Quantum Physics Paper Analysis

Realizing the full potential of quantum computation requires Quantum Error Correction (QEC). QEC reduces error rates by encoding logical information across redundant physical qubits, enabling errors to be detected and corrected. A common decoder used for this task is Minimum Weight Perfect Matching (MWPM) a graph-based algorithm that relies on edge weights to identify the most likely error chains. In this work, we propose a data-driven decoder named Neural Minimum Weight Perfect Matching (NMWPM). Our decoder utilizes a hybrid architecture that integrates Graph Neural Networks (GNNs) to extract local syndrome features and Transformers to capture long-range global dependencies, which are then used to predict dynamic edge weights for the MWPM decoder. To facilitate training through the non-differentiable MWPM algorithm, we formulate a novel proxy loss function that enables end-to-end optimization. Our findings demonstrate significant performance reduction in the Logical Error Rate (LER) over standard baselines, highlighting the advantage of hybrid decoders that combine the predictive capabilities of neural networks with the algorithmic structure of classical matching.

Distributed quantum computing (DQC) is a promising technique for scaling up quantum systems. While significant progress has been made in DQC for quantum circuit models, there exists much less research on DQC for measurement-based quantum computing (MBQC), which is a universal quantum computing model that is essentially different from the circuit model and particularly well-suited to photonic quantum platforms. In this paper, we propose DC-MBQC, the first distributed quantum compilation framework tailored for MBQC. We identify and address two key challenges in enabling DQC for MBQC. First, for task allocation among quantum processing units (QPUs), we develop an adaptive graph partitioning algorithm that preserves the structure of the graph state while balancing the workload across QPUs. Second, for inter-QPU communication, we introduce the layer scheduling problem and propose an algorithm to solve it. Regrading realistic hardware requirements, we optimize the execution time of running quantum programs and the corresponding required photon lifetime to avoid fatal failures caused by photon loss. Our experiments demonstrate a $7.46\times$ improvement on required photon lifetime and $6.82\times$ speedup with 8 fully-connected QPUs, which further confirm the advantage of distributed quantum computing in photonic systems. The source code is publicly available at https://github.com/qfcwj/DC-MBQC.

A common challenge in superconducting quantum circuits is the trade-off between strong coupling and computational subspace integrity. We present Mathieu control, which uses a non-resonant two-photon drive to create a selective nonlinear frequency shift. This shift modifies interactions while preserving qubit states, enabling continuous tuning of the ZZ coupling, including full suppression, and integrating single- and two-qubit gates with low leakage. For a qubit-coupler-qubit device, it allows independent ZZ control, facilitating a programmable Heisenberg (XXZ) Hamiltonian. Extended to a five-qubit chain, the system can be reconfigured to simulate dynamics of quantum magnetic phases. Mathieu control thus provides a framework for high-fidelity quantum logic and programmable simulation.

Since an n-qubit circuit consisting of CNOT gates can have up to $Ω(n^2/\log{n})$ CNOT gates, it is natural to expect that $Ω(n^2/\log{n})$ Toffoli gates are needed to apply a controlled version of such a circuit. We show that the Toffoli count can be reduced to at most n. The Toffoli depth can also be reduced to O(1), at the cost of 2n Toffoli gates, even without using any ancilla or measurement. In fact, using a measurement-based uncomputation, the Toffoli depth can be further reduced to 1. From this, we give two corollaries: any controlled Clifford circuit can be implemented with O(1) T-depth, and any Clifford+T circuit with T-depth D can be controlled with T-depth O(D), even without ancillas. As an application, we show how to catalyze a rotation by any angle up to precision $ε$ in T-depth exactly 1 using a universal $\lceil\log_2(8/ε)\rceil$-qubit catalyst state.

Distributed quantum computing architectures require high-performance quantum interconnects between quantum information processing units, while previous implementations have been fundamentally limited by transmission line losses. Here, we demonstrate a low-loss interconnect between two superconducting modules using an aluminum coaxial cable, achieving a bus mode quality factor of 1.7e6. By employing SNAIL as couplers, we realize inter-modular state transfer in 0.8 μs via a three-wave mixing process. The state transfer fidelity reaches 98.2% for quantum states encoded in the first two energy levels, achieving a Bell state fidelity of 92.5%. Furthermore, we show the capability to transfer high-dimensional states by successfully transmitting binomially encoded logical states. Systematic characterization reveals that performance constraints have shifted from transmission line losses (contributing merely 0.2% infidelity) to module-channel interface effects and local Kerr nonlinearities. Our work advances the realization of quantum interconnects approaching fundamental capacity limits, paving the way for scalable distributed quantum computing and efficient quantum communications.

Scaling quantum computing beyond a single device requires networking many quantum processing units (QPUs) into a coherent quantum-HPC system. We propose the Modular Entanglement Hub (ModEn-Hub) architecture: a hub-and-spoke photonic interconnect paired with a real-time quantum network orchestrator. ModEn-Hub centralizes entanglement sources and shared quantum memory to deliver on-demand, high-fidelity Bell pairs across heterogeneous QPUs, while the control plane schedules teleportation-based non-local gates, launches parallel entanglement attempts, and maintains a small ebit cache. To quantify benefits, we implement a lightweight, reproducible Monte Carlo study under realistic loss and tight round budgets, comparing a naive sequential baseline to an orchestrated policy with logarithmically scaled parallelism and opportunistic caching. Across 1-128 QPUs and 2,500 trials per point, ModEn-Hub-style orchestration sustains about 90% teleportation success while the baseline degrades toward about 30%, at the cost of higher average entanglement attempts (about 10-12 versus about 3). These results provide clear, high-level evidence that adaptive resource orchestration in the ModEn-Hub enables scalable and efficient quantum-HPC operation on near-term hardware.

The performance and scalability of semiconductor quantum-dot (QD) qubits are limited by electrostatic drift and charge noise that shift operating points and destabilize qubit parameters. As systems expand to large one- and two-dimensional arrays, manual recalibration becomes impractical, creating a need for autonomous stabilization frameworks. Here, we introduce a method that uses the full network of charge-transition lines in repeatedly acquired double-quantum-dot charge stability diagrams (CSDs) as a multidimensional probe of the local electrostatic environment. By accurately tracking the motion of selected transitions in time, we detect voltage drifts, identify abrupt charge reconfigurations, and apply compensating updates to maintain stable operating conditions. We demonstrate our approach on a 10-QD device, showing robust stabilization and real-time diagnostic access to dot-specific noise processes. The high acquisition rate of radio-frequency reflectometry CSD measurements also enables time-domain noise spectroscopy, allowing the extraction of noise power spectral densities, the identification of two-level fluctuators, and the analysis of spatial noise correlations across the array. From our analysis, we find that the background noise at 100~$μ$\si{\hertz} is dominated by drift with a power law of $1/f^2$, accompanied by a few dominant two-level fluctuators and an average linear correlation length of $(188 \pm 38)$~\si{\nano\meter} in the device. These capabilities form the basis of a scalable, autonomous calibration and characterization module for QD-based quantum processors, providing essential feedback for long-duration, high-fidelity qubit operations.

Accurate benchmarking of quantum gates is crucial for understanding and enhancing the performance of quantum hardware. A standard method for this is interleaved benchmarking, a technique which estimates the error on an interleaved target gate by comparing cumulative error rates of randomized sequences implemented with the interleaved gate and without it. In this work, we show both numerically and experimentally that the standard approach of interleaved randomized benchmarking (IRB), which uses the multi-qubit Clifford group for randomization, can produce highly inaccurate and even physically impossible estimates for the error on the interleaved gate in the presence of coherent errors. Fortunately we also show that interleaved benchmarking performed with cycle benchmarking, which randomizes with single qubit Pauli gates, provides dramatically reduced systematic uncertainty relative to standard IRB, and further provides as host of additional benefits including data reusability. We support our conclusions with a theoretical framework for bounding systematic errors, extensive numerical results comparing a range of interleaved protocols under fixed resource costs, and experimental demonstrations on three quantum computing platforms.

Quantum information processing platforms based on array of matter qubits, such as neutral atoms, trapped ions, and quantum dots, face significant challenges in scalable addressing and readout as system sizes increase. Here, we propose the "Volcano" architecture that establishes a new quantum processing unit implementation method based on optical channel mapping on a arbitrarily arranged static qubit array. To support the feasibility of Volcano architecture, we show a proof-of-principle demonstration by employing a photonic chip that leverages custom-designed three-dimensional waveguide structures to transform one-dimensional beam arrays into arbitrary two-dimensional output patterns matching qubit array geometries. We demonstrate parallel and independent control of 49-channel with negligible crosstalk and high uniformity. This architecture addresses the challenges in scaling up quantum processors, including both the classical link for parallel qubit control and the quantum link for efficient photon collection, and holds the potential for interfacing with neutral atom arrays and trapped ion crystals, as well as networking of heterogeneous quantum systems.

This document presents a concise overview of the contemporary research directions in quantum computer cybersecurity. The aim of this document is not to be a survey, but rather a succinct summary of the major research directions in quantum computer cybersecurity at the end of the first half of the current decade. The document has been inspired by the presentations and discussions held at the 3$^{rd}$ Quantum Computer Cybersecurity Symposium, but goes beyond the contents of the symposium and aims to summarize at the high level the last five years of quantum computer cybersecurity work in academia. It is hoped that the document can provide researchers as well as government and industry leaders an overview of the current landscape of security threats and defenses against emergent quantum computing technologies. The document also includes a discussion of the current trends in cybersecurity research on quantum computers, and the perceived research gaps that should be filled with future funding and through academic and industry~research.

Hybrid semiconductor-superconductor qubits have recently emerged as a promising alternative to traditional platforms, combining material advantages with device-level tunability. A defining feature is their gate-tunable Josephson coupling, enabling superconducting qubit architectures with full electric-field control and offering a path toward scalable, low-crosstalk quantum processors. This approach seeks to merge benefits of superconducting and semiconductor qubits, for instance by encoding quantum information in the spin of a quasiparticle occupying an Andreev bound state, thus combining long coherence times with fast, flexible control. Progress has accelerated through bottom-up engineering of Andreev states in coupled quantum dot arrays, leading to architectures such as minimal Kitaev chains hosting Majorana zero modes. In parallel, Hamiltonian-protected designs aim to enhance resilience against local noise and decoherence by exploiting superconducting phase dynamics and discrete charge or flux degrees of freedom. This article reviews recent theoretical and experimental advances in hybrid qubits, providing an overview of physical mechanisms, device implementations, and emerging architectures, with emphasis on their potential for (topologically) protected quantum information processing. While many designs remain at proof-of-concept stage, rapid progress suggests practical demonstrations may soon be achievable.

We introduce the Clifford entropy, a measure of how close an arbitrary unitary is to a Clifford unitary, which generalizes the stabilizer entropy for states. We show that this quantity vanishes if and only if a unitary is Clifford, is invariant under composition with Clifford unitaries, and is subadditive under tensor products. Rewriting the Clifford entropy in terms of the stabilizer entropy of the corresponding Choi state allows us to derive an upper bound: that this bound is not tight follows from considering the properties of symmetric informationally complete sets. Nevertheless we are able to numerically estimate the maximum in low dimensions, comparing it to the average over all unitaries, which we derive analytically. Finally, harnessing a concentration of measure result, we show that as the dimension grows large, with probability approaching unity, the ratio between the Clifford entropy of a Haar random unitary and that of a fixed magic gate gives a lower bound on the depth of a doped Clifford circuit which realizes the former in terms of the latter. In fact, numerical evidence suggests that this result holds reliably even in low dimensions. We conclude with several directions for future research.

Circuit simulation tools are critical for developing and assessing quantum-error-correcting and fault-tolerant strategies. In this work, we present SOFT, a high-performance SimulatOr for universal Fault-Tolerant quantum circuits. Integrating the generalized stabilizer formalism and highly optimized GPU parallelization, SOFT enables the simulation of noisy quantum circuits containing non-Clifford gates at a scale not accessible with existing tools. To provide a concrete demonstration, we simulate the state-of-the-art magic state cultivation (MSC) protocol at code distance $d=5$, involving 42 qubits, 72 $T$ / $T^\dagger$ gates, and mid-circuit measurements. Using only modest GPU resources, SOFT performs over 200 billion shots and achieves the first ground-truth simulation of the cultivation protocol at a non-trivial scale. This endeavor not only certifies the MSC's effectiveness for generating high-fidelity logical $T$-states, but also reveals a large discrepancy between the actual logical error rate and the previously reported values. Our work demonstrates the importance of reliable simulation tools for fault-tolerant architecture design, advancing the field from simulating quantum memory to simulating a universal quantum computer.

We revisit the finite Abelian hidden subgroup problem (AHSP) from a mathematical perspective and make the following contributions. First, by employing amplitude amplification, we present an exact quantum algorithm for the finite AHSP, our algorithm is more concise than the previous exact algorithm and applies to any finite Abelian group. Second, utilizing the Chinese Remainder Theorem, we propose a distributed exact quantum algorithm for finite AHSP, which requires fewer qudits, lower quantum query complexity, and no quantum communication. We further show that our distributed approach can be extended to certain classes of non-Abelian groups. Finally, we develop a parallel exact classical algorithm for finite AHSP with reduced query complexity; even without parallel execution, the total number of queries across all nodes does not exceed that of the original centralized algorithm under mild conditions.

We study the ergodic properties of a unitary Floquet dynamics arising from the repeated application of a translationally-invariant Clifford Quantum Cellular Automata to an infinite system of qubits in d dimensions. One expects that if the QCA does not exhibit any periodicity, a generic initial state of qubits will thermalize, that is, approach the infinite-temperature state. We show that this is true for many classes of states, both pure and mixed. In particular, this is true for all initial states that are short-range entangled and close to the equilibrium state. We also point out a subtle distinction between weak and strong thermalization.

We investigate the fluctuation-induced Casimir interactions between two parallel graphene sheets carrying steady-state drift currents. The graphene properties are modeled based on the shifted Fermi disk model to capture the non-equilibrium optical response of the system. We find that the drift current introduces a repulsive correction to the perpendicular to the layers Casimir interaction, thereby reducing the overall attractive force. Although the correction is repulsive, it does not overcome the underlying attraction between the layers. It also generates a lateral force that opposes the carrier flow direction. Both contributions are studied in terms of distance and drift velocity functionalities showing pathways for Casimir force control.

We investigate the band structure and topological phases of one- and two-dimensional bipartite atomic lattices mediated by long-range dissipative radiative coupling. By deriving an effective non-Hermitian Hamiltonian for the single-excitation sector, we demonstrate that the low-energy dynamics of the system are governed by a Dirac equation with a complex Fermi velocity. We analyze the associated topological invariants for both the SSH and honeycomb models, utilizing synthetic gauge fields to break time-reversal symmetry in the latter. Finally, we explicitly verify the non-Hermitian bulk-edge correspondence by deriving analytical solutions for edge states localized at domain boundaries.

