactions, quantum statistics, and non-Hermitian dynamics gives rise to an interaction-induced blockade mechanism, leading to highly asymmetric fermionic transport. We demonstrate that the drag-induced NHSE is dynamically stable and propose a feasible realization in ultracold Bose--Fermi mixtures with Floquet-engineered asymmetric tunneling. Our results establish a general interaction-mediated mechanism for emergent non-Hermitian localization in hybrid quantum matter.

Ising Hamiltonians are basic models of disordered magnets and a standard language for quantum and classical optimization. We study an energy-selective quantum search primitive in which the physical evolution \(\exp(-\mathrm{i} T H)\) is used directly as a Hamiltonian phase oracle. Unlike a Boolean oracle, this oracle marks configurations continuously by their phases and selects a finite resonance band rather than a preassigned marked set. We show that alternating it with the Grover diffusion operator nevertheless produces a Grover-type amplification peak. An exact spectral recurrence and a generating-function representation determine the peak position, width, and height. For an annealed Gaussian density of states, target energies in a high-density tail require \(Θ(\sqrt{2^n/M})\) oracle calls when the resonance contains \(M\) configurations. For random Ising spectra, overlap-induced correlations shift and distort the peak; spectral symmetrization and iterative calibration remove this detuning for prescribed-energy targeting.

Entanglement purification is an essential component of quantum repeaters, as it can improve the fidelity of the distributed entangled states and mitigate the effects of the noisy channel. Successful purification yields entangled states with increased fidelity, whereas failed events can still retain residual entanglement that remains usable for further purification when the error rates of the two degrees of freedom (DOFs) are unbalanced. In this paper, we demonstrate a single-copy entanglement purification scheme based on hyperentanglement using silicon chips and experimentally observe the presence of residual entanglement. Leveraging the reconfigurability of integrated photonics, our scheme ensures that, under bit-flip noise acting on the two DOFs, residual entanglement suitable for further purification can always be obtained, regardless of which DOF has the higher error rate. Our results demonstrate the advantages of integrated photonics for quantum information processing and provide guidance for the optimized utilization of entanglement resources in on-chip entanglement purification and future quantum repeater systems.

Large-size cat states are especially meaningful and fundamental for exploring the quantum-to-classical transition, as well as promising resources for quantum metrology and fault-tolerant quantum computation. However, amplifying the magnitude of cat states remains challenging because of the growing fragility under decoherence. We propose to generate large cat states by using the dynamical invariant of hybrid qubit-bosonic systems under Hermitian or non-Hermitian time-dependent Hamiltonian. It is a study with the universal quantum control (UQC) theory, in which the system dynamics is analyzed in the ancillary picture via a unitary transformation conditional on the qubit state. The controllable dynamics that can be encoded in the evolution of the dynamical invariant is presented by the Heisenberg equation, which imposes constrains on the Hamiltonian. When the qubit is prepared in a balanced superposed state, the bosonic mode can evolve deterministically from the vacuum state to the cat state of a mean photon number over $120$. In the Hermitian case, the generation is perfect; and in the non-Hermitian case, the fidelity is over $0.962$. Our protocol can also be applied to the generation of the intrinsic cat states and the four-component cat states of large size. Through the preparation of macroscopic quantum states, our work essentially advances UQC to hybrid discrete-continuous variable systems.

Engineering proximity effects in twisted van der Waals heterostructures offers a powerful platform for designing electronic properties. While theoretical predictions of quantum interference in transition metal dichalcogenide-encapsulated graphene can selectively control the spin-orbit coupling component, experimental realizations have remained elusive. Here, we report pure valley-Zeeman spin-orbit coupling in monolayer graphene, achieved by encapsulation between two parallel twisted WSe$_2$ monolayers. We observed a symmetry-enforced reordering of Landau levels, which is driven by the competition between the fixed valley-Zeeman energy and the magnetic-field-dependent cyclotron energy. This reordering is characterized by a transition from symmetry-broken states in the quantum Hall effect to a restored fourfold degeneracy with integer or half-integer quantum Hall sequences. We also demonstrate the ability to completely quench the proximity spin-orbit coupling by tuning the encapsulated geometry.

A major open problem in quantum communication complexity is whether quantum protocols can be exponentially more efficient than classical protocols for computing total Boolean functions; the prevailing conjecture is that they cannot be so. In a seminal work, Razborov (2002) resolved this question for AND-functions of the form $$ F(x,y) = f(x_1 \land y_1, \ldots, x_n \land y_n), $$ when the outer function $f$ is symmetric, by proving that their bounded-error quantum and classical communication complexities are polynomially related. Since then, extending this result to all AND-functions has remained open and has been posed by several authors. In this work, we settle this problem in a strong way. We show that for every Boolean function $f$, the bounded-error quantum and classical deterministic communication complexities of the function $f \circ \mathrm{AND}_2$ are polynomially related, up to polylogarithmic factors in $n$. We prove this by showing that both are characterized--up to polynomial loss--by the logarithm of the De Morgan sparsity of $f$. Our results build on the recent work of Chattopadhyay, Dahiya, and Lovett (2025) on structural characterizations of non-sparse Boolean functions, which we extend to resolve the conjecture for general AND-functions.

The fractional Schrödinger equation is studied with a kinetic energy that slightly deviates from the usual nonrelativistic form. The harmonic oscillator and the Kepler problem are both treated in the context of small perturbations. The usual perturbation theory is used and compared with the envelope theory. The analytical results show good agreement between both methods, indicating possible future developments for many-body systems. A possible connection with experimental observations is briefly discussed.

We study the application of Gaussian Boson Sampling (GBS) to the densest k-subgraph problem (DkSP). GBS with hard post-selection suffers from poor sampling efficiency due to strict cardinality constraints. To address this limitation, we introduce effective classical post-processing strategies that transform, otherwise discarded, near-k samples into feasible solutions. A comprehensive set of simulations is carried out, demonstrating that these approaches achieve near-optimal solution quality while improving sampling efficiency by approximately 4X compared to post-selection on community-structured graphs, and also post-selection often fails to reach the optimal solution on sparse random graphs even with large number of samples. Furthermore, the proposed methods perform on par with, and in some cases outperform, established classical approaches for graphs up to moderate size. Overall, the results indicate that while GBS with post-selection alone is insufficient, its combination with lightweight classical refinement can be highly effective. This underscores the potential of hybrid quantum-classical frameworks and positions GBS as a promising sampling primitive for combinatorial graph optimization.

