Quantum Physics Paper Analysis

Mechanical vibrations are fundamental to a wide range of physical phenomena and technologies, yet their ability to actively shape free-electron dynamics remains largely unexplored. Here we theoretically show how an optomechanical membrane provides a phonon-assisted optical interface for controlling free-electron recoil and sensing localized forces. Transverse membrane motion scatters cavity light into high-momentum evanescent sidebands that enable phase-matched interaction with electrons traveling in vacuum. Beyond supplying momentum for phase matching, the vibration amplitude controls the electron-light interaction strength and redistributes electron populations among recoil orders. External forces that perturb the vibration are thereby encoded in the electron recoil spectrum. Under the modeled conditions, electron readout of localized stochastic forces can yield a higher signal-to-noise ratio than a Gaussian optical homodyne benchmark at equal detected probe rates. These results provide a theoretical basis for mechanically reconfigurable free-electron optics and mode-selective mechanical sensing.

A two-level emitter chirally coupled to a waveguide imprints a $π$ conditional phase on a two-photon pulse, a key component assumed in quantum photonic neural network architectures, but whether it survives the pure dephasing of a solid-state emitter is unknown, since no two-photon scattering treatment includes it. We derive the dephased two-photon amplitude in closed form and validate it against an independent Fock-state master equation. The conditional phase is pinned at exactly $π$ at every dephasing rate examined: dephasing destroys the amplitude carrying the nonlinear phase rather than rotating it. The one- and two-photon channels are not attenuated equally, so dephasing does not simply scale the node down but reweights it between photon-number sectors---an error no phase setting can train away. The standard factorization of two-photon correlators, exact for arbitrary loss, fails at first order in $γ_φ$, discarding $16$--$81\%$ of pairs over $γ_φ/γ=0.1$--$1$.

We prove a conjecture of Yu, Lai, and Oh: their rounded family of strengthened quantum Hamming bounds, which interpolates between Hamming-type bounds and the Singleton bound, holds for arbitrary exact quantum subspaces of dimension $K>1$. The result covers every integer local dimension $p\ge2$, every integer $t\ge1$, both distances $2t+1$ and $2t+2$, and every interpolation parameter $e\in\{0,\ldots,t\}$. Yu, Lai, and Oh proved these bounds for pure codes and for general codes of distance three or four; the case $e=0$ contains the ordinary quantum Hamming bound for general codes, recently proved by Zhang and Chen. More generally, for $p\ge3$, we prove the inequality $Kf(0)\le p^n\mathbb{E}f(X)$, where $X\sim\operatorname{Bin}(n,1-p^{-2})$, for every real polynomial $f$ of degree at most $D$, with $2\le D<d$, that is nonnegative on $\{0,\ldots,n\}$ and positive at zero; here $n$ and $d$ are the code length and distance.

We propose a quantum architecture that achieves addressable and parallel universal fault-tolerant logical in high-rate codes. The codes are obtained from the flexible concatenation of small-distance high-rate self-dual CSS codes. Addressable and parallel universal logic on the resulting $K$ logical qubits is injected by fault-tolerantly preparing and then consuming diverse logical $K$-qubit CSS stabilizer states and logical $\lvert H \rangle^{\otimes K}$ global magic states. Flag-at-origin is used to prepare the stabilizer resource states while a concatenated cultivation protocol prepares the global magic states. These resource states are consumed by Steane-QEC or Knill-QEC teleportation gadgets, which simultaneously perform quantum error correction. Any quantum algorithm with $T$-depth $D_T$ can be executed by consuming $12D_T$ or fewer resource states. We benchmark the fault-tolerant preparation of the resource states for several two-level concatenations of the $[[k+4,k,2]]$ H codes and the Hamming $[[15,7,3]]$ code. In particular, we find that the concatenated cultivation offers at least one order of magnitude spacetime reduction compared to cultivation in the surface code.