The conventional design technique of any n-bit quantum gate is mainly achieved using unitary matrices multiplication, where n >= 2 and 1 <= m <= n-1 for m target qubits and n-m control qubits. These matrices represent quantum rotations by an n-bit quantum gate. For a quantum designer, such a conventional technique requires extensive computational time and effort, which may generate an n-bit quantum gate with a too high quantum cost. The Bloch sphere is only utilized as a visualization tool to verify the conventional design correctness for quantum rotations by a quantum gate. In contrast, this paper introduces a new concept of using the Bloch sphere as a "geometrical design tool" to build cost-effective n-bit quantum gates with lower quantum costs. This concept is termed the "Bloch sphere approach (BSA)". In BSA, a cost-effective n-bit quantum gate is built without using any unitary matrices multiplication. Instead, the quantum rotations for such a gate are visually selected using the geometrical planar intersections of the Bloch sphere. The BSA can efficiently map m targets among n-m controls for an n-bit quantum gate, to satisfy the limited layout connectivity for the physical neighboring qubits of a quantum computer. Experimentally, n-bit quantum gates built using the BSA always have lower quantum costs than those for such gates built using the conventional quantum design techniques.

We demonstrate quantum levitation controlled by Casimir forces acting between a polystyrene surface and a Teflon-coated metallic substrate immersed in a mixture of Toluene and magnetite particles. This system experiences repulsion-attraction transitions in the Casimir interaction for distances where the effect is measurable. This Casimir trapping can be controlled by clever choices of metallic and ferrofluid materials, which are directly linked to the emergence of the trapping effect. Thermal and quantum contributions are investigated in detail, showing how the optical and magnetic properties of the ferrofluid and other materials affect the magnitude of the trapping and its distance range of observability.

Gauge/gravity duality is often described as a quantum error correcting code. However, as seen in the Jafferis-Lewkowycz-Maldacena-Suh (JLMS) formula, exact quantum error correction with complementary recovery (and thus entanglement wedge reconstruction) emerges only in the limit $G \to 0$. As a result, precise arguments controlling error terms have focused on what we call `small' codes which, as $G \to 0$, describe only perturbative excitations near a given classical solution. Such settings are quite restrictive and, in particular, they prohibit discussion of any modular flow that would change the classical background. As a result, they forbid consideration of modular flows generated by semiclassical bulk states at order-one modular parameters. In contrast, we present a single `large' code for the bulk theory that can accommodate such flows and, in particular, in the $G \to 0$ limit includes superpositions of states associated with distinct classical backgrounds. This large code is assembled from small codes that each satisfy an approximate Faulkner-Lewkowycz-Maldacena formula. In this extended setting we clarify the meaning of the (approximate) JLMS relation between bulk and boundary modular Hamiltonians and quantify its validity in an appropriate class of states.

This work provides an alternative derivation of third order response functions in four wave mixing spectroscopy of multichromophoric macromolecular systems considering only single exciton states. For the case of harmonic oscillator bath linearly and diagonally coupled to exciton states, closed form expressions showing all the explicit time dependences are derived. These expressions can provide more solid physical basis for understanding 2-dimensional electronic spectroscopy signals. For more general cases of system-bath coupling, the quantum master equation (QME) approach is employed for the derivation of multistep time evolution equations for Green function-like operators. Solution of these equations is feasible at the level of 2nd order non-Markovian QME, and the new approach can account for inter-exciton coupling, dephasing, relaxation, and non-Markovian effects in a consistent manner.

Precise gravitational measurements are vital for geophysics and inertial navigation, but current platforms struggle to combine absolute accuracy with high-bandwidth tracking. We address this challenge with a chip-scale superconducting gravimeter that couples a flux-tunable transmon qubit to a high-$Q$ mechanical resonator. We embed the mechanical element inside the qubit's SQUID loop. This allows us to exploit the Josephson potential's nonlinearity, creating a motion-dependent inductance that maps gravitational displacement onto the qubit's geometric phase. Using a stroboscopic measurement protocol, we suppress mechanical decoherence at revival times. This yields a predicted sensitivity of $10^2\,\mathrm{nGal}/\sqrt{\mathrm{Hz}}$, approaching the performance of atomic sensors but with kilohertz-rate sampling. With electrical {in situ} tunability and SI traceability via microwave spectroscopy, this architecture offers a practical route to high-speed, quantum-limited on-chip gravimetry.

We investigate the topological entanglement entropy of quantum states arising in the context of three-dimensional Chern-Simons theory with compact gauge group $G$ and Chern-Simons level $k$. We focus on the quantum states associated with the $T_{dm,dn}$ torus link complements, which is a $d$-party pure quantum state, and analyze its large-party limit, i.e., $d\to \infty$ limit. We show that the entanglement measures in this limit will receive contributions only from the Abelian anyons, and non-Abelian sectors are suppressed in the large-party limit. Consequently, the large-party limiting value of the entanglement entropy has an upper bound of $\ln |Z_G|$, where $|Z_G|$ is the order of the center of the group $G$. As an explicit example, we perform quantitative analysis for the simplest case of the SU(2) group and $T_{d,dn}$ torus link to obtain the large-party limit of the entanglement entropy. We further investigate the semiclassical ($k \to \infty$) limit of the entropies after taking the large-party limit for this particular example.

These lectures advocate the idea that quantum entanglement provides a unifying foundation for both statistical physics and high-energy interactions. I argue that, at sufficiently long times or high energies, most quantum systems approach a Maximal Entanglement Limit (MEL) in which phases of quantum states become unobservable, reduced density matrices acquire a thermal form, and probabilistic descriptions emerge without invoking ergodicity or classical randomness. Within this framework, the emergence of probabilistic parton model, thermalization in the break-up of confining strings and in high-energy collisions, and the universal small $x$ behavior of structure functions arise as direct consequences of entanglement and geometry of high-dimensional Hilbert space.

This work examines $Δ_T$ noise in two-terminal hybrid nanostructures featuring a quantum point contact (QPC), realized either between two normal metals (NQN) or between a normal metal and a superconductor (NQS). The inclusion of a QPC breaks electron-hole (e-h) symmetry, leading to a finite thermovoltage. In contrast, earlier studies on hybrid junctions incorporating insulating barriers, as e-h symmetry is preserved, have vanishing thermovoltage, and consequently, $Δ_T$ noise is calculated at zero thermovoltage. In our setup, the broken e-h symmetry allows for a finite thermovoltage, at which we compute the corresponding $Δ_T$ noise. Unlike earlier studies restricted by e-h symmetry and vanishing thermovoltage, our work establishes a self-consistent framework in mesoscopic hybrid junctions, revealing how Andreev reflection fundamentally reshapes $Δ_T$ noise once e-h symmetry is broken. This broad access to charge fluctuation signatures provides a more comprehensive understanding of non-equilibrium transport in linear response. To our knowledge, this work provides the first self-consistent analysis of $Δ_T$ noise in superconducting hybrid junctions where e-h symmetry is broken, explicitly revealing how Andreev reflection modifies $Δ_T$ noise beyond the symmetry-protected zero-thermovoltage regime.

Entanglement distillation and entanglement cost are fundamental tasks in quantum entanglement theory. This work studies both in the probabilistic setting and focuses on the asymptotic error exponent of probabilistic entanglement distillation when the operational model is $δ$-approximately nonentangling(ANE) and $δ$-approximately dually nonentangling(ADNE) quantum instruments. While recent progress has clarified limitations of probabilistic transformations in general resource theories, an analytic formula for the error exponent of probabilistic entanglement distillation under approximately (dually) nonentangling operations has remained unavailable. Building on the framework of postselected quantum hypothesis testing, we establish a direct connection between probabilistic distillation and postselected hypothesis testing against the set of separable states. In particular, we derive an analytical characterization of the distillation error exponent under ANE. Besides, we relate the exponent to postselected hypothesis testing with measurements restricted to be separable. We further investigate probabilistic entanglement dilution and establish a relation between probabilistic entanglement costs under approximately nonentangling and approximately dually nonentangling instruments, together with a bound on the probabilistic entanglement cost under nonentangling instruments

Composition is a cornerstone of classical differential privacy, enabling strong end-to-end guarantees for complex algorithms through composition theorems (e.g., basic and advanced). In the quantum setting, however, privacy is defined operationally against arbitrary measurements, and classical composition arguments based on scalar privacy-loss random variables no longer apply. As a result, it has remained unclear when meaningful composition guarantees can be obtained for quantum differential privacy (QDP). In this work, we clarify both the limitations and possibilities of composition in the quantum setting. We first show that classical-style composition fails in full generality for POVM-based approximate QDP: even quantum channels that are individually perfectly private can completely lose privacy when combined through correlated joint implementations. We then identify a setting in which clean composition guarantees can be restored. For tensor-product channels acting on product neighboring inputs, we introduce a quantum moments accountant based on an operator-valued notion of privacy loss and a matrix moment-generating function. Although the resulting Rényi-type divergence does not satisfy a data-processing inequality, we prove that controlling its moments suffices to bound measured Rényi divergence, yielding operational privacy guarantees against arbitrary measurements. This leads to advanced-composition-style bounds with the same leading-order behavior as in the classical theory. Our results demonstrate that meaningful composition theorems for quantum differential privacy require carefully articulated structural assumptions on channels, inputs, and adversarial measurements, and provide a principled framework for understanding which classical ideas do and do not extend to the quantum setting.

The Quantum Approximate Optimization Algorithm (QAOA) is extensively benchmarked on synthetic random instances such as MaxCut, TSP, and SAT problems, but these lack semantic structure and human interpretability, offering limited insight into performance on real-world problems with meaningful constraints. We introduce Quantum King-Ring Domination (QKRD), a NISQ-scale benchmark derived from chess tactical positions that provides 5,000 structured instances with one-hot constraints, spatial locality, and 10--40 qubit scale. The benchmark pairs human-interpretable coverage metrics with intrinsic validation against classical heuristics, enabling algorithmic conclusions without external oracles. Using QKRD, we systematically evaluate QAOA design choices and find that constraint-preserving mixers (XY, domain-wall) converge approximately 13 steps faster than standard mixers (p<10^{-7}, d\approx0.5) while eliminating penalty tuning, warm-start strategies reduce convergence by 45 steps (p<10^{-127}, d=3.35) with energy improvements exceeding d=8, and Conditional Value-at-Risk (CVaR) optimization yields an informative negative result with worse energy (p<10^{-40}, d=1.21) and no coverage benefit. Intrinsic validation shows QAOA outperforms greedy heuristics by 12.6\% and random selection by 80.1\%. Our results demonstrate that structured benchmarks reveal advantages of problem-informed QAOA techniques obscured in random instances. We release all code, data, and experimental artifacts for reproducible NISQ algorithm research.

A quantum model exhibits Hilbert space fragmentation (HSF) if its Hilbert space decomposes into exponentially many dynamically disconnected subspaces, known as Krylov subspaces. A model may however have different HSFs depending on the method for identifying them. Here we establish a connection between two vastly distinct methods recently proposed for identifying HSF: the commutant algebra (CA) method and integer characteristic polynomial factorization (ICPF) method. For a Hamiltonian consisting of operators admitting rational number matrix representations, we prove a theorem that, if its center of commutant algebra have all eigenvalues being rational, the HSF from the ICPF method must be equal to or finer than that from the CA method. We show that this condition is satisfied by most known models exhibiting HSF, for which we demonstrate the validity of our theorem. We further discuss representative models for which ICPF and CA methods yield different HSFs. Our results may facilitate the exploration of a unified definition of HSF.

Recent advances in quantum simulators allow direct experimental access to the ensemble of pure states generated by measuring part of an isolated quantum many-body system. These projected ensembles encode fine-grained information beyond thermal expectation values and provide a new window into quantum thermalization. In chaotic dynamics, projected ensembles exhibit universal statistics, a phenomenon known as deep thermalization. While infinite-temperature systems generate Haar-random ensembles, realistic physical constraints such as finite temperature or conservation laws require a more general framework. It has been proposed that deep thermalization is governed in general by the emergence of Scrooge ensembles, maximally entropic distributions of pure states consistent with the underlying constraints. Here we provide rigorous arguments supporting this proposal. To characterize this universal behavior, we invoke Scrooge $k$-designs, which approximate Scrooge ensembles, and identify three physically distinct mechanisms for their emergence. First, global Scrooge designs can arise from long-time chaotic unitary dynamics alone, without the need for measurements. Second, if the global state is highly scrambled, a local Scrooge design is induced when the complementary subsystem is measured. Third, a local Scrooge ensemble arises from an arbitrary entangled state when the complementary system is measured in a highly scrambled basis. Numerical simulations across a range of many-body systems identify coherence, entanglement, non-stabilizerness, and information scrambling as essential resources for the emergence of Scrooge-like behavior. Taken together, our results establish a unified theoretical framework for the emergence of maximally entropic, information-stingy randomness in quantum many-body systems.

Quasiprobability distributions capture aspects of quantum dynamics that have no classical counterpart, yet the dynamical emergence of their negativity in many-body systems remains largely unexplored. We introduce the \emph{first-time negativity} (FTN) of the Margenau-Hill quasiprobability as a dynamical indicator of when local measurement sequences in an interacting quantum system begin to exhibit genuinely nonclassical behavior. Using the Ising chain, we show that FTN discriminates clearly between interaction-dominated and field-dominated regimes, is systematically reshaped by temperature, and responds sensitively to the breaking of integrability. When measurements are performed on different sites, FTN reveals a characteristic spatio-temporal structure that reflects the finite-time spreading of operator incompatibility across the lattice. We further compare the numerical onset of negativity with a recently proposed quantum speed limit (QSL) for quasiprobabilities, which provides a geometric benchmark for the observed dynamics. Our results identify FTN as a practical and experimentally accessible probe of real-time quantum coherence and contextuality, directly suited to current platforms capable of sequential weak and strong measurements.

Current and near-term quantum hardware is constrained by limited qubit counts, circuit depth, and the high cost of repeated measurements. We address these challenges for solid state Hamiltonians by introducing a logarithmic-qubit encoding that maps a system with $N$ physical sites onto only $\lceil \log_2 N \rceil$ qubits while maintaining a clear correspondence with the underlying physical model. Within this reduced register, we construct a compatible variational circuit and a Gray-code-inspired measurement strategy whose number of global settings grows only logarithmically with system size. To quantify the overall hardware load, we introduce a volumetric efficiency metric that combines the number of qubit, circuit depth, and the number of measurement settings into a single measure, expressing the overall computation costs. Using this metric, we show that the total space-time-sampling volume required in a variational loop can be reduced dramatically from $N^2$ to $(logN)^3$ for hardware efficient ansatz, allowing an exponential reduction in time and size of the quantum hardware. These results demonstrate that large, structured solid-state Hamiltonians can be simulated on substantially smaller quantum registers with controlled sampling overhead and manageable circuit complexity, extending the reach of variational quantum algorithms on near-term devices.