We present a protocol which allows for arbitrary optical quantum states to simultaneously carry and transmit classical data, without sacrificing the integrity of either the quantum or classical information. Our scheme encodes classical information via displacements in the phase space prior to transmission and retrieves each classical symbol via a Gaussian continuous-variable teleportation. The original quantum state is then restored by guessing the the original displacement and performing the appropriate inverse operation. In the limit of sufficiently high classical signal and high squeezing, we show that our scheme is capable of perfectly reconstructing both the input classical signal and the input quantum state without loss of coherence. An example is given in terms of the transmission of a dual-rail Bell state.

Non-Gaussian quantum states are essential resources for continuous-variable quantum information processing and for metrology. Among these, multi-photon added coherent states bridge classical and non-classical behaviors; however, their generation typically relies on small photon numbers and probabilistic heralding schemes. Here, we propose a protocol for the post-selection free generation of high fidelity multi-photon added coherent states using the photon blockade effect in a driven Kerr nonlinear resonator, where such states emerge naturally during the dynamics. We demonstrate that high-fidelity states can be prepared by optimizing the external drive power and the interaction time. Furthermore, we show that the protocol is robust under realistic experimental conditions, achieving fidelities of $\approx 99\%$ with current state-of-the-art parameters. Our results unlock a deterministic route to complex non-classical states using well-established quantum optical platforms.

This perspective article analyzes the potential and critical challenges of employing quantum optimization algorithms to investigate phase transitions in quantum many-body systems during the Noisy Intermediate-Scale Quantum era. The simulation of strongly correlated systems is frequently intractable on classical computers due to the exponential growth of the Hilbert space and the fermionic sign problem. In this context, we review and compare the performance of traditional Variational Quantum Algorithms, such as the Variational Quantum Eigensolver and the Quantum Approximate Optimization Algorithm, against emerging heuristic approaches, specifically Feedback-based Quantum Algorithms, such as FALQON. We explore the applicability of these methods in the study of open phenomena in condensed matter physics, including Deconfined Quantum Criticality, strange metals, Many-Body Localization, topological phase transitions, and quantum spin liquids. We discuss how fundamental operational bottlenecks, notably expressibility- and noise-induced barren plateaus, severely compromise gradient-based optimization. We conclude that deterministic feedback-guided methods provide geometrically more robust trajectories for navigating the energy landscape of these systems, arguing that further advancement in the field will rely on deep hybridization and physics-informed circuit co-design towards fault tolerance.

Strategic decision-making among many agents under incomplete information is central to economics, security, and multi-agent artificial intelligence (AI). Computing equilibria in such settings is challenging because the joint type-action space grows exponentially with the number of players. In binary-type, binary-action Bayesian games, an explicit representation over type-action profiles requires O(22n) entries, making direct linear-programming (LP) formulations memory intensive at moderate player counts. We propose a hybrid quantum-classical framework for approximating Bayes correlated equilibrium using a parameterized quantum circuit (PQC). The PQC represents the conditional strategy distribution with O(nL) trainable parameters, where n is the number of players and L is the circuit depth; for the largest setting studied here, n = 10 and L = 2, this corresponds to 60 trainable angles. The circuit is trained by gradient-based regret minimization with a negative entropy regularizer and a curriculum schedule over player counts. On a poker-style Bayesian game with two to ten players, the proposed solver achieves lower mean clipped regret than MCCFR across all tested player counts and lower regret than DCFR up to eight players, while DCFR performs best at ten players. These results show that compact PQC parameterizations can provide a viable variational representation for approximate equilibrium computation, while highlighting the roles of ansatz expressivity, optimization strategy, and classical simulation cost.

We study a kinematical consequence of the Hopf-algebraic momentum composition law in $κ$-Minkowski spacetime. The same curved momentum space can be described in different coordinates. In the bicrossproduct basis the ordered-plane-wave labels are the translation-generator eigenvalues, so the relevant map is one-to-one. In the classical basis, instead, the translation eigenvalues $P_μ$ are nonlinearly related to the ordered-plane-wave labels $p_μ$. This relation can fail to be globally one-to-one in a high-momentum region. When a given classical-basis four-momentum admits more than one real auxiliary preimage, the branch-sensitive quantity $P_+\equiv P_0+P_4=κe^{p_0/κ}$ enters the coproduct and resolves the branches in two-particle states. Imposing the vanishing total-momentum constraint therefore gives branch-dependent $κ$-deformed back-to-back momentum correlations. In a single-branch regime this is just a deformed correlated product, while in a multibranch regime a state specified only by $P_μ$ can be expanded into distinct auxiliary branches. If $P_μ$ are taken as the directly meaningful momenta, the physical content is the resulting deformed correlation pattern. If the auxiliary variables $p_μ$ are assigned operational meaning, the same constrained state can be interpreted as a superposition over different auxiliary branches. We also compare this structure with standard regular self-adjoint nonrelativistic minimal-length models and find no analogous smooth local two-real-branch inversion on their physical domains.

We report a quantum simulation of the nucleon--antinucleon interaction in large-$N$ two-dimensional quantum chromodynamics (QCD$_2$) on the IBM Quantum Nighthawk processor. In the large-$N$ limit, QCD$_2$ admits a bosonized description in which baryons emerge as topological solitons (kinks) of an effective mesonic field theory, providing a controlled, nonperturbative framework for baryon--antibaryon dynamics. We formulate the problem by mapping the continuum bosonized Hamiltonian to a spin-chain representation equivalent to an XXZ model with anisotropy set by the QCD parameters. In this mapping, nucleon and antinucleon states correspond to kink and antikink excitations, respectively, while their interaction is encoded in the spin correlations of the chain. Using Jordan--Wigner encoding, we implement the resulting XXZ Hamiltonian on a finite set of qubits and realize it via a variational ground state ansatz and postselected nonunitary disorder operator insertions optimized for the Nighthawk architecture. We then show the kink--antikink interaction potential built from the conditional energies of these nonunitary string operators can be robustly extracted from the quantum hardware due to structured error cancelation. The resulting potential exhibits the expected attractive behavior. The quantum simulation results are benchmarked against exact diagonalization, ideal statevector evaluation showing good agreement. To connect the device result to the continuum field theory, we extract the potential in the continuum limit using large-$L$ matrix product state calculations.