We propose an operational resolution of the FLRW big bang singularity using quantum probes satisfying a curvature coupled Klein-Gordon equation. Applying the Madelung-Bohm decomposition of a Klein-Gordon field on a classical near-singularity FLRW background, we show that the induced conformal geometry renders curvature invariants finite and makes past directed causal geodesics complete. The classical big bang surface is therefore inaccessible to this class of quantum probes in finite effective proper time, while the underlying FLRW spacetime remains singular.

We introduce a random sampling method for testing the weak Eigenstate Thermalization Hypothesis (wETH) that is particularly useful for large, sparse Hamiltonians. We test the method on a well-studied Rydberg atom system that exhibits both two- and three-body dipole-dipole interactions. Our results show that our method allows for the study of system sizes significantly beyond the limits of exact diagonalization. We find that the fluctuations in eigenstate expectation values decay as the Hilbert space dimension $D^{-1/2}$, consistent with wETH and in agreement with previous numerical results.

A recent work considered the Page curve for entanglement entropy of a freely expanding one-dimensional Fermi gas starting from a finite box (the system) in a zero-temperature initial state that then expands in to a semi-infinite vacuum (the environment). For the case with a single defect at the system-environment junction, it was shown that the Yang-Yang entropy of the system computed from semiclassical hydrodynamics agrees with the microscopically computed entanglement entropy, yielding the Page curve. On the other hand, the environment Yang-Yang entropy showed a monotonic increase. Here, we propose a hydrodynamic description to obtain the eigenvalues of the microscopic correlation matrix for a nonzero temperature freely-expanding Fermi gas. For the system, the phase space density directly gives the correlation matrix eigenvalues and thus, via the Yang-Yang formula, yields the von-Neumann entropy. For the reservoir, a modification of the phase space density is required in the Yang-Yang formula, to incorporate coherences, in order to reproduce accurately the entropy. The hydrodynamic description of correlation matrix eigenvalues also leads to a Levitov-Lesovik type formula for the full-counting-statistics for a finite system in the transient regime. We provide a heuristic derivation of the correlation matrix eigenvalues based on a semiclassical wave-packet picture.

Fault-tolerant quantum computing requires quantum gates that combine short duration, high fidelity, and robustness to noise. As quantum processors scale, robustness becomes increasingly important because exhaustive characterization and frequent recalibration of individual gates become impractical. We present a comprehensive optimal-control framework for controlled-Z (CZ) gates between directly coupled, frequency-tunable transmons that systematically accounts for intrinsic Hamiltonian errors and realistic decoherence mechanisms, including energy relaxation and dephasing. Using smooth, single-shot flux pulses, we obtain 12-ns CZ gates---close to the theoretical speed limit of 11.6 ns---with intrinsic errors suppressed to the $2\times10^{-5}$ level. We construct dephasing noise models, calibrated against published experimental measurements, that capture fast dephasing from room-temperature control electronics and slow dephasing from $1/f$ flux noise. Using these models, we identify dephasing sweet spots that suppress sensitivity to dephasing noise. We further exploit transmon asymmetry as a design parameter to access distinct noise-resilient operating regimes. These results establish an experimentally applicable framework for balancing gate speed, fidelity, and noise robustness while reducing characterization and recalibration overhead.

We prove that the randomized communication complexity of Vector-in-Subspace in $\mathbb R^n$ with error at most $1/3$ is $Θ(\sqrt n)$. Alice holds a unit vector $u$ and Bob holds an $n/2$-dimensional subspace $H$; they must distinguish $u\in H$ from $u\in H^\perp$. An exact one-way quantum protocol uses $O(\log n)$ qubits, making the problem a geometric example of an exponential quantum advantage over interactive classical communication. Our lower bound matches Raz's $O(\sqrt n)$ upper bound, improves the $Ω(n^{1/3})$ lower bound of Klartag and Regev, and removes the total-rank restriction in Grupel's $Ω(\sqrt n)$ result. The proof establishes a Gaussian moment bound over complete rectangle partitions. A complex Gaussian representation yields a vanishing even moment whose cancellation is preserved when averaging over the partition. We control the signed conditional moments around a real center by decomposing conditional Gaussian measures into fixed coordinates and sub-Gaussian components. Combining this estimate with spherical harmonic analysis gives the communication lower bound.