We study Anderson localisation on high-dimensional graphs with spatial structure induced by long-ranged but distance-dependent hopping. To this end, we introduce a class of models that interpolate between the short-range Anderson model on a random regular graph and fully connected models with statistically uniform hopping, by embedding a random regular graph into a complete graph and allowing hopping amplitudes to decay exponentially with graph distance. The competition between the exponentially growing number of neighbours with graph distance and the exponentially decaying hopping amplitude positions our models effectively as power-law hopping generalisation of the Anderson model on random regular graphs. Using a combination of numerical exact diagonalisation and analytical renormalised perturbation theory, we establish the resulting localisation phase diagram emerging from the interplay of the lengthscale associated to the hopping range and the onsite disorder strength. We find that increasing the hopping range shifts the localisation transition to stronger disorder, and that beyond a critical range the localised phase ceases to exist even at arbitrarily strong disorder. Our results indicate a direct Anderson transition between delocalised and localised phases, with no evidence for an intervening multifractal phase, for both deterministic and random hopping models. A scaling analysis based on inverse participation ratios reveals behaviour consistent with a Kosterlitz-Thouless-like transition with two-parameter scaling, in line with Anderson transitions on high-dimensional graphs. We also observe distinct critical behaviour in average and typical correlation functions, reflecting the different scaling properties of generalised inverse participation ratios.

The second law of thermodynamics dictates that heat flows spontaneously from a high-temperature entity to a lower-temperature one. Yet, recent advances have demonstrated that quantum correlations between a system and its thermal environment can induce a reversal of heat flow, challenging classical thermodynamic expectations. Here, we experimentally demonstrate that internal quantum coherence in a multipartite spin system can also reverse heat flow, without relying on initial correlations with the environment. Under the collision model with cascade interaction, we verify that both the strength and the phase of the coherence term determine the direction and magnitude of energy transfer. These results enable precise control of heat flow using only local quantum properties.

Frequency references based on solid state spins promise simplicity, compactness, robustness, multifunctionality, ease of integration, and high densities of emitters. Nitrogen-vacancy (NV) centers in diamond are a natural candidate, but the electronic zero-field splitting exhibits a large fractional temperature dependence, which has precluded its use as a stable clock transition. Here we show that this limitation can be overcome by forming a composite frequency reference that combines measurements of the electronic splitting D with the nuclear quadrupole splitting of the $^{14}$N nuclear spin intrinsic to the NV center. We further benchmark this composite approach against alternative strategies for mitigating temperature sensitivity. By implementing a specially designed pulse sequence with an eight-phase control scheme that suppresses pulse imperfections, we interleave measurements of D and Q in a high-density NV ensemble and demonstrate a temperature-compensated composite frequency reference. The stability of this composite diamond clock is characterized over a 10-day period at room temperature through a comparison to a Rb vapor-cell clock, yielding a fractional instability below $5 \times 10^{-9}$ for an averaging time of $τ= 200$ s and below $1 \times 10^{-8}$ at $τ= 2 \times 10^5$ s, corresponding to measured improvements by a factor of 4 and 200, respectively, over a clock based purely on the single frequency D for the same periods. By characterizing the residual sensitivity to magnetic fields, optical power, and radio-frequency drive amplitudes, we find that temperature is no longer the dominant source of instability. These results establish complementary electron- and nuclear-spin transitions in diamond as a viable route to thermally robust frequency metrology, providing a pathway toward compact, multifunctional solid-state clocks and quantum sensors.

This is an updated version of my PhD thesis, defended at the University of Waterloo on the 2nd of April 2025, uploaded to the ArXiv with the goal of reaching a wider audience. The thesis is divided into 5 chapters, respectively containing (I) a brief introduction to local quantum field theory (QFT), (II) a description of local probes in QFT, (III) a discussion of entanglement in QFT and how to probe it, (IV) a description of the regimes where QFT interactions can be approximated by direct interactions, and (V) a discussion the information about the geometry of spacetime contained in quantum fields. The partial goal of this thesis is to serve as a guide for students aiming to tackle these different research programs. If the reader is interested in pursuing one or more research projects detailed here, they are encouraged to contact me for collaboration in these topics.

On physical grounds, one expects locally interacting quantum many-body systems to feature a finite group velocity. This intuition is rigorously underpinned by Lieb-Robinson bounds that state that locally interacting Hamiltonians with finite-dimensional constituents on suitably regular lattices always exhibit such a finite group velocity. This also implies that causality is always respected by the dynamics of quantum lattice models. It had been a long-standing open question whether interacting bosonic systems also feature finite speeds of sound in information and particle propagation, which was only recently resolved. This work proves a strikingly simple such bound for particle propagation - shown in literally a few elementary, yet not straightforward, lines - for generalized Bose-Hubbard models defined on general lattices, proving that appropriately locally perturbed stationary states feature a finite speed of sound in particle numbers.

Superconducting standing$-$wave parametric amplifiers are crucial for the readout of microwave quantum devices. Despite significant improvements in recent years, the need to operate near an instability point imposes a fundamental constraint: the instantaneous bandwidth decreases with increasing amplifier gain. Here we show that it is possible to obtain parametric amplification without instability by using two simultaneous drives that activate phase-preserving gain and frequency conversion. Realized in a granular aluminum dimer with Kerr nonlinearity, our method demonstrates a sixfold bandwidth increase at 20 dB gain, surpasses the conventional gain$-$bandwidth scaling up to 25 dB, and remains near the quantum limit.

This article provides a comprehensive review of the critical role of detection efficiency in demonstrating non-classicality across various device-independent and semi-device-independent scenarios. The central focus is the detection loophole, a challenge in which imperfect detectors can allow classical hidden variable models to mimic quantum correlations, thus masking genuine non-classicality. As a review, the article revisits the paradigmatic Bell scenario, detailing the efficiency requirements for the CHSH inequality, such as the 2/3 threshold for symmetric efficiencies, and traces the historical trajectory toward the first loophole-free tests. The analysis extends to other causal structures to explore how efficiency requirements are affected in different contexts. These include the instrumental scenario, which for binary variables has recently been shown to follow the same inefficiency bounds as the bipartite dichotomic Bell scenario; the prepare-and-measure scenario, where inefficiencies impact the certification of a quantum system's dimension and create security breaches in protocols such as Quantum Key Distribution (QKD); and the bilocality scenario, which exemplifies how employing multiple independent sources can significantly relax the required efficiencies to certify non-classical correlations.

As quantum dot (QD)-based spin qubits advance toward larger, more complex device architectures, rapid, automated device characterization and data analysis tools become critical. The orientation and spacing of transition lines in a charge stability diagram (CSD) contain a fingerprint of a QD device's capacitive environment, making these measurements useful tools for device characterization. However, manually interpreting these features is time-consuming, error-prone, and impractical at scale. Here, we present an automated protocol for extracting underlying capacitive properties from CSDs. Our method integrates machine learning, image processing, and object detection to identify and track charge transitions across large datasets without manual labeling. We demonstrate this method using experimentally measured data from a strained-germanium single-quantum-well (planar) and a strained-germanium double-quantum-well (bilayer) QD device. Unlike for planar QD devices, CSDs in bilayer germanium heterostructure exhibit a larger set of transitions, including interlayer tunneling and distinct loading lines for the vertically stacked QDs, making them a powerful testbed for automation methods. By analyzing the properties of many CSDs, we can statistically estimate physically relevant quantities, like relative lever arms and capacitive couplings. Thus, our protocol enables rapid extraction of useful, nontrivial information about QD devices.

We study a periodically driven macrospin system with anisotropic long-range interactions and collective dissipation, described by a Lindblad master equation. In the thermodynamic limit ($N\to\infty$), a mean-field treatment yields classical equations of motion, whose dynamics are characterized via the maximal Lyapunov exponent (MLE). Focusing on the thermodynamic limit, we map out chaotic, quasiperiodic, and periodic phases via bifurcation diagrams, MLEs, and Fourier spectra of evolved observables, identifying classic period-doubling bifurcations and fractal boundaries in the regions of attractors. Finite-size quantum simulations in the Dicke basis reveal that while both quantum and classical systems exhibit diverse dynamical phases, finite-size effects suppress some behaviors present in the thermodynamic limit. The sign of $λ_{\mathrm{max}}$ serves as a key indicator of convergence between quantum and classical dynamics, which agree over timescales up to the Lyapunov time. Analysis of the density matrix shows that convergence occurs only when its nonzero elements are sharply localized. However, the nonconvergence does not imply a fundamental difference between quantum and classical dynamics: in chaotic regimes, although the evolution orbits of quantum and classical systems show significant differences, quantum evolution becomes mixed and diffusively explores the Hilbert space, signaling quantum chaos, which can be confirmed by the delocalized nature of the density matrix.

Topological quantum field theory (TQFT) provides a unifying framework for describing topological phases of matter and for constructing quantum error-correcting codes, playing a central role across high-energy physics, condensed matter, and quantum information. A central challenge is to formulate topological order on the lattice and to extract the properties of topological excitations from microscopic Hamiltonians. In this work, we construct new classes of lattice gauge theories as Pauli stabilizer models, realizing a wide range of TQFTs in general spacetime dimensions. We develop a lattice description of the resulting extended excitations and systematically determine their generalized statistics. Our main example is the $(4+1)$D \emph{fermionic-loop toric code}, obtained by condensing the $e^2 m^2$-loop in the $(4+1)$D $\mathbb{Z}_4$ toric code. We show that the loop excitation exhibits fermionic loop statistics: the 24-step loop-flipping process yields a phase of $-1$. Our Pauli stabilizer models realize all twisted 2-form gauge theories in $(4+1)$D, the higher-form Dijkgraaf-Witten TQFT classified by $H^{5}(B^{2}G, U(1))$. % Beyond $(4+1)$D, the fermionic-loop toric codes form a family of $\mathbb{Z}_2$ topological orders in arbitrary dimensions featuring fermionic loop excitations, realized as explicit Pauli stabilizer codes using $\mathbb{Z}_4$ qudits. % Finally, we develop a Pauli-based framework that defines generalized statistics for extended excitations in any dimension, yielding computable lattice unitary processes to detect nontrivial generalized statistics. For example, we propose anyonic membrane statistics in $(6+1)$D, as well as fermionic membrane and volume statistics in arbitrary dimensions. We construct new families of $\mathbb{Z}_2$ topological orders: the \emph{fermionic-membrane toric code} and the \emph{fermionic-volume toric code}.

The emergence of statistical mechanics from quantum dynamics is a central problem in quantum many-body physics. Deriving observables aligned with the prediction of the canonical ensemble for a quantum system relies on the presence of a bath provided either as an external environment or as a larger part of a closed system. We demonstrate that thermal (canonical) observables for a whole closed quantum system of finite size can arise in the absence of a bath. These thermal observables stem from classical averaging over randomized unitary evolutions for a few-body system. The temperature in the canonical ensemble appears as a global constraint on the total energy of the system, determined by the choice of the initial state. From averaging randomized evolutions, we derive spin-spin correlation functions for a finite spin chain and show that they exhibit a temperature-dependent finite correlation length, in agreement with the prediction of the canonical ensemble. This establishes a method for computing thermal observables in a closed, finite-size system from real-time propagation without a bath. An implementation of this thermalization approach on a quantum computer can be utilized for thermal state preparation.

Randomness generation through quantum-chaotic evolution underpins foundational questions in statistical mechanics and applications across quantum information science, including benchmarking, tomography, metrology, and demonstrations of quantum computational advantage. While statistical mechanics successfully captures the temporal averages of local observables, understanding randomness at the level of higher statistical moments remains a daunting challenge, with analytic progress largely confined to random quantum circuit models or fine-tuned systems exhibiting space-time duality. Here we study how much randomness can be dynamically generated by generic quantum-chaotic evolution under physical, non-random Hamiltonians. Combining theoretical insights with numerical simulations, we show that for broad classes of initially unentangled states, the dynamics become effectively Haar-random well before the system can ergodically explore the physically accessible Hilbert space. Both local and highly nonlocal observables, including entanglement measures, equilibrate to their Haar expectation values and fluctuations on polynomial timescales with remarkably high numerical precision, and with the fastest randomization occurring in regions of parameter space previously identified as maximally chaotic. Interestingly, this effective randomization can occur on timescales linear in system size, suggesting that the sub-ballistic growth of Renyi entropies typically observed in systems with conservation laws can be bypassed in non-random Hamiltonians with an appropriate choice of initial conditions.

Tomographic measurements are the standard tool for characterizing quantum states, yet they are usually regarded only as means for state reconstruction or fidelity measurement. Here, we show that the same Pauli-basis measurements (X, Y, Z) can be directly employed for the certification of nonlocality at no additional experimental cost. Our framework allows any tomographic data - including archival datasets -- to be reinterpreted in terms of fundamental nonlocality tests. We introduce a generic, constructive method to generate tailored Bell inequalities and showcase their applicability to certify the non-locality of states in realistic experimental scenarios. Recognizing the stabilizer nature of the considered operators, we analyze our inequalities in the context of witnessing quantum magic - a crucial resource for quantum computing. Our approach requires Pauli measurements only and tests the quantum magic solely through the resources present in the state. Our results establish a universal standard that unifies state tomography with nonlocality certification and its application to quantum magic witnessing, thereby streamlining both fundamental studies and practical applications.

Symmetry-protected topological (SPT) phases in interacting bosonic systems have been extensively studied, yet most realizations rely on fine-tuned interactions or enlarged symmetries. Here we show that a qualitatively different mechanism--parity order coupled to bond dimerization--acts as a fundamental driver of bosonic topology. Using density matrix renormalization group simulations, we identify two distinct topological phases absent in the purely dimerized model: an SPT phase at half filling stabilized by positive parity coupling, and a topological phase at unit filling stabilized by negative coupling that can be adiabatically connected to a trivial phase without breaking any symmetry. Our results establish parity order as a new organizing principle for correlation-driven bosonic topology.

The adaptive derivative-assembled problem-tailored variational quantum eigensolver (ADAPT-VQE) provides a promising approach for simulating highly correlated quantum systems on quantum devices, as it strikes a balance between hardware efficiency, trainability, and accuracy. Although ADAPT-VQE avoids many of the shortcomings of other VQEs, it is sometimes hindered by a phenomenon known as gradient troughs. This refers to a non-monotonic convergence of the gradients, which may become very small even though the minimum energy has not been reached. This results in difficulties finding the right operators to add to the ansatz, due to the limited number of shots and statistical uncertainties, leading to stagnation in the circuit structure optimization. In this paper, we propose ways to detect and mitigate this phenomenon. Leveraging the non-commutative algebra of the ansatz, we develop heuristics for determining where to insert new operators into the circuit. We find that gradient troughs are more likely to arise when the same locations are used repeatedly for new operator insertions. Our novel protocols, which add new operators in different ansatz positions, allow us to escape gradient troughs and thereby lower the measurement cost of the algorithm. This approach achieves an effective balance between cost and efficiency, leading to faster convergence without compromising the low circuit depth and gate count of ADAPT-VQE.