Subwavelength atomic tweezer arrays, in which atoms can be positioned at distances smaller than their emission wavelength, have been proposed as a versatile platform to study collective emission phenomena, such as superradiance and subradiance. Experimentally, the realization of such arrays has been a challenge as typical emission wavelengths in the visible or near-infrared are short compared to typical tweezer spacings in the micrometer range. Here, we use $^{88}$Sr atoms in optical tweezer arrays to access a mid-infrared transition at 2,923 nm ($5s5p\:^{3}P_{2} \rightarrow\, 5s4d\:^{3}D_{3}$). We identify a magic trapping wavelength at 597.14(3) nm and demonstrate single-atom preparation and imaging with high fidelity. In addition, using 2,923 nm light, we demonstrate resolved-sideband cooling of tweezer-trapped strontium. Beyond enabling studies of collective emission phenomena in flexible arrangements of atoms, our platform opens novel opportunities for dipolar many-body physics and enhanced control over Rydberg dynamics and the strontium fine-structure qubit.

Strong-to-weak spontaneous symmetry breaking (SW-SSB) has recently emerged as a useful framework for studying phases of matter in open systems, quantum or classical. Beginning with the simple idea of extending symmetry breaking to general mixed states, and the familiar equivalence between canonical and grand-canonical ensembles in statistical mechanics, the concept has grown into a unifying perspective connecting many different ideas in physics, including topological orders, emergent hydrodynamics, and information-theoretic characterization of phases of matter. This review provides a bird's-eye view of some of these recent developments.

Recent experiments have demonstrated the successful generation and detection of moderately squeezed vacuum states with integrated photonics. However, in order to benefit from the reduced noise of highly squeezed light, many different noise sources must be mitigated. Here, we quantify the fundamental limits these noise sources impose on squeezing measurements and find surprising generality across different platforms and designs. We combine these different limitations into a simple model that provides practical guidance for the design and benchmarking of next-generation integrated squeezed-light systems.

We present entanglement measures between spatially separated regions and between two distinguishable or indistinguishable particles in one-dimensional two-particle continuous-time quantum walks governed by the Hubbard Hamiltonian. The left-right entanglement checks the entropy of coarse-grained states counting the numbers of particles on the left and right halves of the lattice while the particle-particle entanglement is based on the entropy of the singular values of the time-evolved Fock state. With separable, entangled, and doubly occupied initial states, we examine initial entanglement and the following growth in different entanglement measures. While the entanglement measures of the indistinguishable cases resemble those of the distinguishable cases when the initial states are comparable, the long-time limits of the entanglement measures are typically non-monotonic as the onsite repulsion increases. We also discuss possible implications for future research of entanglement in multi-particle quantum dynamics.

In previous work (Rave, 2008) it was proposed that closed loops should be treated as fundamental quantum entities, and such loops were presented in a quasi-probability framework. We demonstrate that the closed-loop decomposition of quantum probabilities is a direct consequence of unitarity, and that Bargmann invariants arise naturally as the phase-invariant quantities associated with these loops, rather than being introduced independently. This identifies interference not as mysterious cross terms, but as contributions from distinct classes of closed loops weighted by their associated Bargmann phases. Additionally, the Born rule is seen to reflect the fundamental quadratic structure arising from the product of forward and reverse amplitudes, which together define such loops.

Polar molecules are a promising platform for quantum-enhanced sensing and precision tests of fundamental physics, owing to their strong long-range dipolar interactions, broad sensitivity to electromagnetic fields, and sensitivity to potential physics beyond the Standard Model. However, the creation of metrologically useful entangled states in molecular systems has remained elusive. Here, we report the first observation of a class of metrologically useful entangled states - spin-squeezed states - in polar CaF molecules trapped in an optical tweezer array. The spin degree of freedom is encoded in rotational levels which are directly coupled by dipolar exchange interactions. By harnessing appropriate dynamical decoupling schemes we observe up to 3.0(3)dB of metrological gain, (2.2(3)dB without measurement correction) from direct exchange interactions. Using Floquet engineering, we further realize richer Hamiltonians that preserve spin squeezing while enabling the development of longer-range quantum correlations. Using site- and spin-resolved measurements we demonstrate that these entangled states enhance sensitivity to both homogeneous and spatially varying fields, and reveal strong non-classical correlations, including bipartite entanglement and Einstein-Podolsky-Rosen steering. Finally, we transfer the spin-squeezed states into long-lived and non-interacting hyperfine states, where the metrological enhancement persists for up to 100ms. Our results establish molecular optical tweezer arrays as a scalable platform for generating, controlling, characterizing, and storing entangled states of molecules, opening new opportunities for quantum-enhanced sensing and precision tests of fundamental physics.

Chern numbers are central to correlated and topological phenomena, yet most topological systems are associated with Chern numbers of order unity. Here we propose a scheme to achieve large Chern numbers in an optical Floquet quasicrystal with cold atoms, which can be directly measured via Thouless pumping. We study the quasienergy spectrum of Floquet quasicrystals and characterize the emergent Chern numbers using gap labeling theorem. We further investigate the Thouless pumping in the Floquet quasicrystal at different driving frequencies and amplitudes, revealing the connection between transport features and the quasienergy spectrum. Our findings open new avenues for exploring rich topological dynamics in Floquet quasicrystals and realizing fractional Chern insulating states.

Density cube theory extends the canonical quantum density matrix $ρ_{ij}$ with the addition of an extra index to $ρ_{ijk}$. The elements of the density cube with two different indices, $ρ_{iij}$ and $ρ_{ijj}$, correspond to the real and imaginary parts of the off-diagonal element $ρ_{ij}$ of the density matrix and describe double-path interference, while those with three different indices describe non-canonical triple-path interference. In this letter, we propose an equation of motion for the density cube, obtained from the quantization of ternary Nambu dynamics, and find that pairs of triple-path interferences oscillate into each other.