Majorana drew a symmetric multiqubit state as points on the Bloch sphere, antipodal to the zeros of its overlap with spin coherent states. Projecting only one qubit of a general state leaves the others in a state that varies with direction. Its entanglement invariants are eigenvalues of a non-Hermitian matrix and form bands over the sphere. Exceptional points appear, without gain or loss, where the entanglement family of the rest changes. Circling one exchanges two bands, so the bands form one Riemann surface. At five qubits it fixes the entanglement class up to finitely many choices.

I discuss two important quantum optics experiments which depend on two particle interference. In the years since their first demonstration many interesting and instructive variants have appeared, including the use of atoms instead of photons as the interfering particles. This chapter gives a pedagogical overview of some of these results and argues that the two effects are closely related.

Modular quantum architecture requires long-distance quantum interconnects to stitch together individual processor modules. Such interconnects, long-distance couplers or L-couplers, must support coherent quantum operation over meter-scale distances and scale to multiple connections between any two modules. Here we demonstrate four L-couplers operating between two 120-qubit IBM Nighthawk R1 superconducting qubit processors. Each L-coupler joins two Nighthawk lattice qubits through two frequency-tunable L-qubits, two RF-SQUID based "i2m" couplers, and 80 cm of superconducting aluminum coax. Each cable installs perpendicular to the processor surface, to enable denser connections, and is joined to the chip by an indium-to-indium room temperature pressure bond made after both modules were mounted. L-coupler modes near 5 GHz, with internal quality factors of 0.86 to 1.09e6, carry relay-based state transfer at a mean network benchmarking fidelity of 99.00%, with a best link of 99.29 +/- 0.07%. We then realize distant CZ gates between lattice qubits in separate modules at a mean fidelity of 94.75%, with a best link of 96.42 +/- 0.28%, and use them to generate entangled states across the two processors, including a demonstration of simultaneous Bell pair generation using two adjacent L-couplers. These four high-fidelity L-couplers establish a practical path to scalable quantum interconnects for modular quantum computing.

Two single-ion optical clocks, located in the United Kingdom and in Germany, are compared remotely via a 2220\,km long optical fiber link. Both clocks are based on the ${}^2S_{1/2} (F=0)\leftrightarrow {}^2F_{7/2} (F=3)$ electric octupole (E3) transition in $^{171}\text{Yb}^+$. Using more than $10^6$ seconds of measurement data, we determine a fractional frequency difference of $1.0(4.8)\times 10^{-18}$, demonstrating agreement of the independently developed systems. To our knowledge, this constitutes the first international clock comparison reaching a fractional uncertainty below $5\times 10^{-18}$, an important milestone towards an anticipated optical redefinition of the SI second. The measurement uncertainty is dominated by that of the relativistic redshift correction between the two sites, which includes time-varying gravity potential differences. We exploit the large baseline between the two clocks to search for violations of Lorentz invariance. In the absence of statistically significant modulations, we improve constraints on the Robertson-Mansouri-Sexl parameter $α$ by approximately a factor of five in the uncertainty, and provide limits on corresponding parameters within the Standard-Model Extension framework.

We establish that transversal diagonal gates on exact qubit codes of distance at least two can be exhaustively classified within a finite search space. Although code-preserving physical gates can have continuous phases, any projective logical action induced by a transversal diagonal gate can always be realized by a physical gate of finite order. Crucially, we prove that this physical order has an upper bound determined solely by the code parameters. This order bound enables the subset-sum-linear-programming (SSLP) framework introduced in arXiv:2504.20847 to exhaustively enumerate all candidate discrete symmetries, after which the Knill-Laflamme equations determine the remaining continuous code parameters. Applying this method to the nontrivial diagonal sector of exact $((6,2,3))$ codes, SSLP yields $66$ candidate symmetry classes, of which exactly $15$ are realizable, supporting full projective diagonal logical cyclic groups of orders $2$, $3$, and $5$. In particular, for order $5$, the code is unique up to local unitaries and qubit permutations, equivalent to the code constructed in arXiv:2504.20847. This code also attains the minimum length $n=6$ among exact $((n, 2, \ge 3))$ codes whose full projective transversal group cannot be conjugated into the projective Clifford group.