The continuous matrix product state (cMPS) ansatz is a promising numerical tool for studying quantum many-body systems in continuous space. Although it provides a clean framework that allows one to directly simulate continuous systems, the optimization of cMPS is known to be a very challenging task, especially in the case of multi-component systems. In this work, we have developed an improved optimization scheme for multi-component cMPS that enables simulations of bosonic quantum mixtures with substantially larger bond dimensions than previous works. We benchmark our method on the two-component Lieb-Liniger model, obtaining numerical results that agree well with analytical predictions. Our work paves the way for further numerical studies of quantum mixture systems using the cMPS ansatz.

A parity-time (PT) transition is a spectral transition characteristic of non-Hermitian generators; it typically occurs at an exceptional point, where multiple eigenvectors coalesce. The concept of a PT transition has been extended to Markovian open quantum systems, which are described by the GKSL equation. Interestingly, the PT transition in many-body Markovian open quantum systems, the so-called \textit{Lindbladian PT (L-PT) phase transition}, is closely related to two classes of exotic nonequilibrium many-body phenomena: \textit{continuous-time crystals} and \textit{non-reciprocal phase transitions}. In this review, we describe the recent advances in the study of L-PT phase transitions. First, we define PT symmetry in three distinct contexts: non-Hermitian systems, nonlinear dynamical systems, and Markovian open quantum systems, highlighting the interconnections between these frameworks. Second, we develop mean-field theories of L-PT phase transitions for collective-spin systems and for bipartite bosonic systems with particle-number conservation. Within these classes of models, we show that L-PT symmetry can induce a breaking of continuous time-translation symmetry down to a discrete one, leading to persistent periodic dynamics. We further demonstrate that the L-PT phase transition point is typically \textit{a critical exceptional point}, where multiple collective excitation modes with zero excitation spectrum coalesce. These findings establish an explicit connection to continuous-time crystals and non-reciprocal phase transitions. Third, going beyond the mean-field theory, we analyze statistical and quantum properties, such as purity and quantum entanglement indicators of time-independent steady states for several specific models with the L-PT symmetry. Finally, we discuss future research directions for L-PT phase transitions.

This work presents a Python framework named after the General Equation of Quantum Image Encoding (GEQIE). The framework creates the image-encoding state using a unitary gate, which can later be transpiled to target quantum backends. The benchmarking results, simulated with different noise levels, demonstrate the correctness of the already implemented encoding methods and the usability of the framework for more sophisticated research tasks based on quantum image encodings. Additionally, we present a showcase example of Cosmic Web dark-matter density snapshot encoding and high-accuracy retrieval (PCC = 0.995) to demonstrate the extendability of the GEQIE framework to multidimensional data and its applicability to other fields of research.

Thermodynamic uncertainty relations (TURs) bound the precision of currents by entropy production, but quantum transport of noncommuting (non-Abelian) charges challenges standard formulations because different charge components cannot be monitored within a single classical frame. We derive a process-level matrix TUR starting from the operational entropy production $Σ= D(ρ'_{SE}\|ρ'_S\!\otimes\!ρ_E)$. Isolating the experimentally accessible bath divergence $D_{\mathrm{bath}}=D(ρ'_E\|ρ_E)$, we prove a fully nonlinear, saturable lower bound valid for arbitrary current vectors $Δq$: $D_{\mathrm{bath}} \ge B(Δq,V,V')$, where the bound depends only on the transported-charge signal $Δq$ and the pre/post collision covariance matrices $V$ and $V'$. In the small-fluctuation regime $D_{\mathrm{bath}}\geq\frac12\,Δq^{\mathsf T}V^{-1}Δq+O(\|Δq\|^4)$, while beyond linear response it remains accurate. Numerical strong-coupling qubit collisions illustrate the bound and demonstrate near-saturation across broad parameter ranges using only local measurements on the bath probe.

Intracavity absorption spectroscopy (ICAS) is a well-established technique for detecting weak absorption signals with ultrahigh sensitivity. Here, we extend this concept to magnetometry using nitrogen-vacancy (NV) centers in diamond. We introduce laser intracavity absorption magnetometry (LICAM), a concept that is in principle applicable to a broader class of optical quantum sensors, including optically pumped magnetometers. Using an electrically driven, edge-emitting diode laser that operates self-sustainably, we show that LICAM enables highly sensitive magnetometers operating under ambient conditions. Near the lasing threshold, we achieve a 475-fold enhancement in optical contrast and a 180-fold improvement in magnetic sensitivity compared with a conventional single-pass geometry. The experimental results are accurately described by a rate-equation model for single-mode diode lasers. From our measurements, we determine a projected shot-noise-limited sensitivity in the $\mathrm{pT}\,\mathrm{Hz}^{-1/2}$ range and show that, with realistic device improvements, sensitivities down to the $\mathrm{fT}\,\mathrm{Hz}^{-1/2}$ scale are attainable.

Uncertainty is a fundamental and important concept in quantum mechanics. Recent works have revealed both the product and sum forms of uncertainty constants for three observables. Such a result is intimately to the properties of Pauli operators. In this work, using the technique in matrix theory, we give an alternative proof for the case of three observables, and generalize the result to the case of four measurements. Comparing with the original proof, such a derivation is simplified. Moreover, the discussions can deal with the summation form of uncertainty relation for two, three and four observables in a unified way.

We extend the Worldline Monte Carlo approach to computationally simulating the Feynman path integral of non-relativistic multi-particle quantum-mechanical systems. We show how to generate an arbitrary number of worldlines distributed according to the (free) kinetic part of the multi-particle quantum dynamics and how to simulate interactions between worldlines in the ensemble. We test this formalism with two- and three-particle quantum mechanical systems, with both long range Coulomb-like interactions between the particles and external fields acting separately on the particles, in various spatial dimensionality. We extract accurate estimations of the ground state energy of these systems using the late-time behaviour of the propagator, validating our approach with numerically exact solutions obtained via straightforward diagonalisation of the Hamiltonian. Systematic benchmarking of the new approach, presented here for the first time, shows that the computational complexity of Wordline Monte Carlo scales more favourably with respect to standard numerical alternatives. The method, which is general, numerically exact, and computationally not intensive, can easily be generalised to relativistic systems.

We investigate the quantum correlations in an axially symmetric hybrid qubit-qutrit system subjected to different noisy environments. We first introduce a physical model and analyze its Hamiltonian structure, emphasizing the role of hybrid dimensionality and axial symmetry. The effects of decoherence are then examined under two local noise mechanisms, namely dephasing and phase-flip channels, acting on the qubit and qutrit subsystems in both symmetric and asymmetric configurations. Quantum correlations are quantified using negativity to capture entanglement and quantum discord based on linear entropy to characterize more general nonclassical correlations. Our results show that both thermal fluctuations and phase noise lead to a monotonic degradation of quantum correlations, with increasing temperature accelerating coherence loss and inducing entanglement sudden death at finite temperatures. While negativity vanishes abruptly under sufficiently strong noise, quantum discord persists beyond the entanglement threshold, revealing residual quantum correlations in mixed states. We further demonstrate that asymmetric noise configurations significantly enhance the robustness of both entanglement and discord by partially shielding coherence in the less affected subsystem. A comparative analysis reveals that phase-flip noise is more destructive than pure dephasing, leading to faster suppression of quantum correlations.

Recent advances in time-resolved cathodoluminescence have enabled ultrafast studies of single emitters in quantum materials with femtosecond temporal resolution. Here, we develop a quantum theory modeling the dynamics of free electrons interacting with quantum emitters in arbitrary initial states. Our analysis reveals that a free electron can induce transient coherent oscillations in the populations when the system is initially prepared in a coherent superposition of its states. Moreover, the electron energy spectrum exhibits a clear signature of the quantum coherence and sensitivity to the transition frequency of the emitter. These coherence effects manifest themselves as oscillations in the zero-loss peak of the spectral energy-loss probability. Our findings pave the way for characterization of quantum-coherent dynamics of individual quantum emitters by electron-probes.

Spatially entangled photon pairs (biphotons) generated by spontaneous parametric down-conversion offer unique opportunities for quantum imaging, but image-plane biphoton correlations are difficult to observe with camera-based detectors. Previous camera-based biphoton imaging experiments have relied on photon-counting detection, which necessitates operation deep in the photon-sparse regime and requires extremely low dark rates. Here, we demonstrate the detection of spatial biphoton joint probability distributions in both the image plane and the pupil plane (also termed "near-field plane" and "far-field plane" respectively) using a conventional scientific CMOS camera operated in linear mode. We work at mesoscopic intensity levels, corresponding to a photon flux approximately four orders of magnitude higher than typical photon-counting approaches. From the measured image- and pupil plane correlations, we observe position and momentum correlations consistent with an EPR-type entanglement witness. A tailored correlation analysis suited for image plane imaging suppresses detector artifacts and intensity fluctuations, enabling acquisition with significantly fewer frames. Our results demonstrate that spatially entangled-light imaging can be performed efficiently with standard imaging hardware, extending quantum imaging techniques beyond the photon-counting regime.

Pure-state manifestations of geometric phase are well established and have found applications across essentially all branches of physics, yet their generalization to mixed-state regimes remains largely unexplored experimentally. The Uhlmann geometric phase offers a natural extension of pure-state paradigms and can exhibit a topological character. However, observation of this invariant is impeded by the incompatibility between Uhlmann parallel transport and Hamiltonian dynamics, as well as the difficulty of preparing topologically nontrivial mixed states. To address this challenge, we report an experimentally accessible protocol for directly measuring the mixed-state topological invariant. By engineering controlled nonunitary dynamics in a photonic quantum walk, we prepare topologically nontrivial mixed states from a trivial initial state. Furthermore, by machine-learning the full density matrix in momentum space, we directly extract the quantized geometric phase of the nontrivial mixed states. These results highlight a geometric phase framework that naturally extends to open quantum systems both in and out of thermal equilibrium.

We investigate the quantum Mpemba effect in a dissipative Dicke model, which consists of a spin-1/2 ensemble coupled to a bosonic mode, which in turn is coupled to a bosonic bath. We derive a sufficient criterion for occurrence of the quantum Mpemba effect, characterized by quantum coherence, in this model. We introduce the phenomenon of role reversal in the Mpemba effect, wherein changes in the system parameters invert the relaxation ordering of a given pair of initial states that exhibit the Mpemba effect, causing the faster-relaxing state to become slower and vice versa. We find the existence of role reversal in Mpemba effect for this Dicke model using different relaxation measures, including differential quantum coherence and entanglement, and trace distance, between the time-evolved and steady states.

Floquet engineering offers an unparalleled platform for realizing novel non-equilibrium topological phases. However, the unique structure of Floquet systems, which includes multiple quasienergy gaps, poses a significant challenge to classification using conventional analytical methods. We propose a novel unsupervised machine learning framework that employs a kernel defined in momentum-time ($\boldsymbol{k},t$) space, constructed directly from Floquet-Bloch eigenstates. This approach is intrinsically data-driven and requires no prior knowledge of the underlying topological invariants, providing a fundamental advantage over prior methods that rely on abstract concepts like the micromotion operator or homotopic transformations. Crucially, this work successfully reveals the intrinsic topological characteristics encoded within the Floquet eigenstates themselves. We demonstrate that our method robustly and simultaneously identifies the topological invariants associated with both the $0$-gap and the $π$-gap across various symmetry classes (1D AIII, 1D D, and 2D A), establishing a robust methodology for the systematic classification and discovery of complex non-equilibrium topological matter.

We argue that Hopf-algebra deformations of symmetries -- as encountered in non-commutative models of quantum spacetime -- carry an intrinsic content of $operator$ $entanglement$ that is enforced by the coproduct-defined notion of composite generators. As a minimal and exactly solvable example, we analyze the $U_q(\mathfrak{su}(2))$ quantum group and a two-qubit realization obtained from the coproduct of a $q$-deformed single-spin Hamiltonian. Although the deformation is invisible on a single qubit, it resurfaces in the two-qubit sector through the non-cocommutative coproduct, yielding a family of intrinsically nonlocal unitaries. We compute their operator entanglement in closed form and show that, for Haar-uniform product inputs, their entangling power is fully determined by the latter. This provides a concrete mechanism by which non-commutative symmetries enforce a baseline of entanglement at the algebraic level, with implications for information dynamics in quantum-spacetime settings and quantum information processing.

Sampling tasks have been successful in establishing quantum advantages both in theory and experiments. This has fueled the use of quantum computers for generative modeling to create samples following the probability distribution underlying a given dataset. In particular, the potential to build generative models on classically hard distributions would immediately preclude classical simulability, due to theoretical separations. In this work, we study quantum generative models from the perspective of output distributions, showing that models that anticoncentrate are not trainable on average, including those exhibiting quantum advantage. In contrast, models outputting data from sparse distributions can be trained. We consider special cases to enhance trainability, and observe that this opens the path for classical algorithms for surrogate sampling. This observed trade-off is linked to verification of quantum processes. We conclude that quantum advantage can still be found in generative models, although its source must be distinct from anticoncentration.

We construct holonomic quantum gates for qubits that are encoded in the near-degenerate vibrational $E$-doublet of a deformable three-body system. Using Kendall's shape theory, we derive the Wilczek--Zee connection governing adiabatic transport within the $E$-manifold. We show that its restricted holonomy group is $\mathrm{SU}(2)$, implying universal single-qubit control by closed loops in shape space. We provide explicit loops implementing a $π/2$ phase gate and a Hadamard-type gate. For two-qubit operations, we outline how linked holonomic cycles in arrays generate a controlled Chern--Simons phase, enabling an entangling controlled-$X$ (CNOT) gate. We present a Ramsey/echo interferometric protocol that measures the Wilson loop trace of the Wilczek--Zee connection for a control cycle, providing a gauge-invariant signature of the non-Abelian holonomy. As a physically realizable demonstrator, we propose bond-length modulations of a Cs($6s$)--Cs($6s$)--Cs($nd_{3/2}$) Rydberg trimer in optical tweezers and specify operating conditions that suppress leakage out of the $E$-manifold.

We solve the static isoperimetric problem underlying the Mandelstam-Tamm bound. Among one-dimensional confining potentials with a fixed spectral gap, we prove that the harmonic trap is the unique maximizer of the ground-state position variance. As a consequence, we obtain a sharp geometric quantum speed-limit bound on the position-position component of the quantum metric, and we give a necessary-and-sufficient condition for when the bound is saturated. Beyond the exact extremum, we establish quantitative rigidity. We control the Thomas-Reiche-Kuhn spectral tail and provide square-integrable structural stability for potentials that nearly saturate the bound. We further extend the analysis to magnetic settings, deriving a longitudinal necessary-and-sufficient characterization and transverse bounds expressed in terms of guiding-center structure. Finally, we outline applications to bounds on static polarizability, limits on the quantum metric, and benchmarking of trapping potentials.