Information Causality was introduced as a physical principle for constraining the set of nonlocal correlations. In recent work, we proposed an extension of Information Causality that allows correlations among Alice's inputs. This extended principle yields tighter constraints than the original formulation and recovers part of the quantum boundary in certain Bell scenarios. In this work, we further investigate the implications of extended Information Causality and apply it to scenarios beyond binary inputs and outputs. We derive a family of quantum Bell inequalities that strengthen previously known constraints on quantum correlations. Using these inequalities, we obtain an improved analytical bound for the Collins-Gisin family of Bell inequalities. We also apply Information Causality to entanglement-assisted random access codes and derive new theory-independent analytical bounds on the winning probability. For this latter task, we prove that, despite being stronger in general, the extended principle does not improve the bounds obtained from the original Information Causality principle. This suggests that the existing Information Causality bounds are optimal for this class of random access codes.

The nitrogen vacancy (NV) center has emerged as a powerful quantum sensor in high-pressure research, with the observation of optically detected magnetic resonance at megabar pressures. However, some aspects of NV physics require further investigation to optimize the development of NV-based sensing under pressure. Here, we study both experimentally and theoretically the optical properties of the NV center under hydrostatic pressure. We investigate the evolution of the zero-phonon line (ZPL) position, radiative lifetimes, optical lineshapes, and photoionization thresholds of the NV center under pressures up to ~120 GPa. We also provide spectroscopic guidelines for performing high-pressure optical experiments. Our results confirm that the NV center remains a robust quantum sensor under extreme hydrostatic pressures, especially for magnetic characterization.

In this work we present a pedagogically motivated analysis of spin-correlation calculations in a quantum system composed of two spin-$1/2$ particles. Rather than aiming at new physical results, our purpose is to clarify and bring attention to different strategies for evaluating expectation values of the form $\langle ψ| S^{(1)}_{\hat{\boldsymbol{u}}} S^{(2)}_{\hat{\boldsymbol{v}}} | ψ\rangle$, which play an important role in discussions of entanglement and Bell-type correlations. We compare three complementary approaches. The first follows a direct algebraic evaluation in the product basis, closely related to standard textbook methods. The second uses a matrix representation of bipartite states, in which the tensor-product structure is expressed in terms of $2\times2$ complex matrices. This representation keeps the calculation close to the familiar Pauli-matrix algebra and makes the independent action of operators on each subsystem more transparent. The third explores a symmetry-based argument, highlighting both its usefulness and its limitations when applied beyond the singlet state. We show explicitly that the singlet state is rotationally invariant, which explains why the symmetry argument successfully reproduces its correlation function, while a naive extension fails for triplet states. The discussion illustrates how entanglement, tensor-product structure, and rotational symmetry interplay in spin correlations.

We investigate the geometry of mixed quantum states near rank-changing points, showing that these singularities function as effective geometric defects. The Uhlmann connection is well-defined only on the full-rank sector of the density-matrix manifold, while rank-deficient states form singular boundary strata where the bundle structure degenerates. By restricting to a punctured state manifold that excludes the singular set, we obtain a well-defined gauge structure and identify an asymptotically robust invariant: the Uhlmann holonomy around noncontractible loops encircling the defect. In an exactly solvable qutrit model, a restricted submanifold emerges on which the connection is locally flat yet carries nontrivial monodromy, analogous to flat connections with Aharonov--Bohm-type transport. The holonomy depends only on the ratios of the vanishing eigenvalues under frozen radial dependence of the eigenbasis geometry and a fixed angular loop. In contrast, the Uhlmann curvature may diverge path-dependently when eigenvalues shrink with distinct powers, with a leading spectral-prefactor scaling law, establishing that the holonomy survives as a universal asymptotic invariant while the curvature remains non-universal. Within the effective SU(2) defect sector, the conjugacy class of the holonomy, equivalently the Wilson loop variable, provides a continuous, non-quantized classification of the asymptotic monodromy surrounding the rank-deficient defect. This non-quantization does not imply a lack of robustness: the asymptotic holonomy is protected by the topology of the punctured manifold and is insensitive to smooth deformations of the loop or the radial profile.

Continuous-variable quantum key distribution (CV-QKD) requires highly efficient reconciliation techniques to operate at low signal-to-noise ratios and long distances. Multidimensional reconciliation addresses this challenge by transforming the physical Gaussian quantum channel into a virtual binary-input additive white Gaussian noise (BIAWGN) channel, enabling the use of modern errorcorrecting codes. In this work, we review the principles of multidimensional reconciliation, with a particular focus on high-dimensional constructions beyond the algebraic dimensions 1, 2, 4, 8. We describe the construction of the virtual channel, discuss practical coding schemes for reverse reconciliation, and analyse their integration with linear error-correcting codes. We also present an opensource simulation framework, HDirac, implementing multidimensional reconciliation for arbitrary dimensions, and use it to evaluate state-of-the-art LDPC codes. The results highlight key trade-offs between dimension, reconciliation efficiency, and frame error rate, providing practical guidance for CV-QKD system design.

We investigate localization in two models: a single particle in a two-dimensional square lattice described by the tight binding Hamiltonian, and a two-dimensional square qubit lattice. It is well-known that Anderson localization occurs under suitable conditions in which the system parameters are chosen randomly from some statistical distribution. We propose a situation in which the parameters, specifically the on-site energies, are carefully chosen in such a way that a localization-quantifying parameter is maximized. We demonstrate the optimization procedure with numerical calculations in which the engineered localization significantly exceeds the average localization caused by a random distribution of the on-site energies. We explore the relation between spatial patterns and localization efficiency. Furthermore, we use perturbation theory to gain insight into the localization mechanism and obtain an improved cost function for optimization calculations, leading to enhanced localization in both the single-particle and full Hilbert spaces. Although large-scale simulations for qubit lattices are computationally infeasible, we use small-system simulations to demonstrate that results obtained using the single-particle tight binding model can be adapted to identify optimal settings for qubit lattice systems to achieve maximum decoupling between the qubits, which can be valuable for optimizing the idle-state settings on a quantum processor.