Variational Quantum Algorithms (VQAs) are promising approaches for solving combinatorial optimization problems on near-term quantum devices. However, the role played by quantum resources such as entanglement and coherence during the optimization process remains poorly understood. In this work, we investigate the evolution of these resources in two VQAs--the Quantum Approximate Optimization Algorithm (QAOA) and the Feedback-based Algorithm for Quantum Optimization (FALQON)--applied to the Minimum Vertex Cover problem. We employ a variational resource-quantification framework based on the Bures metric and Uhlmann's theorem, in which an auxiliary quantum circuit is optimized to identify the closest resource-free states. This approach allows us to quantify Bures entanglement and Bures coherence of the algorithmic states without requiring full quantum state tomography. For the considered problem instance, QAOA exhibits a pronounced accumulation of entanglement in its initial layers, followed by a progressive reduction as the algorithm converges toward the optimal solution. Its coherence likewise decreases overall with increasing circuit depth, although a finite residual value persists due to the degeneracy of the optimal-solution subspace. In contrast, FALQON exhibits a substantially lower entanglement peak, reached at larger circuit depth, followed by a decay as convergence proceeds. Its coherence decreases smoothly and monotonically together with the optimization error. These results reveal distinct quantum-resource trajectories associated with the two optimization strategies and illustrate how entanglement and coherence evolve as variational quantum states approach solutions of a classical combinatorial optimization problem.

Impedance matching is a crucial feature of an amplifier used to increase its instantaneous bandwidth and is typically achieved using static LC resonators. Here we show an approach to impedance matching in parametric amplifiers using arrays of unequal Josephson-junction-based elements (rf/dc SQUIDs, SNAILs, etc). The elements act either as small-footprint flux-tunable inductors forming an impedance-matching circuit, or 'active' amplifier elements which result in amplifier gain. We develop an analytical theory describing these systems, predicting a quasi-non-periodic amplifier frequency and gain modulation with applied flux and the broadening of gain bandwidths. We demonstrate this in devices using arrays of flux-focused SNAILs where flux biasing varies across the array. We find instantaneous bandwidths of 200 MHz with $>$17 dB of gain centred at $\sim$5.4 GHz in a device without a static impedance matcher. This broadening of amplifier bandwidth is stable with $>$100 MHz bandwidth at 17 dB gain across $>$1.2 GHz tunable bandwidth. Our analytical model captures flux dependence and qualitatively reproduces gain-bandwidths giving confidence in our understanding of these systems and allowing operational figures of merit to be optimised in future devices.

The superconducting diode effect requires the forward and reverse bias currents to differ, a scenario achieved via inversion and time-reversal symmetries broken together. The latter, and the more crucial one, is inevitably achieved by a magnetic field. Here, we show that a spatio-temporally driven chemical potential of the form, $μ_j(t)=μ+V\cos(ωt+\kd j)$, achieves both at once. Applied to a helical Shiba chain, the drive transmutes a traveling Peierls phase via generating an odd-in-momentum term, equivalent to an imaginary next-nearest-neighbour Haldane-like hopping in real space. Remarkably, the protocol is spin-blind, which renders the time-reversal breaking via a synthetic gauge flux rather than an effective Zeeman field. The rectification is odd in the drive wavevector, with exact zeros at $\kd=nπ$ and an analytical optimum at $\kd=2π/3$. It is however, even in the exchange coupling, $J$ and persists even at $J=0$. Furthermore, the rectification scales inversely with the pair-breaking gap, yielding approximately $50\%$ rectification in the topological phase and $10\%$ in the trivial phase. Symmetry breaking is thus drive-controlled, allowing it to be switched on, tuned, and reversed without an external magnetic field.