Double perovskites containing 4d--4f interactions provide a platform to study complex magnetic phenomena in correlated systems. Here, we investigate the magnetic ground state and quasiparticle excitations of the fascinating double perovskite system, Ba$_2$DyRuO$_6$, through Time of flight (TOF) neutron diffraction (TOF), inelastic neutron scattering (INS), and theoretical modelling. The compound Ba$_2$DyRuO$_6$ is reported to exhibit a single magnetic transition, in sharp contrast to most of the other rare-earth (R) members in this family, A$_2$RRuO$_6$ (A = Ca/Sr/Ba), which typically show magnetic ordering of the Ru ions, followed by R-ion ordering. Our neutron diffraction results confirm that long-range antiferromagnetic order emerges at $T_\mathrm{N} \approx 47$~K, primarily driven by 4d--4f Ru$^{5+}$--Dy$^{3+}$ exchange interactions, where both Dy and Ru moments start to order simultaneously. The ordered ground state is a collinear antiferromagnet with Ising character, carrying ordered moments of $μ_{\mathrm{Ru}} = 1.6(1)~μ_\mathrm{B}$ and $μ_{\mathrm{Dy}} = 5.1(1)~μ_\mathrm{B}$ at 1.5~K. Low-temperature INS reveals well-defined magnon excitations below 10~meV. SpinW modelling of the INS spectra evidences complex exchange interactions and the presence of magnetic anisotropy, which governs the Ising ground state and accounts for the observed magnon spectrum. Combined INS and Raman spectroscopy reveal crystal-electric-field (CEF) excitations of Dy$^{3+}$ at 46.5 and 71.8~meV in the paramagnetic region. The observed CEF levels are reproduced by point-charge calculations consistent with the $O_h$ symmetry of Dy$^{3+}$. A complementary machine-learning approach is used to analyse the phonon spectrum and compare with INS data. Together, these results clarify the origin of phonon and magnon excitations and their role in the ground-state magnetism of Ba$_2$DyRuO$_6$.

Quantum annealers can solve QUBO problems efficiently but struggle with continuous optimization tasks like regression due to their discrete nature. We introduce Quadratic Continuous Quantum Optimization (QCQO), an anytime algorithm that approximates solutions to unconstrained quadratic programs via a sequence of QUBO instances. Rather than encoding real variables as binary vectors, QCQO implicitly represents them using continuous QUBO weights and iteratively refines the solution by summing sampled vectors. This allows flexible control over the number of binary variables and adapts well to hardware constraints. We prove convergence properties, introduce a step size adaptation scheme, and validate the method on linear regression. Experiments with simulated and real quantum annealers show that QCQO achieves accurate results with fewer qubits, though convergence slows on noisy hardware. Our approach enables quantum annealing to address a wider class of continuous problems.

Continuous-variable quantum key distribution (CVQKD) features a high key rate and compatibility with classical optical communication. Developing expandable and efficient CVQKD networks will promote the deployment of large-scale quantum communication networks in the future. This paper proposes a CVQKD network based on the entangled states of an optical frequency comb. This scheme generates Einstein-Podolsky-Rosen entangled states with a frequency comb structure through the process of a type-II optical parametric oscillator. By combining with the scheme of entanglement in the middle, a fully connected CVQKD network capable of distributing secret keys simultaneously can be formed. We analyze the security of the system in the asymptotic case. Simulation results show that under commendable controlling of system loss and noise, the proposed scheme is feasible for deploying a short-distance fully connected CVQKD network. Loss will be the main factor limiting the system's performance. The proposed scheme provides new ideas for a multi-user fully connected CVQKD network.

We apply methods of equivariant homotopy theory, which may not previously have found due attention in condensed matter physics, to classify first the fragile/unstable topological phases of 2D crystalline Chern insulator materials, and second the possible topological order of their fractional cousins. We highlight that the phases are given by the equivariant 2-Cohomotopy of the Brillouin torus of crystal momenta (with respect to wallpaper point group actions) -- which, despite the attention devoted to crystalline Chern insulators, seems not to have been considered before. Arguing then that any topological order must be reflected in the adiabatic monodromy of gapped quantum ground states over the covariantized space of these band topologies, we compute the latter in examples where this group is non-abelian, showing that any potential FQAH anyons must be localized in momentum space. We close with an outlook on the relevance for the search for topological quantum computing hardware. Mathematical details are spelled out in a supplement.

These lecture notes discuss applications of atom-light interactions in cavities to quantum metrology, simulation, and computation. A focus is on nonlocally interacting spin systems realized by coupling many atoms to a delocalized mode of light. We will build up from the fundamentals: understanding how a cavity enables light to coherently imprint information on atoms and atoms to imprint information on the light, enabling quantum non-demolition measurements that constitute a powerful means of engineering nonclassical states. By extension, letting the intracavity light act back on the atoms enables coherent photon-mediated interactions. I start by discussing collective spin models, emphasizing applications in entanglement-enhanced metrology, before proceeding to richer many-body physics enabled by incorporating spatiotemporal control or employing multiple cavity modes. I will highlight opportunities for leveraging these tools for quantum simulations inspired by problems in condensed matter and quantum gravity. Along the way, I provide a pedagogical introduction to criteria for strong atom-light coupling, illustrate how the corresponding figure of merit -- the cooperativity -- sets fundamental limits on the coherence of atom-light interactions, and discuss prospects for harnessing high-cooperativity cavity QED in quantum simulation and computation.

Visual word sense disambiguation focuses on polysemous words, where candidate images can be easily confused. Traditional methods use classical probability to calculate the likelihood of an image matching each gloss of the target word, summing these to form a posterior probability. However, due to the challenge of semantic uncertainty, glosses from different sources inevitably carry semantic biases, which can lead to biased disambiguation results. Inspired by quantum superposition in modeling uncertainty, this paper proposes a Quantum Inference Model for Unsupervised Visual Word Sense Disambiguation (Q-VWSD). It encodes multiple glosses of the target word into a superposition state to mitigate semantic biases. Then, the quantum circuit is executed, and the results are observed. By formalizing our method, we find that Q-VWSD is a quantum generalization of the method based on classical probability. Building on this, we further designed a heuristic version of Q-VWSD that can run more efficiently on classical computing. The experiments demonstrate that our method outperforms state-of-the-art classical methods, particularly by effectively leveraging non-specialized glosses from large language models, which further enhances performance. Our approach showcases the potential of quantum machine learning in practical applications and provides a case for leveraging quantum modeling advantages on classical computers while quantum hardware remains immature.

Quantum advantage is widely understood to rely on key quantum resources beyond entanglement, among which nonstabilizerness (quantum ``magic'') plays a central role in enabling universal quantum computation. However, a direct brute-force enumeration of all Pauli strings and the corresponding expectation values from a length-$2^N$ state vector, where $N$ is the system size, yields an overall computational cost scaling as $O(8^N)$, which quickly becomes infeasible as the system size grows. Here we reformulate the second-order stabilizer Rényi entropy in a bitstring language, expose an underlying XOR-convolution structure on $\mathbb Z_2^N$, and reduce the computation to $2^N$ fast Walsh-Hadamard transforms of length, together with pointwise operations, yielding a deterministic and exact XOR fast Walsh-Hadamard transforms algorithm with runtime scaling $O(N4^N)$ and natural parallelism. This algorithm enables high-precision, medium-scale exact calculations for generic state vectors. It provides a practical tool for probing the scaling, phase diagnostics, and dynamical fine structure of quantum magic in many-body systems.

In this paper, we study the momentum distribution of an electron gas in a $3$-dimensional torus. The goal is to compute the occupation number of Fourier modes for some trial state obtained through random phase approximation. We obtain the mean-field analogue of momentum distribution formulas for electron gas in [Daniel and Voskov, Phys. Rev. 120, (1960)] in high density limit and [Lam, Phys. Rev. \textbf{3}, (1971)] at metallic density. Our findings are related to recent results obtained independently by Benedikter, Lill and Naidu, and our analysis applies to a general class of singular potentials rather than just the Coulomb case.

We introduce a trajectory-based decomposition of quantum variances within Bohmian mechanics. By extending the weak actual value to a field on configuration space, we prove, under strong regularity conditions for stationary bound states, that the standard quantum variance splits into two non-negative terms: the ensemble variance of weak actual value and a quantum termarising from phase-amplitude coupling. For momentum, linking variance-level fluctuations to the average quantum potential. The decomposition fails to provide a physical interpretation for spin, reinforcing the Bohmian tenet that only position is fundamental. The work provides a formal tool for analyzing quantum fluctuations and clarifies the interpretative limits of such a trajectory-based approach.

We study the unitary almost Mathieu operator (UAMO), a one-dimensional quasi-periodic unitary operator arising from a two-dimensional discrete-time quantum walk on $\mathbb Z^2$ in a homogeneous magnetic field. In the positive Lyapunov exponent regime $0\le λ_1<λ_2\le 1$, we establish an arithmetic localization statement governed by the frequency exponent $β(ω)$. More precisely, for every irrational $ω$ with $β(ω)<L$, where $L>0$ denotes the Lyapunov exponent, and every non-resonant phase $θ$, we prove Anderson localization, i.e. pure point spectrum with exponentially decaying eigenfunctions. This extends our previous arithmetic localization result for Diophantine frequencies (for which $β(ω)=0$) to a sharp threshold in frequency.

We present a framework to investigate the collective properties of atomic lattices in one, two, and three dimensions. We analyze the single-photon band structure and associated atomic decay rates, revealing a fundamental dependence on dimensionality. One- and two-dimensional arrays are shown to be inherently radiative, exhibiting band gaps and decay rates that oscillate between superradiant and subradiant regimes, as a function of lattice spacing. In contrast, three-dimensional lattices are found to be fundamentally non-radiative due to the inhibition of spontaneous emission, with decay only at discrete Bragg resonances. Furthermore, we demonstrate that this structural difference dictates the system dynamics, which crosses over from dissipative decay in lower dimensions to coherent transport in three dimensions. Our results provide insight into cooperative effects in atomic arrays at the single-photon level.

Using a global rotation by theta about the z-axis in the spin sector of the Jordan-Wigner transformation rotates Pauli matrices X and Y in the x-y-plane, while it adds a global complex phase to fermionic quantum states that have a fixed number of particles. With the right choice of angles, this relates expectation values of Pauli strings containing products of X and Y to different products, which can be employed to reduce the number of measurements needed when simulating fermionic systems on a quantum computer. Here, we derive this symmetry and show how it can be applied to systems in Physics and Chemistry that involve Hamiltonians with only single-particle (hopping) and two-particle (interaction) terms. We also discuss the consequences of this for finding efficient measurement circuits in variational ground state preparation.

Materials with interesting physical properties are often designed based on our understanding of the target physical effects. The physical properties can be either explicitly observed ("apparent") or concealed by the perceived symmetry ("hidden") but still exist. Both are enabled by specific symmetries and induced by certain physical interactions. Using the underlying approach of condensed matter theory of real materials (rather than schematic model Hamiltonians), we discuss apparent and hidden physics in real materials focusing on the properties of spin splitting and spin polarization. Depending on the enabling symmetries and underlying physical interactions, we classify spin effects into four categories with each having two subtypes; representative materials are pointed out. We then discuss the electric tunability and switch of apparent and hidden spin splitting and polarization in antiferromagnets. Finally, we extend "hidden effects" to views that are farsighted in the sense of resolving the correct atomistic and reciprocal symmetry and replaced by the incorrect higher symmetry. This framework could guide and enable systematic discovery of such intriguing effects.

The QAOA has been the subject of intense study over recent years, yet the corresponding Dynamical Lie Algebra (DLA)--a key indicator of the expressivity and trainability of VQAs--remains poorly understood beyond highly symmetric instances. An exponentially scaling DLA dimension is associated with the presence of so-called barren plateaus (BP) in the optimization landscape, which renders training intractable. In this work, we investigate the DLA of QAOA applied to the canonical MaxCut, for both weighted and unweighted graphs. For weighted graphs, we show that when the weights are drawn from a continuous distribution, the DLA dimension grows as $Θ(4^n)$ almost surely for all connected graphs except paths and cycles. In the more common unweighted setting, we show that asymptotically all but an exponentially vanishing fraction of graphs have $Θ(4^n)$ large DLA dimension. The entire simple Lie algebra decomposition of the corresponding DLAs is also identified, from which we prove that the variance of the loss function is $O(1/2^n)$, implying that QAOA on these weighted and unweighted graphs all suffers from BP. Moreover, we give explicit constructions for families of graphs whose DLAs have exponential dimension, including cases whose MaxCut is in $\mathsf P$. Our proof of the unweighted case is based on a number of splitting lemmas and DLA-freeness conditions that allow one to convert prohibitively complicated Lie algebraic problems into amenable graph theoretic problems. These form the basis for a new algorithm that computes such DLAs orders of magnitude faster than previous methods, reducing runtimes from days to seconds on standard hardware. We apply this algorithm to MQLib, a classical MaxCut benchmark suite covering over 3,500 instances with up to 53,130 vertices, and find that, ignoring edge weights, at least 75% of the instances possess a DLA of dimension at least $2^{128}$.

Neural quantum states efficiently represent many-body wavefunctions with neural networks, but the cost of Monte Carlo sampling limits their scaling to large system sizes. Here we address this challenge by combining sparse Boltzmann machine architectures with probabilistic computing hardware. We implement a probabilistic computer on field programmable gate arrays (FPGAs) and use it as a fast sampler for energy-based neural quantum states. For the two-dimensional transverse-field Ising model at criticality, we obtain accurate ground-state energies for lattices up to 80 $\times$ 80 (6400 spins) using a custom multi-FPGA cluster. Furthermore, we introduce a dual-sampling algorithm to train deep Boltzmann machines, replacing intractable marginalization with conditional sampling over auxiliary layers. This enables the training of sparse deep models and improves parameter efficiency relative to shallow networks. Using this algorithm, we train deep Boltzmann machines for a system with 35 $\times$ 35 (1225 spins). Together, these results demonstrate that probabilistic hardware can overcome the sampling bottleneck in variational simulation of quantum many-body systems, opening a path to larger system sizes and deeper variational architectures.

We present experimental evidence of a thermally-driven amplitude-frequency nonlinearity in a thin-film quartz phononic crystal resonator at millikelvin temperatures. The nonlinear response arises from the coupling of the mechanical mode to an ensemble of microscopic two-level system defects driven out of equilibrium by a microwave drive. In contrast to the conventional Duffing oscillator, the observed nonlinearity exhibits a mixed reactive-dissipative character. Notably, the reactive effect can manifest as either a softening or hardening of the mechanical resonance, depending on the ratio of thermal to phonon energy. By combining the standard TLS theory with a thermal conductance model, the measured power-dependent response is quantitatively reproduced and readout-enhanced relaxation damping from off-resonant TLSs is identified as the primary mechanism limiting mechanical coherence. Within this framework, we delineate the conditions under which similar systems will realize this nonlinearity.