We investigate a three-dimensional ghostly Hamiltonian realisation of the fully degenerate resonant sixth-order Pais-Uhlenbeck oscillator. On the classical level, the phase-space flow is non-diagonalisable and decomposes into two complex-conjugate Jordan chains of length three, explaining the appearance of oscillatory solutions with secular terms. Upon quantisation, we construct intertwining operators whose quadratic combinations generate a hidden spectrum-generating $\mathfrak{u}(2,1)$-algebra. The associated descendant spaces are finite-dimensional invariant subspaces carrying non-trivial Jordan structure. Although these spaces admit a natural decomposition into irreducible modules of a distinguished $\mathfrak{sl}_2$-subalgebra, this decomposition does not in general coincide with the Jordan decomposition of the Hamiltonian. We further derive a tri-Hamiltonian formulation from Lie point symmetries of the classical flow and show that the corresponding Hamiltonians are naturally encoded by the same hidden algebra. Nevertheless, unlike in the non-resonant case, no positive-definite linear combination of them generates the same dynamics. Finally, we analyse the common centraliser of the tri-Hamiltonian family in $U(\mathfrak u(2,1))$, showing that the natural higher-order candidate $Q$ is reducible and yields no independent classical or quantum integral. The model thus provides a resonant higher-derivative system in which hidden $\mathfrak{u}(2,1)$ symmetry, classical and quantum Jordan structures, and multi-Hamiltonian geometry coexist.

The ability to engineer and control quantum states of many-body systems is a central challenge in quantum information science. For a register of $N$ qubits, the full Hilbert space dimension grows exponentially as $2^N$, rendering generic state preparation and control infeasible without exploiting structure or symmetry. A particularly important and physically motivated restriction is to the fully symmetric subspace, spanned by the Dicke states, which are simultaneous eigenstates of collective spin $J=N/2$. Ensembles of Rydberg atoms interacting via electric dipoles in two-dimensional tweezer arrays form a promising platform for achieving such control. However, the finite range of dipole-dipole interactions poses a challenge to generating and controlling the Dicke manifold because the Hamiltonian incurs leakage from the computational subspace. To counteract this leakage, we perform quantum optimal control algorithms on a truncated Hilbert space according to our newly developed method of ``irrep distillation'' (IRD), which captures the process by which the symmetric subspace couples to leakage error-spaces, using only linear-scaling Hilbert dimension. We implement gradient ascent pulse engineering (GrAPE) on control schemes with little or no local addressing, to generate resourceful states like Greenberger-Horne-Zeilinger, Dicke, and extremal quantum states. We benchmark each scheme of IRD-GrAPE for its quantum speed limit (QSL), as well as exactly testing pulse fidelities on small system sizes and predicting fidelities using higher-order IRD on larger systems.

Information scrambling is a hallmark of quantum chaos and thermalization in isolated quantum many-body systems. We investigate scrambling dynamics in the all-to-all interacting spin Sachdev-Ye-Kitaev (SYK)-$q$ model using both pure- and mixed-state entanglement measures. We show that von-Neumann and Rényi entropies exhibit rapid growth followed by saturation near Haar-random values, signaling efficient scrambling. The scrambling rate reveals a nontrivial dependence on the interaction order, system size, and Hamiltonian scaling. We further employ mixed-state entanglement as a powerful probe of information scrambling. We numerically find a universal relation between the Rényi-1/2 mutual information and entanglement negativity for minimal interaction order in the early growth regime. Furthermore, entanglement negativity displays a Page-curve-like behavior under unequal subsystem partitioning, characterized by the birth, spread, and eventual death of quantum correlations. Our results provide a generic description of information scrambling using entanglement dynamics in all-to-all interacting spin systems with multi-body interactions.

Squeezed optical Schrödinger cat states constitute a key resource for both fundamental tests of quantum theory and up-to-date quantum technologies. We propose a measurement-assisted gate for the generation and manipulation of the cat states. In this scheme, an ancilla in the non-Gaussian small-amplitude (in general, squeezed) Schrödinger cat state and the target oscillator initially prepared in a squeezed vacuum (or coherent) state are subjected to a quantum nondemolition (QND) entangling operation followed by projective homodyne measurement. The proposed gate enables generation of high-fidelity squeezed Schrödinger cat states with controllable size and squeezing with tunable fidelity/success-probability trade-off. We also introduce an iterative, homodyne-conditioned $C_Z$-based protocol for cat-state amplification. The parameter regimes required to achieve the desired fidelity and the success probability are analyzed. The approach is well suited for applications in measurement-based quantum computing and hybrid quantum networks where non-Gaussian resources enhance computational and communication capabilities.

We challenge the long-unquestioned triangulation in distant stereovision, where shape rather than distance is the relevant observable. Our information-regret analysis reveals that the optimal measurements for absolute distance and distance gradient are unexpectedly different and incompatible. To resolve this observable-measurement mismatch, we introduce stereo regularization to address stereo anisotropies that violate prevailing emitter-number conservation, and propose the topographic interferometer, which exploits cross-detector correlations to probe topography without measuring the distance profile. Our interferometer turns parallaxing paths into Mach-Zehnder arms and incorporates a central path as the local oscillator for balanced homodyne detection, saturating the quantum Fisher information with improved topographic error scaling. Our work enables topographic stereovision of thermal sources beyond the Rayleigh limit, thereby establishing a quantum-inspired framework for heat-assisted detection and ranging in remote sensing and astronomy.

We present an algorithm that computes the action of a generic spin Hamiltonian on a state vector on the fly, entirely avoiding explicit matrix assembly. This is achieved through mixed-radix indexing of the full tensor-product basis, which translates local spin operations into simple integer offsets. The result is an explicit framework for evaluating single- and two-site terms across arbitrary spin lattices, including mixed-spin systems. Our construction bridges the basis-indexing logic familiar from exact diagonalization with the matrix-free state-update philosophy of address-based frameworks. By writing the indexing logic in closed form, a single uniform loop applies to every site regardless of its local Hilbert-space dimension. The method is parallelizable and memory-conserving, and can be extended to restricted basis or truncated bosonic levels.