Teaching quantum mechanics at the secondary school level remains a major educational challenge. Traditional historical approaches often present the theory as a sequence of disconnected phenomena, requiring extensive prior knowledge of classical physics before students can appreciate the conceptual structure of quantum physics. In this work, we present the design, implementation, and evaluation of a curriculum based on the two state (qubit first) approach, in which the fundamental postulates of quantum mechanics are introduced through mathematically accessible two level systems and realized with light polarization. The curriculum integrates theoretical instruction, laboratory activities, a coherent progression grounded in the interactive simulations, and inquiry based learning into a coherent pathway that progresses from quantum states and superposition to entanglement and the experimental violation of Bell's inequalities. A distinctive feature of the project is the experimental realization of the violation of Bell's inequalities obtained in a newly established quantum optics laboratory in an Italian high school, where students performed, for the first time in Italy, an authentic Bell test using polarization-entangled photons. The same educational framework was adopted for in service teacher professional development courses. Learning outcomes were evaluated through mixed methods. Preliminary analysis indicates significant improvements in conceptual understanding, confidence in using mathematical formalism, and appreciation of the relationship between theory, experimentation, and the foundations of quantum mechanics. The proposed curriculum shows that two-state formalism and supported by real laboratory experiences enables secondary-school students to engage more meaningfully with both the conceptual foundations of quantum mechanics and their experimental verification.

In quantum mechanics, conservation laws are usually understood only statistically and only in the context of unitary evolution: during such evolution, if an observable commutes with the Hamiltonian, its expectation value and Born-rule probability distribution remain unchanged. Individual measurement outcomes, however, disrupt even this weak form of statistical conservation. Recently, though, it has been argued that a stronger, non-statistical form of conservation, valid at the level of individual measurement outcomes, can be recovered. The proposal relies on the claim that any superposition of eigenstates of a conserved quantity must ultimately be prepared relative to another physical system, which serves as the relevant reference frame and remains correlated with the system being prepared. On this enlarged description, the change observed in the measured system is claimed to be exactly compensated by an opposite change in the preparer, thereby restoring conservation at the level of individual measurement outcomes. We analyze this proposal and argue that it faces significant conceptual difficulties. We show that the proposed mechanism is not adequately justified and, moreover, does not establish conservation in individual measurement outcomes as claimed.

We show that the concept of particles and antiparticles is related to the Weyl-Heisenberg group $W\!H_3$. Its generators are the position operators $\hat x^a$, the momentum operators $\hat p_a$, and the central element $Q_{\sf{v}}$, which defines a subgroup U(1)$_{\sf v}$ of $W\!H_3$. We show that the wave functions have a charge relative to the group U(1)$_{\sf{v}}$ equal to either $q_+=1/\hbar$ (particle $ψ_+$) or $q_-=-1/\hbar$ (antiparticle $ψ_-$). We call these eigenvalues of the operator $Q_{\sf{v}}$ quantum charges: $Q_{\sf{v}}ψ_\pm^{}=q_\pm^{}ψ_\pm^{}$. The wave functions $ψ_+$ and $ψ_-$ belong to the Hilbert spaces $\mathcal{H}_+$ and $\mathcal{H}_-$, on which unitarily inequivalent representations $π_\hbar$ and $π_{-\hbar}$ of the Weyl-Heisenberg group $W\!H_3$ are defined. These representations are related to each other by the antilinear charge conjugation operator $\hat C$, which maps $\mathcal{H}_+, q_+$ to $\mathcal{H}_-, q_-$. Charges $q_\pm^{}$ are intrinsic characteristics of the wave functions $ψ_\pm^{}$, similar to spin and electric charge. The wave function possesses one of these charges, $q_+$ or $q_-$, prior to the specification of any equations. We show that negative probabilities/energies and the Klein paradox in Klein-Gordon and Dirac theories are consequences of the violation of U(1)$_{\sf v}$-invariance in these theories. Restoring this invariance separates particle and antiparticles and eliminates all paradoxes at the level of first-quantized relativistic theories.