Non-Hermitian operators and exceptional points (EPs) are now routinely realized in few-mode systems such as optical resonators and superconducting qubits. However, their foundations in genuine scattering problems with unbounded Hamiltonians remain much less clear. In this work, we address how the geometric phase associated with encircling an EP should be formulated when the underlying eigenstates are quantum resonances within a one-dimensional scattering model. To do this, we employ the complex scaling method, where resonance poles of the S-matrix are realized as discrete eigenvalues of the non-Hermitian dilated Hamiltonian, to construct situations in which resonant and scattering states coalesce into an EP in the complex energy plane, that is, the resonance pole is embedded into the continuum spectrum. We analyze the self-orthogonality in the vicinity of an EP and the Berry phase. Our results provide a bridge between non-Hermitian spectral theory and the traditional theory of quantum resonances.

This study presents an evaluation of derivative-free optimization algorithms for the direct minimization of Hartree-Fock-Roothaan energy functionals involving nonlinear orbital parameters and quantum numbers with noninteger order. The analysis focuses on atomic calculations employing noninteger Slater-type orbitals. Analytic derivatives of the energy functional are not readily available for these orbitals. Four methods are investigated under identical numerical conditions: Powell's conjugate-direction method, the Nelder-Mead simplex algorithm, coordinate-based pattern search, and a model-based algorithm utilizing radial basis functions for surrogate-model construction. Performance benchmarking is first performed using the Powell singular function, a well-established test case exhibiting challenging properties including Hessian singularity at the global minimum. The algorithms are then applied to Hartree-Fock-Roothaan self-consistent-field energy functionals, which define a highly non-convex optimization landscape due to the nonlinear coupling of orbital parameters. Illustrative examples are provided for closed$-$shell atomic configurations, specifically the He, Be isoelectronic series, with calculations performed for energy functionals involving up to eight nonlinear parameters.

Parametrically driven oscillators can emerge as a basis for the next generation of qubits. Classically, these systems exhibit two stable oscillatory states with opposite phases. Upon quantization, these states turn into a pair of closely spaced Floquet states, which can serve as the logical basis for a qubit. However, interaction with the environment induces phase-slip events which set a limit on qubit coherence. Such phase slips persist even at zero temperature due to a mechanism known as quantum activation \cite{QuantumActivation}. In contrast to conventional tunneling, the quantum activation is described by a {\em real-time} instanton trajectory in the complexified phase space of the system. In this work, we show that the phase-slip rate is exponentially sensitive to weak AC perturbations. The spectrum of the system's response -- captured by the so-called logarithmic susceptibility (LS) -- enables a direct observation of characteristic features of real-time instantons. Studying this spectrum suggests new means of efficient qubit control.

We prove that the ``chordality condition'', which was established in arXiv:2412.18018 as a necessary condition for an entropy vector to be realizable by a holographic simple tree graph model, is also sufficient. The proof is constructive, demonstrating that the algorithm introduced in arXiv:2512.18702 for constructing a simple tree graph model realization of a given entropy vector that satisfies this condition always succeeds. We emphasize that these results hold for an arbitrary number of parties, and, given that any entropy vector realizable by a holographic graph model can also be realized, at least approximately, by a stabilizer state, they highlight how techniques originally developed in holography can provide broad insights into entanglement and information theory more generally, and in particular, into the structure of the stabilizer and quantum entropy cones. Moreover, if the strong form of the conjecture from arXiv:2204.00075 holds, namely, if all holographic entropy vectors can be realized by (not necessarily simple) tree graph models, then the result of this work demonstrates that the essential data that encodes the structure of the holographic entropy cone for an arbitrary number of parties, is the set of ``chordal'' extreme rays of the subadditivity cone.

This paper presents novel interpretations to the field of classical signal processing of the Wigner-Ville transform as an information measurement tool. The transform's utility in detecting and localizing information-laden signals amidst noisy and cluttered backgrounds, and further providing measure of their information volumes, are detailed herein using Tsallis' entropy and information and related functionals. Example use cases in radio frequency communications are given, where Wigner-Ville-based detection measures can be seen to provide significant sensitivity advantage, for some shown contexts greater than 15~dB advantage, over energy-based measures and without extensive training routines. Such an advantage is particularly significant for applications which have limitations on observation resources including time/space integration pressures and transient and/or feeble signals, where Wigner-Ville-based methods would improve sensing effectiveness by multiple orders of magnitude. The potential for advancement of several such applications is discussed.

Spin squeezing in collective atomic ensembles enables quantum-enhanced metrology by reducing noise below the standard quantum limit through nonlinear interactions. Extending the one-axis and two-axis twisting paradigms of Kitagawa and Ueda, we introduce a general class of three-axis spin squeezed states within the anisotropic Lipkin-Meshkov-Glick model. The model features direction-dependent quadratic couplings that interpolate between uniaxial and biaxial regimes and can be interpreted as an asymmetric quantum rotor. Using semiclassical dynamics, Majorana representations, and Husimi-Q distributions, we analyze the structure and metrological properties of the resulting states. The three-axis framework reproduces the known N^(-2/3) scaling of one-axis twisting and the Heisenberg-limited N^(-1) scaling of two-axis twisting, while allowing additional tunability and enhanced entanglement generation in low-spin systems. We further show that tuning the anisotropy parameters induces ground-state and excited-state quantum phase transitions, including a second-order transition associated with level clustering and critical dynamics. These results unify spin squeezing, quantum criticality, and rotor analogies, and suggest implementations in Rydberg arrays and cavity-QED platforms for precision sensing and quantum simulation.

We identify quantum geometric bounds for observables in non-Hermitian systems. We find unique bounds on non-Hermitian quantum geometric tensors, generalized two-point response correlators, conductivity tensors, and optical weights. We showcase these findings in topological systems with non-Hermitian Chern numbers. We demonstrate that the non-Hermitian geometric constraints on response functions naturally arise in open quantum systems governed by out-of-equilibrium Lindbladian dynamics. Our findings are relevant to experimental observables and responses under the realistic setups that fall beyond the idealized closed-system descriptions.

Gapless quantum phases can become distinct when internal symmetries are enforced, in analogy with gapped symmetry-protected topological (SPT) phases. However, this distinction does not always lead to protected edge modes, raising the question of how the bulk-boundary correspondence is generalized to gapless cases. We propose that the spatial interface between gapless phases -- rather than their boundaries -- provides a more robust fingerprint. We show that whenever two 1+1d conformal field theories (CFTs) differ in symmetry charge assignments of local operators or twisted sectors, any symmetry-preserving spatial interface between the theories must flow to a non-invertible defect. We illustrate this general result for different versions of the Ising CFT with $\mathbb{Z}_2 \times \mathbb{Z}_2^T$ symmetry, obtaining a complete classification of allowed conformal interfaces. When the Ising CFTs differ by nonlocal operator charges, the interface hosts 0+1d symmetry-breaking phases with finite-size splittings scaling as $1/L^3$, as well as continuous phase transitions between them. For general gapless phases differing by an SPT entangler, the interfaces between them can be mapped to conformal defects with a certain defect 't Hooft anomaly. This classification also gives implications for higher-dimensional examples, including symmetry-enriched variants of the 2+1d Ising CFT. Our results establish a physical indicator for symmetry-enriched criticality through symmetry-protected interfaces, giving a new handle on the interplay between topology and gapless phases.

The study of quantum correlations within relativistic spacetimes, and the consequences of relativistic causality on information processing using such correlations, has gained much attention in recent years. In this paper, we establish a unified framework in the form of operational no-signalling constraints to study both nonlocal and temporal correlations within general relativistic spacetimes. We explore several intriguing consequences arising from our framework. Firstly, we show that the violation of the operational no-signalling constraints in Minkowski spacetime implies either a logical paradox or an operational infringement of Poincaré symmetry. We thereby examine and subvert recent claims in [Phys. Rev. Lett. 129, 110401 (2022)] on the possibility of witnessing operationally detectable causal loops in Minkowski spacetime. Secondly, we explore the possibility of jamming of nonlocal correlations, controverting a recent claim in [Nat. Comm. 16, 269 (2025)] that a physical mechanism for jamming would necessarily lead to superluminal signalling. Finally, we show that in black hole spacetimes certain nonlocal correlations under and across the event horizon can be jammed by any agent without spoiling the operational no-signalling constraints.

We consider minisuperspace models with quadratic kinetic terms, assuming a flat target space and a closed Universe. We show that, upon canonical quantization of the Hamiltonian, only a restricted subset of operator orderings is consistent with the path-integral viewpoint. Remarkably, all consistent orderings are physically equivalent to all orders in $\hbar$. Specifically, each choice of path-integral measure in the definition of the wavefunction path integral uniquely determines an operator ordering and hence a corresponding Wheeler-DeWitt equation. The consistent orderings are in one-to-one correspondence with the Jacobians associated with all field redefinitions of a set of canonical degrees of freedom. For each admissible operator ordering--or equivalently, each path-integral measure--we identify a definite, positive Hilbert-space inner product. All such prescriptions define the same quantum theory, in the sense that they lead to identical physical observables. We illustrate our formalism by applying it to de Sitter Jackiw-Teitelboim gravity and to the Starobinsky model.

We present an analytical model showing how the gauge-invariant loop phase in a three-level closed-loop atomic system imprints as bright-dark lobes in Laguerre Gaussian probe beam intensity patterns. In the weak probe limit, the output intensity in such systems include Beer-Lambert absorption, a scattering term and loop phase dependent interference term with optical depth controlling visibility. These systems enable mapping of arbitrary phases via interference rotation and offer a platform to measure Berry phase. Berry phase emerge as a geometric holonomy acquired by the dark states during adiabatic traversal of LG phase defined in a toroidal parameter space. Manifesting as fringe shifts which are absent in open systems, experimental realization using cold atoms or solid state platforms appears feasible, positioning structured light in closed-loop systems as ideal testbeds for geometric phases in quantum optics.

The emerging field of quantum magnonics seeks to understand and harness the quantum properties of magnons -- quantized collective spin excitations in magnets. Squeezed magnon states arise naturally as the equilibrium ground states of anisotropic ferromagnets and antiferromagnets, representing an important class of nonclassical magnon states. In this work, we show how a qubit-conditioned quantum quench of an anisotropic ferromagnet can be used for Heisenberg-limited parameter estimation based on measurements of the qubit only. In the presence of ground-state squeezing, the protocol yields information about the eigenmode frequency of the coupled magnon-qubit system, whereas no information is gained in the absence of such squeezing. The protocol therefore leverages genuine quantum correlations in the form of magnonic squeezing while simultaneously relying on the equilibrium character of this squeezing -- a feature distinctive to magnetic systems.

Closed timelike curves (CTCs) challenge our conception of causality by allowing information to loop back into its own past. Any consistent description of such scenarios must avoid time-travel paradoxes while respecting the no-new-physics principle, which requires that the set of operations available within any local spacetime region remain unchanged, irrespective of whether CTCs exist elsewhere. Within an information-theoretic framework, this leads to process functions: deterministic classical communication structures that remain logically consistent under arbitrary local operations, yet can exhibit correlations incompatible with any definite causal order - a phenomenon known as non-causality. In this work, we provide the first complete recursive characterization of process functions and of (non-)causal process functions. We use it to establish a correspondence between process functions and unambiguous complete product bases, i.e., product bases in which every local state belongs to a unique local basis. This equivalence implies that non-causality of process functions is exactly mirrored by quantum nonlocality without entanglement (QNLWE) - the impossibility of perfectly distinguishing separable states using local operations and causal classical communication - for such bases. Our results generalize previous special cases to arbitrary local dimensions and any number of parties, enable systematic constructions of non-causal process functions and unambiguous QNLWE bases, and reveal an unexpected connection between certain non-signaling inequalities and causal inequalities.

MulAtoLEG (Multi-Atom Liouville Equation Generator) is an open-source Mathematica package for generating Liouville superoperators and Liouville equations, specialized for multilevel atomic systems comprising an arbitrary number of atoms. This scheme is based on an extension to multilevel atomic systems, originally developed by Lehmberg [R. H. Lehmberg, Phys. Rev. A 2, 883 (1970)] as an adjoint master equation for ensembles of two-level emitters and later reformulated by Genes [M. Reitz, C. Sommer and C. Genes, PRX Quantum 3, 010201 (2022)] as a master equation. The package facilitates the generation of equations for complex transition configurations in alkali atoms. Although primarily designed for atomic systems, it can also generate the master and adjoint master equations for general Hamiltonians and Lindbladians. In addition, it includes functionalities to construct the differential equations in the dressed-state basis, where, in many cases, the non-unitary evolution operator can be determined explicitly. To maximize computational efficiency, the package leverages Mathematica's vectorization and sparse linear algebra capabilities. Since MulAtoLEG produces exact equations without approximations, the feasible system size is naturally limited by the available computational resources.

Recent years have seen a proliferation in investigations on Altermagnetism due to its exciting prospects both from an applications perspective and theoretical standpoint. Traditionally, altermagnets are distinguished from collinear antiferromagnets using the central concept of halving subgroups within the spin space group formalism. In this work, we propose the Fundamental Lemma of Altermagnetism (FLAM) deriving the exact conditions required for the existence of altermagnetic phase in a magnetic material on the basis of site-symmetry groups and halving subgroups for a given crystallographic space group. The spin group formalism further clubs ferrimagnetism with ferromagnetism since the same-spin and opposite-spin sublattices lose their meaning in the presence of multiple magnetic species. As a consequence of FLAM, we further propose a class of fully compensated ferrimagnets, termed as Alterferrimagnets (AFiMs), which can show alternating momentum-dependent spin-polarized non-relativistic electronic bands within the first Brillouin zone. We show that alterferrimagnetism is a generalization of traditional collinear altermagnetism where multiple magnetic species are allowed to coexist forming fully compensated magnetic-sublattices, each with individual up-spin and down-spin sublattices.

Twirling, uniform averaging over symmetry actions, is a standard tool for reducing the description of quantum states and channels to symmetry-invariant data. We develop a framework for averaging quantum channels based on channel-state duality that converts pre- and post-processing averages into a group twirl acting directly on the Choi operator. For arbitrary unitary representations on the input and output spaces, the twirled channel is obtained as an explicit projection onto the commutant of the induced representation on $\mathcal H_{\rm out}\otimes \mathcal H_{\rm in}$. In the collective setting, where the commutant is the walled Brauer algebra, we introduce a partial-transpose reduction that maps channel twirling to an ordinary Schur-Weyl twirl of the partially transposed Choi operator, enabling formulas in terms of permutation operators. We further extend the construction beyond compact symmetries to reductive non-unitary groups via Cartan decomposition, yielding a weighted sum of invariant-sector projections with weights determined by the Abelian component. Finally, we provide two finite realizations of channel averaging. The first one is a ``dual'' averaging protocol as a convex mixture of unitary-$1$-design channels on invariant sectors. The second one is a notion of channel $t$-designs induced by weighted group $t$-designs for $t=t_{\rm in}+t_{\rm out}$.