Many-body topology is a central concept in modern theories of solids, and identifying effective degrees of freedom that capture it is important both fundamentally and practically. This work studies the extent to which geometric information of an interacting many-body ground state can be inferred from a finite number of local correlations. Starting from the Resta formula, $ z=\left\langle \exp\!\left(\frac{2πi}{L}\hat X\right)\right\rangle$, we view $\log z$ as the cumulant generating function and establish a generic information hierarchy across cumulant orders. We show that, for an $N$-particle system, even complete knowledge of all density correlators up to order $N-1$ does not, in general, uniquely determine the Berry phase $γ=\operatorname{Im}\log z \, (\mathrm{mod}\ 2π)$. In the thermodynamic limit, the statement becomes stronger: no finite set of local correlators suffices to determine the global holonomy. We also identify two exceptional yes-go cases in which the hierarchy is broken. First, for quasi-free models, all cumulants are determined by the particle two-point correlation function. Second, symmetry-enforced constraints can reduce the infinite cumulant sum entering $\log z$ to finite information. The argument is analytic and does not rely on a specific microscopic Hamiltonian. Our results clarify a limitation of approaches based on local degrees of freedom for many-body holonomy and provide a minimal framework for distinguishing when global holonomies are encoded in local correlations and when they are not. We also comment on the possibility of analogous hierarchies in other contexts, such as the quantum marginal problem in quantum information theory and many-body scattering problems. Finally, we discuss implications for future numerical work, including machine-learning approaches to the search for topological phases.

Quantum state distinguishability is a fundamental concept in quantum information science that underpins a wide range of important practical tasks. Traditionally formulated for pairs of states, quantum state distinguishability is here extended to quantum state ensembles, which we characterize through the average pairwise trace distance. Motivated by both theoretical and practical interest in noisy quantum information processing, we ask whether ``minimally'' scrambled ensembles modeled by 2-designs protect distinguishability under noise, which sheds light on the fundamental competition between noise and information scrambling. Using a rigorous decoupling approach, we establish tight bounds on noisy ensemble distinguishability. We show that the distinguishability of noisy 2-design ensembles exhibits a sharp threshold and phase-transition behavior governed by channel conditional entropy: below the threshold, the states remain mutually distinguishable with high probability, while above it, distinguishability undergoes a sudden power-law decay and then collapses exponentially. On the other hand, under local purity-shrinking noise, post-measured noisy 2-design ensembles become exponentially indistinguishable for any measurement, precluding a noise threshold for learning tasks such as shadow tomography. These results reveal a sharp difference between unmeasured and post-measured scrambled ensembles: the former can retain high distinguishability for sufficiently small noise, whereas the latter exhibits no such protected regime. We discuss the implications of these results for crucial tasks ranging from quantum communication and cryptography to learning.

We investigate the quantum dynamics of a particle subjected to a linear potential using the Lewis--Riesenfeld invariant operator method. Starting from the time-dependent Schrödinger equation associated with a constant external force, we construct the most general Hermitian quadratic invariant and derive the corresponding coupled differential equations for its time-dependent coefficients. By means of an appropriate sequence of unitary transformations, the invariant operator is reduced to the form of a harmonic oscillator Hamiltonian. This reduction enables a clear classification of the system according to the sign of the conserved quantity ω2. Particular attention is devoted to the physically relevant case ω2 >0, which yields a discrete eigenspectrum. Explicit analytical expressions for the invariant coefficients, the displacement parameters, and the transformed wave functions are obtained. The resulting formalism provides an exact quantum description of a particle under a constant force and establishes a direct connection between invariant theory and harmonic oscillator quantization.

Identifying minimum-energy structures of lattice proteins is a challenging discrete optimization problem. Quantum approaches such as analog quantum annealing and the gate-based quantum approximate optimization algorithm (QAOA) can address this problem after mapping it to a binary representation, which typically involves introducing penalty terms to enforce valid chain configurations. However, in this and many related problems, the use of quadratic penalty terms can be avoided by restricting the search space to independent sets in a conflict graph and using a QAOA mixer designed for the maximum independent set problem. In this work, we implement and explore this QAOA variant for lattice protein folding. Here, the objective function consists solely of the protein energy together with a simple linear bias term, without quadratic penalties. We validate this approach through classical simulations of the quantum circuits for lattice proteins of lengths $N=4$ and $N=6$. To explore larger systems, we further introduce a heuristic iterative local-search scheme, with which we successfully fold lattice proteins with lengths up to $N=14$ using local subgraphs with at most 26 qubits.

We propose a quantum probability-flow principle for deriving local learning rules in associative memory. A transverse field defines leakage channels from data states, and minimizing the measured survival loss gives stability-driven updates. For imaginary-time, dephased dynamics, the local leakage free energy is the log-sum-exp of energy gaps; its gradient is a softmax-weighted Hebbian rule. Real-time stability instead yields a power-law weighting. D-Wave standard- and fast-anneal tests of a one-hot attention forward map are better fitted by an effective softmax than by a Lorentzian power law.

We present a framework combining Lie group theory and feed-forward neural networks to efficiently generate quantum optimal control pulses for arbitrary unitary operations in superconducting qubit systems, bypassing the need for explicit optimization at inference time. The exponential scaling of the Hilbert space dimension with qubit number makes standard optimization approaches computationally prohibitive when large ensembles of distinct propagators must be processed, a bottleneck that is particularly acute in Trotterized quantum simulation. Our method addresses this limitation by pre-computing a representative set of control pulses via Lie group theory and training neural networks to map target propagators to their corresponding pulses. We demonstrate the approach on superconducting qubit systems of 2, 3, and 4 qubits, finding high reconstruction fidelity for specific combinations of Lie algebra parameters. As a physically motivated benchmark, we apply the methodology to reconstruct control pulses for the Trotter propagators of a neutrino system undergoing collective flavor oscillations. The successful generalization across system types demonstrates that a single model -- trained once on hardware-specific random propagators -- can serve as a universal control-pulse generator for any target quantum system of compatible Hilbert space dimension, offering a promising route toward scalable quantum simulation.

In a shared quantum computer, how to ensure data privacy and protection from access by unauthorized parties? We propose a genuine quantum protocol for protecting user's data which is not accessible even to the service provider. The protocol is based on quantum kicked top -- the dynamics of a spin system --operating at quantum resonance regime. This protocol ensures perfect recovery for authorized users while making intercepted states appear mixed to eavesdroppers, with built-in tampering detection. This protocol can also be used for secure communication between two parties in geographically different locations, and also for quantum key distribution. The effectiveness of this protocol is demonstrated by assuming a quantum computer with quantum memory and functioning quantum networks. In the absence of the latter, at present, the protocol can be demonstrated in laboratory using currently available quantum computing platforms.