Predicting molecular electronic structure using Quantum Computing approaches is a challenge in Computational Chemistry. Traditional Variational Quantum Eigensolvers (VQEs) are typically hindered by optimization challenges. The alternative Generative Quantum Eigensolver (GQE) mitigates this by reformulating ground-state search as discrete sequence generation, but its Transformer backbone suffers from quadratic computational complexity, bottlenecking scalability for larger molecules. To address this, we introduce the Mamba Quantum Eigensolver (Mamba-QE), which replaces the Transformer with a Selective State Space Model (SSM) to process operator sequences with linear $\mathcal{O}(L)$ complexity. Additionally, we integrate a distance-conditioned mechanism enabling the direct prediction of complete potential energy surfaces (PES). Evaluated on the $H_2$ molecule, Mamba-QE reproduces Full Configuration Interaction (FCI) reference energies well within chemical accuracy, achieving an energy error below $3\times10^{-6}$ Ha across 16 geometries with zero variational violations. Mamba-QE maintains high expressive power while establishing a robust, scalable foundation for quantum simulations of complex molecular systems.

We explore the space-time cost of encoding of a bosonic mode into a set of qubits via various encodings, and their resilience to noise. In particular, we compare the performance of the unary Fock state encoding, an unexplored encoding of Fock states into Dicke states (``Dicke'' encoding), and the binary quadrature encoding. We do so by considering a displacement as well as a simulation of a Dicke model, coupling a bosonic mode to a set of atoms represented as qubits. Using classical simulations, we assess the accuracy and optimized space-time costs in terms of number of qubits, circuit depth and CNOT count of a quantum simulation of the time dynamics using these encodings. Although our study is far from comprehensive, we find that the binary quadrature encoding is overall most favorable in terms of being very space-efficient and relatively time-efficient due to the use of the quantum Fourier transform. Our novel Dicke encoding leads to very shallow circuits, but pays in terms of using many more qubits. We probe the use of an H2-2 Quantinuum trapped-ion qubit device (56 qubits) for displacement and Dicke model simulation in the low boson-number regime, where we find that noise leads to visible deviations from ideal circuit dynamics.

Motional modes of trapped-ion crystals in Penning traps can now be cooled to near their ground states via electromagnetically induced transparency (EIT) cooling. Numerical simulations are valuable tools for interpreting EIT cooling results and optimizing experimental protocols, but existing molecular dynamics codes are limited to the simulation of Doppler cooling. In this work, we fill this gap by implementing a semiclassical model of EIT cooling in a novel MD code. By simultaneously evolving the ions' internal quantum states and classical motion, we are able to calculate the instantaneous EIT laser forces acting on the ions. We first validate our code by comparing the single-ion cooling rate to fully quantum simulation results. Next, we analyze cooling of the drumhead modes in planar ion crystals, quantifying the effects of planar ion motion and a finite laser beam width. Finally, we demonstrate efficient EIT cooling of the axial modes in 3D ellipsoidal crystals containing up to 500 ions. Such crystals are a promising platform for future quantum sensing experiments with enhanced sensitivity. We find that the mode spectra of 3D crystals can be engineered to enable sympathetic cooling of the low-frequency $\boldsymbol{E}\times\boldsymbol{B}$ modes. This numerical framework provides a powerful tool for modeling sub-Doppler cooling techniques and for optimizing future quantum sensing and quantum information experiments.

The same classical f-divergence admits inequivalent extensions to quantum states. The question is whether these extensions can be obtained from a common operational variational principle. Here we generalize Matsumoto's reverse-test optimization by introducing a reference prior state. More explicitly, we minimize the statistical distinguishability between a forward and a reverse prepare-and-measure process, related by retrodiction through the chosen reference and subject to prescribed quantum averages. Distinguishability is quantified by the classical f-divergence between their complete records. For faithful states in finite dimension, we prove that the same spectral implementation attains the minimum simultaneously for every operator-convex f. Varying the reference allows us to interpolate between standard and maximal quantum f-divergences of the prescribed states, passing through the geodesic family. More precisely, a flat reference yields the standard quantum f-divergences, thereby giving the Nussbaum-Szkoła distributions a variational characterization as optimal records. Choosing either prescribed state as reference recovers maximal quantum f-divergences and Matsumoto's reverse tests, while power references realize the geodesic interpolation. In the relative-entropy case, this gives the passage from Umegaki to Belavkin-Staszewski relative entropy by changing the prior for retrodiction.