Linearly polarized projections are the tacit means for performing Clauser-Horne-Shimony-Holt (CHSH) Bell-inequality tests using polarization-entangled photon pairs. The inequality is valid for all states on the Poincaré-Bloch sphere, but few laboratory studies have investigated violations with the full sphere. In this article, we explore the experimental verifications of the predicted violations of the CHSH inequality with Bell and non-Bell states with same and different linear and elliptically polarized basis states for each photon. We find that Bell states violate CHSH when using the same basis for both photons, regardless of their ellipticity, whereas they show no violations for photon projections in different bases. We found non-Bell maximally-entangled states for which the converse is true.

Germanium hole spin qubits based on strained Ge/SiGe quantum well have attracted much research attention due to the strong spin-orbit coupling. In particular, the strain dependence of the heavy-hole--light-hole mixing and thus the $g$-tensor anisotropy offer unique opportunities for acoustic driving and spin-phonon coupling. In this work we numerically simulate the coherent control of a Ge hole spin using surface acoustic waves. The periodic strain dynamically modulates the $g$-tensor matrix and causes fast spin rotation under a small acoustic amplitude. Moreover, we show a strong anisotropy and confinement dependence of the Rabi frequency coming from the phase-shifted longitudinal and shear strain components. Our work lays the foundations for acoustic-driven spin control and spin-phonon coupling using Ge hole spin qubits.

The van der Waals interaction between neutral atoms is typically studied using stationary perturbation theory for the short-distance (London) limit, while long-distance (Casimir-Polder) results are usually derived via semiclassical, time-dependent approaches. In this pedagogical article, we demonstrate that reformulating stationary perturbation theory calculations in terms of time-ordered correlation functions significantly simplifies the mathematical treatment. This reformulation is particularly advantageous for higher-order calculations required in the long-distance regime, where retardation effects become important. Our approach provides a unified framework that connects both limiting cases while offering a clear conceptual picture suitable for advanced quantum mechanics courses.

We investigated experimentally and theoretically a cavity-free microwave field that couples the two ground states of a Λ-type atomic system, thereby forming a closed Δ configuration. In this regime, the absence of cavity-imposed phase matching leads to a strong sensitivity of the ground-state coherence to the microwave field parameters. We observe that the coherent population trapping (CPT) resonance exhibits a pronounced dependence on the microwave power and detuning, resulting in measurable changes in resonance contrast, linewidth, and center frequency. To explain these effects, we develop a numerical density-matrix model in which the ground-state coherence explicitly incorporates the microwave coupling strength, capturing the essential physics of this no-phase-matching Δ system. The excellent agreement between theory and experiment establishes a simple and robust framework for microwave control of cavity-free Δ-type atomic systems, with direct implications for compact atomic clocks and quantum-enhanced quantum sensing platforms.

Quantum annealing offers a promising strategy for solving complex optimization problems by encoding the solution into the ground state of a problem Hamiltonian. While most implementations rely on spin-$1/2$ systems, we explore the performance of quantum annealing on a spin-$1$ system where the problem Hamiltonian includes a single ion anisotropy term of the form $D\sum (S^z)^2$. Our results reveal that for a suitable range of the anisotropy strength $D$, the spin-$1$ annealer reaches the ground state with higher fidelity. We attribute this performance to the presence of the intermediate spin level and the tunable anisotropy, which together enable the algorithm to traverse the energy landscape through smaller, incremental steps instead of a single large spin flip. This mechanism effectively lowers barriers in the configuration space and stabilizes the evolution. These findings suggest that higher spin annealers offer intrinsic advantages for robust and flexible quantum optimization, especially for problems naturally formulated with ternary decision variables.

Adiabatic topological pumping promises robust transport of energy and information, but its speed is fundamentally limited by the instantaneous adiabatic condition, which demands prohibitively slow parameter variations. Here we develop a paradigm shift from instantaneous to global adiabaticity. We derive a global adiabatic criterion (GAC), which sets an absolute fidelity bound by controlling the root-mean-square value of nonadiabaticity factor. We further introduce a fluctuation-suppression acceleration criterion, which minimizes spatial inhomogeneity and allows us to safely increase the mean nonadiabaticity. Experimentally, we implement this principle in femtosecond-laser-written photonic Su-Schrieffer-Heeger waveguide arrays via scalable power-law coupling modulation. Our accelerated topological pumping achieves >0.95 fidelity over a fivefold reduced device length compared to the conventional scheme, exhibits the predicted linear scaling with the system size, and maintains robust performance across a >400 nm bandwidth. This principle of GAC provides a universal design rule for fast, compact, and robust adiabatic devices across quantum and classical topological platforms.

In arXiv:2405.04947, it was shown that the GNS spectral gap of a Gaussian quantum Markovian generator is strictly positive if and only if there exists a maximal number of linearly independent noise operators, under the assumption that the generated semigroup admits a unique faithful normal invariant state. In this paper, we provide a necessary and sufficient condition for the existence of the KMS spectral gap, which also depends only on the noise operators of the generator. We further show that the existence of the GNS spectral gap implies the existence of the KMS spectral gap.

Quantum communication exploits non-classical correlations to achieve efficient and unconditionally secure exchange of information. In particular, the quantum teleportation protocol allows for a deterministic and secure transfer of unknown quantum states by using pre-shared quantum entanglement and classical feedforward communication. Quantum teleportation in the microwave regime provides an important tool for high-fidelity remote quantum operations, enabling distributed quantum computing with superconducting circuits and potentially facilitating short-range, open-air microwave quantum communication. In this context, we consider practical application scenarios for the microwave analog quantum teleportation protocol based on continuous-variable states. We theoretically analyze the effect of feedforward losses and noise on teleportation fidelities of coherent states and show that these imperfections can be fully corrected by an appropriate feedforward gain. Furthermore, we consider quantum teleportation with finite-size codebooks and derive modified no-cloning thresholds as a function of the codebook configuration. Finally, we analyze the security of quantum teleportation under public channel attacks and demonstrate that the corresponding secure fidelity thresholds may drastically differ from the conventional no-cloning values. Our results contribute to the general development of quantum communication protocols and, in particular, illustrate the feasibility of using quantum teleportation in realistic microwave networks for robust and unconditionally secure communication.

Characterizing universal entanglement features in higher-dimensional quantum matter is a central goal of quantum information science and condensed matter physics. While the subleading corner terms in two-dimensional quantum systems encapsulate essential universal information of the underlying conformal field theory, our understanding of these features remains remarkably limited compared to their one-dimensional counterparts. We address this challenge by investigating the entanglement dynamics of fermionic systems along the imaginary-time evolution. We uncover a pioneering non-equilibrium scaling law where the corner entanglement entropy grows linearly with the logarithm of imaginary time, dictated solely by the universality class of the quantum critical point. Through unbiased Quantum Monte Carlo simulations, we verify this scaling in the interacting Gross-Neveu-Yukawa model, demonstrating that universal data can be accurately recovered from the early stages of relaxation. Our findings significantly circumvent the computational bottlenecks inherent in reaching full equilibrium convergence. This work establishes a direct link between the fundamental theory of non-equilibrium critical phenomena and the high-precision determination of universal entanglement properties on both classical and quantum platforms, paving the way for probing the rich entanglement structure of quantum critical systems.

Recently Szangolies has argued (in the setting of extended Wigner's-friend scenarios) that quantum theory permits ``Rashomon'' situations: multiple internally coherent accounts of events that cannot be combined into a single, consistent global narrative. This note explains why the Rashomon phenomenon can be understood as a \emph{failure of gluing}: local descriptions over different contexts exist, but they do not admit a single global ``all-perspectives-at-once'' description. This is the same mathematical obstruction that underlies modern sheaf-theoretic treatments of contextuality. I then indicate why the same perspective is useful in parts of the social sciences (quantum-like modelling of cognition, judgment, and decision-making), where ``context effects'' can likewise be interpreted as the absence of a single joint probability space.

We investigate the generation of squeezed Fock states (SFSs) via particle-number measurements in the modes of multimode Gaussian states. We identify a universal class of $N$-mode Gaussian states for which measuring $N-1$ modes results in the generation of SFSs. The key feature of these states is that the generated SFSs depend only on the total number of detected particles and are independent of their distribution among the detectors. Based on the general form of the wave functions of multimode Gaussian states, we propose a universal scheme for SFS generation. For this scheme, we evaluate the probability of SFS generation and analyze the robustness of the process against imperfections in particle-number-resolving detectors. In addition, we compare the universal scheme with a nonuniversal scheme, in which the generation of SFSs depends on a specific distribution of particle numbers across the detectors. We demonstrate that the universal scheme provides a higher probability of SFS generation, at the cost of increased experimental resources.

If the phase space-based Sudarshan-Glauber distribution, $P_ρ$, has negative values the quantum state, $ρ$, it describes is nonclassical. Due to $P$'s singular behavior this simple criterion is impractical to use. Recent work [Bohmann and Agudelo, Phys. Rev. Lett. 124, 133601 (2020)] presented a general, sensitive, and noise-tolerant certification functional, $ξ_{P}$, for the detection of non-classical behavior of quantum states $P_ρ$. There, it was shown that when this functional takes on negative values somewhere in phase space, $ξ_{P}(x,p) < 0$, this is \emph{sufficient} to certify the nonclassicality of a state. Here we give examples where this certification fails. We investigate states which are known to be nonclassical but the certification functions is positive $ξ(x,p) \geq 0$ everywhere in phase space. We generalize $ξ$ giving it an appealing form which allows for improved certification. This way we generate the best family of certification functions available so far. Yet, they also fail for very weakly nonclassical states, in other words, the question how to faithfully certify quantumness remains an open question.

The energy-transfer efficiency of the natural photosynthesis system seems to be perfectly optimized during the evolution for millions of years. However, how to enhance the efficiency in the artificial light-harvesting systems is still unclear. In this paper, we investigate the energy-transfer process in the photosystem I (PSI). When there is no effective coupling between the outer antenna (OA) and the reaction center (RC), the two light-harvesting networks are disconnected and thus the energy transfer is inefficient. In order to repair these disconnected networks, we introduce a bridge with three sites between them. We find that by modulating the level structure of the 3-site bridge to be resonant, the energy transfer via the dark state will be enhanced and even outperform the original PSI. Our discoveries may shed light on the designing mechanism of artificial light-harvesting systems.

Quantum phase transitions (QPTs) in coherent Ising machines (CIMs) are studied via a spectral mapping between the one-dimensional XY spin model and a network of degenerate optical parametric oscillators (DOPOs). This exact correspondence reveals that the DOPO network faithfully reproduces the quantum critical behavior of the XY model across its anisotropic, isotropic, and transverse-field Ising regimes. The ground-state energy density and its derivatives are analyzed to reveal second-order QPTs characterized by singularities in magnetic susceptibility at critical points. These results show that CIMs do not only serve as powerful platforms for solving combinatorial optimization problems but also provide a versatile optical simulator for studying universal quantum critical phenomena, bridging quantum-spin models and photonic quantum systems.

We introduce a conceptual reformulation of the Mott-Berezinskiĭ (MB) theory of low-frequency AC conductivity in disordered systems based on localization landscape theory. Instead of assuming uniform localization and fixed hopping distances, transport is described through an effective potential whose geometry encodes the spatial organization and energy-dependent localization of quantum states. Using the associated Agmon metric, we define a generalized Mott scale that replaces the classical hopping length with a geometric criterion set by the disorder landscape. This framework naturally incorporates strong spatial inhomogeneity and yields the AC conductivity directly from the effective potential. The standard MB result is recovered as a limiting case. Our approach extends the conceptual foundation of MB theory to arbitrary disordered media and energies approaching the mobility edge, providing a unified description of AC transport in complex quantum materials.

Developing robust and high performance quantum software is challenging due to the dynamic nature of existing Python-based frameworks, which often suffer from runtime errors and scalability bottlenecks. In this work, we present LogosQ, a high performance backend agnostic quantum computing library implemented in Rust that enforces correctness through compile time type safety. Unlike existing tools, LogosQ leverages Rust static analysis to eliminate entire classes of runtime errors, particularly in parameter-shift rule gradient computations for variational algorithms. We introduce novel optimization techniques, including direct state-vector manipulation, adaptive parallel processing, and an FFT optimized Quantum Fourier Transform, which collectively deliver speedups of up to 900 times for state preparation (QFT) and 2 to 5 times for variational workloads over Python frameworks (PennyLane, Qiskit), 6 to 22 times over Julia implementations (Yao), and competitive performance with Q sharp. Beyond performance, we validate numerical stability through variational quantum eigensolver (VQE) experiments on molecular hydrogen and XYZ Heisenberg models, achieving chemical accuracy even in edge cases where other libraries fail. By combining the safety of systems programming with advanced circuit optimization, LogosQ establishes a new standard for reliable and efficient quantum simulation.

Criticality-based quantum sensing exploits hypersensitive response to system parameters near phase transition points. This work uncovers two metrological advantages offered by topological phase transitions when the probe is prepared as topological edge states. Firstly, the order of topological band touching is found to determine how the metrology sensitivity scales with the system size. Engineering a topological phase transition with higher-order band touching is hence advocated, with the associated quantum Fisher information scaling as $ \mathcal{F}_Q \sim L^{2p}$, with $L$ the lattice size in one dimension, and $p$ the order of band touching. Secondly, with a topological lattice accommodating degenerate edge modes (such as multiple zero modes), preparing an $N$-particle entangled state at the edge and then adiabatically tuning the system to the phase transition point grows quantum entanglement to macroscopic sizes, yielding $\mathcal{F}_Q \sim N^2 L^{2p}$. This work hence paves a possible topological phase transition-based route to harness entanglement, large lattice size, and high-order band touching for quantum metrology.

Nonclassical light sources are central to emerging quantum technologies, yet current platforms offer limited tunability and typically operate at low photon numbers. In parallel, strong-field physics provides widely tunable, bright coherent radiation through high-order harmonic generation (HHG), but its quantum optical character has remained largely unexplained. While recent experiments have revealed signatures of entanglement, squeezing, and quantum-state modification in both the driving and generated fields, a unified theoretical framework capable of identifying the origin and controllability of these effects has been missing. Here we introduce a fully quantum, analytically tractable theory of intense light-matter interaction that rigorously captures the emergence of nonclassicality in HHG. Our approach employs a parametric factorization of the coupled electron-field system into a driven electronic state and a dynamically perturbed quantum optical field, derived directly from the time-dependent Schrödinger equation without requiring conditioning, homodyne detection, or mode-selection techniques. We show how quantum correlations, squeezing, and Wigner-function negativity arise intrinsically from the interaction dynamics, and we identify the precise conditions under which specific nonclassical features are amplified or suppressed. The theory enables predictive design of bright, high-photon-number quantum states at tunable frequencies, and we demonstrate its utility by outlining realistic conditions for generating bright nonclassical ultraviolet light. Our results establish a comprehensive foundation for strong-field quantum optics and open new avenues toward tabletop quantum light sources for sensing, communication, and photonic quantum information processing.