We propose two types of protocols for quantum secure blind decryption, involving two users and servers. User 1 holds the encrypted ciphertext. The servers store several indexed keys including the key encrypting the ciphertext. User 2 aims to obtain the decrypted text. The protocols are designed to preserve the following types of secrecy: Users ensure the secrecy of the text from the servers. Servers maintain the secrecy of the keys from the users. Our protocols enable User 2 to obtain the decrypted text while preserving these secrecy requirements. Additionally, the second protocol ensures the secrecy of the key index to identify the key encrypting the ciphertext from the servers, and the second protocol requires two non-commuting servers. Furthermore, we analyze the secrecy of the second protocol under post-attack scenarios, where the two servers communicates with each other after the completion of the protocol. We show that our quantum protocol satisfies the secrecy under these attacks, whereas its classical counterpart fails to do so.

Absolutely maximally entangled (AME) states and, more generally, $k$-uniform states in $(\C^q)^{\otimes n}$ are central objects in multipartite entanglement theory, with applications to quantum secret sharing, quantum masking, and quantum error correction. In the extremal case $k=\lfloor n/2\rfloor$, Scott (2004) proved a sharp nonexistence bound showing that AME states cannot exist once the number of parties $n$ exceeds a threshold of order $2q^{2}$ (with a parity dependence on $n$), where $q$ is the local dimension. Recently, Ning et al.\ studied \emph{defective} AME states (i.e., $k=\lfloor n/2\rfloor-l$ with $l>0$), gave explicit Scott-type bounds for defects $l=1,2$ and conjectured a general $(2l+2)q^{2}+o(q^{2})$ behavior. In this paper, we solve this conjecture and establish a fully explicit Scott-type upper bound for AME states with arbitrary defect $l\ge 0$, yielding Scott's bound for $l=0$ and Ning et al.'s bounds for $l=1,2$ as special cases. Equivalently, this gives nonexistence bounds for one-dimensional pure quantum error-correcting codes near the quantum Singleton regime. The proof uses a truncated MacWilliams linear-programming system and an explicit infeasibility certificate. As a direct application, we derive explicit asymptotic upper bounds on $k/n$ for fixed local dimension $q$, improving the implicit upper bounds given by Ning et al.

The Klein tunnel effect phenomenon makes it impossible to permanently confine charge carriers in massless nanostructures. However, applying a constant magnetic field allows these electrons to be temporarily localized, thus forming quasi-bound states. In this study, we analyze the mechanism of electron diffusion through a silicene quantum dot (SQD) subjected to a perpendicular magnetic field. To enhance spatial localization, we exploit the spin-orbit coupling (SOC) specific to silicene, which generates a natural energy gap by acting as an effective mass. We first derive the solutions to the Dirac equation at low energy. Subsequently, by imposing the continuity conditions at the SQD interfaces, we obtain exact expressions for the diffusion coefficients. These results are then used to map the scattering efficiency together with the spatial distributions of probability and current densities. Our simulations demonstrate that the presence of this intrinsic gap significantly enhances electron trapping at the center of the SQD. Finally, we prove that the interplay between the external field and SOC breaks spin symmetry, thereby enabling robust and spin-selective confinement.

We study correlation-guided cluster algorithms for solving the Max-Cut problem that iteratively try to improve solutions by updating clusters of nodes. Building on the recently proposed quantum-guided cluster algorithm (QGCA) [arXiv:2508.10656], which leverages precomputed two-point correlations to guide collective updates, we extend the cluster construction by incorporating next-nearest-neighbor (NNN) information. We evaluate this extension across different correlation sources on random regular graphs and non-degenerate tile-planted instances. Notably, we observe particularly strong performance on non-degenerate instances and provide a scaling analysis for this class. Finally, we outline an extension toward a correlation-guided Markov-chain Monte Carlo algorithm, whose detailed analysis remains an open direction for future work.

We develop a susceptibility-based open-system theory for two localized qubits coupled through a candidate two-dimensional $\mathrm{U}(1)$ Dirac-spin-liquid-like bath. The central input is the gauge-invariant retarded physical spin susceptibility $\Chi^R(q,ω)$ of the bath. We show that this single response kernel controls both coherent and dissipative qubit dynamics: its real part generates the nonlocal mediated exchange, while its absorptive part determines relaxation and dephasing through the equilibrium noise spectrum. This gives a unified reduced two-qubit description in which the usefulness of the bath as an entanglement bus is governed by the competition between susceptibility-mediated exchange and bath-induced decoherence. As an analytically transparent benchmark, we evaluate the spinon mean-field Dirac susceptibility and recover the static algebraic exchange $J_{\mathrm{eff}}(R)\propto J_{\rm local}^2/(v_F R^3)$, together with pseudogap-suppressed relaxation $Γ_1\propto J_{\rm local}^2ω_0^3/v_F^4$. We then formulate a beyond-mean-field extension in which gauge-field dressing and other interaction effects are absorbed into a dressed physical susceptibility, without changing the reduced qubit-sector mapping. The resulting framework provides a direct route from the many-body spin response of a correlated two-dimensional bath to reduced-dynamics simulations of entanglement generation, coherence loss, and the operational phase space of a candidate Dirac spin-liquid quantum interconnect.

We study finite-time quantum Otto cycles whose working medium is a harmonic oscillator undergoing a quantum Brownian motion described by the Caldeira-Leggett model when the oscillator is in contact with heat baths in isochoric processes. The time evolution of the Otto cycle is studied by analytically solving the exact Heisenberg-Langevin equations for the system variables and the interaction energy between the system and the bath. This enables us to investigate non-Markovian strong-coupling effects on the quantum Otto cycle. We obtain cyclic steady states and study the thermodynamic properties of the Otto cycle for various values of the parameters describing the heat baths and the coupling between the system and the bath. We compare our results with those obtained in the Markovian limit, where the time evolution is described by the Lindblad equation. We find that the change in the interaction energy during the isochoric process contributes to both work and heat, and plays a crucial role in determining thermodynamic behavior of the cycle. In particular, we find that when the Otto cycle operates as an engine, the effect of the interaction energy is to reduce the work output. We also compare our results with the power-efficiency trade-off relation recently proposed for the Markovian quantum Otto engine. We find that the power of our non-Markovian engine for a given efficiency value falls below the Markovian power-efficiency bound.