We demonstrate the efficient modulation of flux-tunable superconducting resonators (FTRs) using flip-chip or on-chip-based input coils. The FTRs we use are aluminum-based quarter-wave coplanar waveguide resonators terminated with 100um or 200um-wide square loop dc superconducting quantum interference devices (SQUIDs) employing 1um-sized Josephson junctions. We employ SQUIDs with a geometric loop inductance of up to 0.7nH to increase the flux transfer efficiency. The geometric inductance of the SQUID results in a non-zero screening parameter $β_L$, whose branch switching effect is mitigated by using asymmetric junctions. We achieve flux modulation of the FTRs by more than one GHz and flux responsivities of up to tens of GHz/$Φ_0$ with uA-scale on-chip currents. We compare flip-chip with on-chip input-coil-based flux modulation, where the former is realized through galvanically connected and closely spaced chips, while the latter is achieved through superconducting air-bridge connections. We achieve a flux-transfer efficiency from the input coil to the SQUID loop of up to 20%. Our work paves the way for efficient low current flux modulation of FTRs and sensitive measurement of flux signals.

Developing and deploying advanced Quantum Repeater (QR) technologies will be necessary to scale quantum networks to longer distances. Depending on the error mitigation mechanisms adopted to suppress loss and errors, QRs are typically classified into memory-based or all-photonic QRs; and each type of QR may be best suited for a specific type of underlying quantum technology, a particular scale of quantum networks, or a specific regime of operational parameters. We perform theoretical analysis and simulations of quantum repeaters and networks to investigate the relative performance and resource requirements of different quantum network paradigms. Our results will help guide the optimization of quantum hardware and components and shed light on the role of a robust control plane. We present our research findings on theoretical analysis and simulations of memory-based first-generation trapped-ion quantum repeaters and networks, and all-photonic entanglement-based quantum repeaters and networks. We study the relative performance in terms of entanglement generation rate and fidelity, as well as the resource requirements of these two different quantum network paradigms.

The Quantum Approximate Optimization Algorithm (QAOA) is among leading candidates for achieving quantum advantage on near-term processors. While typically implemented with a transverse-field mixer (XM-QAOA), the Grover-mixer variant (GM-QAOA) offers a compelling alternative due to its global search capabilities. This work investigates the application of GM-QAOA to Higher-Order Unconstrained Binary Optimization (HUBO) problems, also known as Polynomial Unconstrained Binary Optimization (PUBO), which constitute a generalized class of combinatorial optimization tasks characterized by intrinsically multi-variable interactions. We present a comprehensive numerical study demonstrating that GM-QAOA, unlike XM-QAOA, exhibits monotonic performance improvement with circuit depth and achieves superior results for HUBO problems. An important component of our approach is an analytical framework for modeling GM-QAOA dynamics, which enables a classical approximation of the optimal parameters and helps reduce the optimization overhead. Our resource-efficient parameterized GM-QAOA nearly matches the performance of the fully optimized algorithm while being far less demanding, establishing it as a highly effective approach for complex optimization tasks. These findings highlight GM-QAOA's potential and provide a practical pathway for its implementation on current quantum hardware.

In the present study, we apply shortcut to adiabaticity pulses (time-dependent Rabi frequency and detuning) for the efficient population transfer from the ground to the exciton state in a GaAs/InGaAs quantum dot with phonon-induced dephasing. We use the time-evolving matrix product operator (TEMPO) method to propagate system in time and find that, for temperatures below $ 20 \ \text{K} $ and pulse duration up to $ 10 \ \text{ps} $, a very good transfer efficiency is obtained in general. We explain these results using a Bloch-like equation derived from a generalized Lindblad equation, which adequately describes system dynamics at lower temperatures. For higher temperatures, the transfer efficiency is significantly reduced except for subpicosecond pulses, where the shortcut Rabi frequency reduces to a delta pulse attaining a fast population inversion. The present work is expected to find application in quantum technologies which exploit quantum dots for single-photon generation on demand.

We consider the costs and benefits of embedding the states of one quantum system within those of another. Such embeddings are ubiquitous, e.g., in error correcting codes and in symmetry-constrained systems. In particular we investigate the impact of embeddings in terms of the resource theory of nonstabilizerness (also known as magic) quantified via the stabilizer entropy (SE). We analytically and numerically study the stabilizer entropy gap or magic gap: the average gap between the SE of a quantum state realized within a subspace of a larger system and the SE of the quantum state considered on its own. We find that while the stabilizer entropy gap is typically positive, requiring the injection of magic, both zero and negative magic gaps are achievable. This suggests that certain choices of embedding subspace provide strong resource advantages over others. We provide formulas for the average nonstabilizerness of a subspace given its corresponding projector and sufficient conditions for realizing zero or negative gaps: in particular, certain classes of stabilizer codes provide paradigmatic examples of the latter. Through numerical optimization, we find subspaces which achieve both minimal and maximal average SE for a variety of dimensions, and compute the magic gap for specific error-correcting codes and symmetry-induced subspaces. Our results suggest that a judicious choice of embedding can lead to greater efficiency in both classical and quantum simulations.

Variational quantum algorithms are among the most promising approaches for simulating interacting quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. However, the practical success of variational quantum eigensolvers (VQE) critically depends on the structure of the chosen variational ansatz. In this work, we investigate the ground-state properties of the one-dimensional antiferromagnetic Heisenberg spin-1/2 chain using both generic hardware-efficient ansatz and physics-informed, symmetry-preserving variational circuits. We benchmark variational results against exact diagonalization and noiseless simulations, and subsequently validate the approach on real IQM Garnet quantum hardware. Our results demonstrate that incorporating physical symmetries into the circuit design leads to significantly improved energy estimates, enhanced robustness against hardware noise, and clearer convergence behavior when compared to hardware-efficient ansatz under identical resource constraints. These findings highlight the importance of problem specific ansatz construction for reliable quantum simulations in the NISQ era.

We analyze few-body quantum states with particular correlation properties imposed by the requirement of maximal bipartite entanglement for selected partitions of the system into two complementary parts. A novel framework to treat this problem by encoding these constraints in a graph is advocated; the resulting objects are called ``graph-restricted tensors''. This framework encompasses several examples previously treated in the literature, such as 1-uniform multipartite states, quantum states related to dual unitary operators and absolutely maximally entangled states (AME) corresponding to 2-unitary matrices. Original examples of presented graph-restricted tensors are motivated by tensor network models for the holographic principle. In concrete cases we find exact analytic solutions, demonstrating thereby that there exists a vast landscape of non-stabilizer tensors useful for the lattice models of holography.

In this work, we formulate the problem of achieving in minimum-time perfect chiral resolution with bounded control fields, as an optimal control problem on two non-interacting spins-$1/2$. We assume the same control bound for the two Raman fields (pump and Stokes) and a different bound for the field connecting directly the two lower-energy states. Using control theory, we show that the optimal fields can only take the boundary values or be zero, the latter corresponding to singular control. Subsequently, using numerical optimal control and intuitive arguments, we identify some three-stage symmetric optimal pulse-sequences, for relatively larger values of the ratio between the two control bounds, and analytically calculate the corresponding pulse timings as functions of this ratio. For smaller values of the bounds ratio, numerical optimal control indicates that the optimal pulse-sequence loses its symmetry and the number of stages increases in general. In all cases, the analytical or numerical optimal protocol achieves a faster perfect chiral resolution than other pulsed protocols, mainly because of the simultaneous action of the control fields. The present work is expected to be useful in the wide spectrum of applications across the natural sciences where enantiomer separation is a crucial task.

We introduce generalisations of von Neumann entanglement entropy that are invariant with respect to certain scale transformations. These constructions are based on Unit-Invariant Singular Value Decomposition (UISVD) with its right-, left-, and bi-invariant incarnations, which itself are variations of the standard Singular Value Decomposition (SVD) that remain invariant under (appropriate set of) diagonal transformations. These measures are naturally defined for non-Hermitian or rectangular operators and remain useful when the input and output spaces possess different dimensions or metric weights. We apply the UISVD entropy and discuss its advantages in the physically interesting framework of Biorthogonal Quantum Mechanics, whose important aspect is indeed the behavior under scale transformations. Further, we illustrate features of UISVD-based entropies in other representative settings, from simple quantum mechanical bipartite states to random matrices relevant to quantum chaos and holography, and in the context of Chern-Simons theory. In all cases, the UISVD yields stable, physically meaningful entropic spectra that are invariant under rescalings and normalisations.

In a recent preprint [1] Jeffrey Bub presents a discussion of neo-Bohrian interpretations of quantum mechanics, and also of von Neumann's work on infinite tensor products [2]. He rightfully writes that this work provides a theoretical framework that deflates the measurement problem and justifies Bohr's insistence on the primacy of classical concepts. But then he rejects these ideas, on the basis that the infinity limit is "never reached for any real system composed of a finite number of elementary systems". In this note we present opposite views on two major points: first, admitting mathematical infinities in a physical theory is not a problem, if properly done; second, the critics of [3,4,5] comes with a major misunderstanding of these papers: they don't ask about "the significance of the transition from classical to quantum mechanics", but they start from a physical ontology where classical and quantum physics need each other from the beginning. This is because they postulate that a microscopic physical object (or degree of freedom) always appears as a quantum system, within a classical context. Here we argue why this (neo-Bohrian) position makes sense.

Inspired by previous works on epidemic-like processes in open quantum systems, we derive an elementary quantum epidemic model that is simple enough to be studied via Quantum Jump Monte Carlo simulations at reasonably large system sizes. We show how some weak symmetries of the Lindblad equation allow us to map the dynamics onto a classical Kinetic Monte Carlo; this simplified, effective dynamics can be described via local stochastic jumps coupled with a local deterministic component. Simulations are then used to reconstruct a phase diagram which displays stationary features completely equivalent to those of completely classical epidemic processes, but richer dynamics with multiple, recurrent waves of infection.

We study the average bipartite entanglement entropy of Haar-random pure states in quantum many-body systems with global $\mathrm{SU}(2)$ symmetry, constrained to fixed total spin $J$ and magnetization $J_z = 0$. Focusing on spin-$\tfrac12$ lattices and subsystem fractions $f < \frac{1}{2}$, we derive a asymptotic expression for the average entanglement entropy up to constant order in the system volume $V$. In addition to the expected leading volume law term, we prove the existence of a $\frac{1}{2}\log V$ finite-size correction resulting from the scaling of the Clebsch-Gordon coefficients and compute explicitly the $O(1)$ contribution reflecting angular-momentum coupling within magnetization blocks. Our analysis uses features of random matrix ensembles and provides a fully analytical treatment for arbitrary spin densities, thereby extending Page type results to non-Abelian sectors and clarifying how $\mathrm{SU}(2)$ symmetry shapes average entanglement.

We present MQNS, a discrete-event simulator for rapid evaluation of entanglement routing under dynamic, heterogeneous configurations. MQNS supports runtime-configurable purification, swapping, memory management, and routing, within a unified qubit lifecycle and integrated link-architecture models. A modular, minimal design keeps MQNS architecture-agnostic, enabling fair, reproducible comparisons across paradigms and facilitating future emulation.

Quantum simulation of non-Abelian gauge theories requires careful handling of gauge redundancy. We address this challenge by presenting universal principles for treating gauge symmetry that apply to any quantum simulation approach, clarifying that physical states need not be represented solely by gauge singlets. Both singlet and non-singlet representations are valid, with distinct practical trade-offs, which we elucidate using analogies to BRST quantization. We demonstrate these principles within a complete quantum simulation framework based on the orbifold lattice, which enables explicit and efficient circuit constructions relevant to real-world QCD. For singlet-based approaches, we introduce a Haar-averaging projection implemented via linear combinations of unitaries, and analyze its cost and truncation errors. Beyond the singlet-approach, we show how non-singlet approaches can yield gauge-invariant observables through wave packets and string excitations. This non-singlet approach is proven to be both universal and efficient. Working in temporal gauge, we provide explicit mappings of lattice Yang-Mills dynamics to Pauli-string Hamiltonians suitable for Trotterization. Classical simulations of small systems validate convergence criteria and quantify truncation and Trotter errors, showing concrete resource estimates and scalable circuit recipes for SU($N$) gauge theories. Our framework provides both conceptual clarity and practical tools toward quantum advantage in simulating non-Abelian gauge theories.

In this paper, we investigate coherent control of nonadiabatic dynamics at a conical intersection (CI) using engineered ultrafast laser pulses. Within a model vibronic system, we tailor pulse chirp and temporal profile and compute the resulting wave-packet population and coherence dynamics using projections along the reaction coordinate. This approach allows us to resolve the detailed evolution of wave-packets as they traverse the degeneracy region with strong nonadiabatic coupling. By systematically varying pulse parameters, we demonstrate that both chirp and pulse duration modulate vibrational coherence and alter branching between competing pathways, leading to controlled changes in quantum yield. Our results elucidate the dynamical mechanisms underlying pulse-shaped control near conical intersections and establish a general framework for manipulating ultrafast nonadiabatic processes.

Regular graphs find broad applications ranging from quantum communication to quantum computation. Motivated by this, we investigate the design of a quantum battery based on a K-regular graph, where K denotes the number of edges incident on each vertex. We prove that a 0-regular graph battery exhibits extractable work that scales linearly with the system-size when charged using a K-regular graph. This linear scaling is shown to persist even when the charging is implemented via a collective K-regular charger with power-law decaying interactions. While no superlinear scaling is observed, the work output is found to improve systematically with increasing regularity K. Furthermore, by introducing the notion of the fraction of extractable work when only subsystems are accessible, we identify this fraction to be independent of system-size if the battery is prepared in the down-polarized product state. This independence breaks down when the battery is oriented along the x- and y-directions of the Bloch sphere.

In this paper, we introduce "the Schrödinger plate." This is an infinite two-dimensional linear micro-polar elastic medium, with out-of-plane degrees of freedom, lying on a linear elastic foundation of a special kind. Any free motion of the plate can be corresponded to a solution of the two-dimensional Schrödinger equation for a single particle in the external potential field $V$. The specific dependence of the potential $V$ on the position is taken into account in the properties of the plate elastic foundation. The governing equations of the plate are derived as equations of the two-dimensional constraint Cosserat continuum using the direct approach. The plate dynamics can be described by the classical Germain-Lagrange equation for a plate, but the strain energy is different from the one used in the classical Kirchhoff-Love plate theory. Namely, the Schrödinger plate cannot be imagined as a thin elastic body composed of an isotropic linear material. The main property of the Schrödinger plate is as follows: the mechanical energy propagates in the plate exactly in the same way as the probability density propagates according to the corresponding Schrödinger equation.