We propose a non-destructive method to measure the population of molecules in a selected rotational-hyperfine state by coupling them to a high-finesse optical cavity. In contrast to traditional techniques, our approach enables fast (less than 1 ms) repeated measurements with reduced heating and losses, and with precision below the standard quantum limit. The method is particularly advantageous for radioactive molecules, systems of high interest for symmetry violation searches, for which production and sample size are limited, and repeated interrogation is essential for improved sensitivity.

Preconditioning is a fundamental technique for accelerating classical linear system solvers, and understanding when its benefits persist in quantum linear system (QLS) solvers is important for assessing the practical resource requirements of quantum linear algebra. In QLS algorithms, however, the potential advantage of preconditioning may be offset by the normalization overhead incurred by composing separate block-encodings of the system matrix and the preconditioner, as observed in recent work. This limitation leaves open whether additional algebraic structure can make preconditioning effective in quantum access models. Motivated by this question, we show that Pauli-structured representations of both the system matrix and the preconditioner allow the preconditioned operator to be accessed through regrouped Pauli expansions. In this setting, algebraic regrouping of Pauli products can reduce the Pauli coefficient weight of the preconditioned operator, thereby altering the normalization parameters relevant to quantum algorithms. We derive explicit size and coefficient-weight bounds for the regrouped Pauli representations, and we trace their consequences for both direct block-encoding constructions and randomized Pauli linear system solvers. These results identify when Pauli-structured preconditioning can reduce the effective complexity parameters of QLS algorithms, rather than merely improving the classical condition number. Numerical experiments on a finite-dimensional synthetic benchmark show reductions in norm-aware direct block-encoding diagnostics and in the randomized QLS per-sample depth proxy.

This paper studies the Fourier spectral method (FSM) for the Schrödinger equation with singular potentials $V \in H^{s}$, where $s > \max\{d/2-2,-1\}$ and $d$ denotes the spatial dimension. This setting includes a broad class of singular potentials, such as the 3D Coulomb potential and the 1D Dirac-delta potential. First, we combine the Feshbach-Schur map with a refined perturbation argument to derive sharp convergence orders for FSM, yielding order $2s+2$ for eigenvalues and order $s+1$ for eigenfunctions in the $H^1$ norm. More importantly, the $H^1$ error with respect to the projected eigenfunction converges with a higher order $s+1+b$, where $b=\min\{s+2-d/2-\varepsilon,\; s+1,\; 2\}>0$ for arbitrarily small $\varepsilon>0$, revealing a super-convergence phenomenon. Second, in the presence of potentials with isolated point singularities, we develop an asymptotic-recovery (AR) technique to post-process the FSM solutions. The resulting method, dubbed AR-FSM, fully exploits the super-convergence property and achieves convergence orders $2s+2+2b$ for eigenvalues and $s+1+b$ for eigenfunctions in the $H^1$ norm, while the AR post-processing requires only a computational cost that is linear in the number of FSM degrees of freedom. The analysis introduces a rigorous definition of point singularities and develops a foundational framework for their study. It further establishes an asymptotic expansion of eigenfunctions consisting of a regular component in $H^{s+4}$ together with $d+1$ asymptotic functions associated with each singular point. Numerical experiments confirm the sharpness of these theoretical bounds.

We explore the nonequilibrium dynamics of a density-ordered dipolar Bose gas in a finite one-dimensional optical lattice following a negative interaction quench, using the numerically exact multiconfigurational time-dependent Hartree method for bosons. The interaction sign reversal, effectively driving a crossover from long-range to short-range interactions, generates rich intra- and interwell tunneling dynamics spanning superfluid, Mott-insulating, and fragmented regimes. A striking finding is the robustness of the underlying crystal-state correlations against the quench, despite the strong dynamical response. We identify emergent excitation modes, including local breathing and dipole-like oscillations, via real- and momentum-space observables, and quantify tunneling through site-resolved position variance. One- and two-body Glauber correlation functions further uncover a direct connection between tunneling and correlation dynamics. Moreover, we show that combining interaction quenches with lattice-depth ramping enables controllable dynamical engineering, establishing dipolar lattice systems as a promising platform for nonequilibrium quantum simulation.

It is a difficult task to detect the indivisible quanta of weakly interacting radiation fields, and even more challenging to probe their quantum statistics. Nevertheless, if barely functional high-quality resonant detectors are feasible for weakly interacting radiation fields, they do come with certain statistical advantages to probe quantum effects at the seemingly classical limit of a large number of quanta of the incoming radiation field. We present correlated counting, homodyne, and heterodyne detection strategies using high-quality resonant quantum harmonic detectors operating at this limit, initialized in bolometry-inspired zero-mean preparations such as thermal states. We compare the bolometric regime of good resonant harmonic detectors in quantum optics to the bolometric regime of barely functional resonant mass quadrupole oscillators as detectors for quantum gravity. Simple statistical tests are proposed using symmetric correlators for two and three such barely functional resonant mass detectors that could reveal the complementary quantum noise characteristics of gravitons in tabletop experiments.

Thin-film lithium tantalate (TFLT) has emerged as a promising integrated photonic platform owing to its low photorefractive noise, high optical damage threshold, and reduced birefringence, attracting increasing interest for scalable photonic technologies. Here, to the best of our knowledge, we demonstrate the first quantum light source with TFLT via spontaneous four-wave mixing, bridging the gap between the rapidly advancing classical TFLT ecosystem and integrated quantum photonics. The fabricated microring exhibits a free spectral range of 350~GHz and an optical quality factor of $10^6$, enabling efficient cavity-enhanced nonlinear interactions. Correlated photon pairs are generated across the telecom band from 1510 to 1570~nm, with a photon pair generation rate of 24 $\mathrm{MHz/mW^{2}}$ at a wavelength of 1535.04 nm. The source delivers strongly antibunched heralded single photons with $g^{(2)}_{H}(0)=0.071\pm0.004$ at a heralding rate of 170 kHz, while the unheralded statistics yield $g^{(2)}(0)=1.93 \pm 0.05$, indicating near-single-temporal-mode emission. Energy-time entanglement is further confirmed by a raw two-photon interference visibility of $92.55\pm0.94\%$, well above the Bell-inequality violation threshold. These results establish TFLT as a manufacturing-compatible platform for scalable photonic quantum circuits, paving the way for the monolithic co-integration of classical and quantum photonic functionalities.