The local distinguishability of five bipartite and tripartite orthogonal product states (OPSs) has been effectively resolved, while that of five quadripartite OPSs has not yet been effectively addressed. In this paper, we give the local distinguishability of five quadripartite OPSs, where any two of these five states are orthogonal on exactly one subsystem. Based on the vectors of the numbers of pairwise orthogonality relations, we classify different sets of five quadripartite OPSs into nine categories, which correspond to 371 distinct orthogonality graphs. We show that the sets of five quadripartite OPSs corresponding to 355 of the 371 cases can be perfectly distinguished by local operations and classical communication (LOCC), whereas the sets of five quadripartite OPSs for the remaining 16 cases cannot exactly distinguished by LOCC. Our results enrich the theory of nonlocality for sets of OPSs.

We apply a large Gaussian basis set of size up to $N = 500$ to calculate the all-order Wichmann-Kroll vacuum polarization correction in highly-charged ion. For a hydrogen-like system, this allows us to obtain an accurate correction value with a level of precision comparable to that of traditional methods. We demonstrate that values of effects that can be calculated as the difference between two quantities, such as the nuclear model correction, converge faster than the absolute value of the correction. We discuss the basis extrapolation methods and show their use in estimating the error due to incomplete convergence. Finally, we show an application of the Gaussian basis set to calculation of the vacuum polarization screening correction in lithium-like ions.

We propose a quantum-enhanced matter-wave interferometry protocol based on fractional-revival dynamics of a Bose-Einstein condensate in a ring, combined with a controlled interaction quench. Using the Truncated Wigner Approximation, we show that nonlinear evolution to the quarter revival generates modest spin squeezing of $-2.03\pm0.28\;$dB, which subsequently degrades under further nonlinear evolution. In contrast, starting from a non-interacting condensate, a controlled interaction quench applied after the initial quarter-revival beam-splitter operation generates substantially stronger spin squeezing of $-14.57\pm0.27\;$dB. We further show that phase control at $t=3T_r/8$ rotates the squeezed quadrature onto the phase-sensitive direction $\hat{J}_y$, producing a phase-squeezed state at $t=T_r/2$. The subsequent quarter-revival evolution converts this phase-squeezed state into a number-squeezed state, enabling population-difference readout. The resulting sequence provides a route to quantum-enhanced interferometry using the intrinsic fractional-revival dynamics of a ring together with controlled interaction and phase operations.

We consider a continuous-time quantum walk stroboscopically subjected to projective measurements on two distinct targets with sampling time period $τ$. We construct a general renewal framework for the first-detection amplitude at each target, from which we obtain the associated splitting probabilities. For Hamiltonians with reflection symmetry, we further show that each dual-target first-detection amplitude can be viewed as an interference effect between a pair of single-target first-detection amplitudes. This formulation yields exact expressions for the splitting probabilities and gives special sampling times at which they undergo pointwise discontinuous jumps due to a form of ergodicity breaking associated with dark states. As an illustrative example, we apply the framework to a one-dimensional tight-binding lattice chain with nearest-neighbor hopping, and study the splitting probabilities as functions of the initial position and sampling time. Below a critical sampling time, $0<τ< τ_c$ where $τ_c = 2 π/ ΔE$ with $ΔE$ being the energy bandwidth, the splitting probabilities for large system sizes become equal to $1/2$, independent of the initial position, as long as this position does not coincide with target sites. Above the critical sampling time, $τ\geq τ_c$, the splitting probabilities deviate from $1/2$ and develop oscillations as a function of initial position. The wavenumber associated with these oscillations is $Q=2\sin^{-1}(rτ_c/τ)$, where $r$ is a positive integer. We also explore the effects of relative phase and spatial separation between different components of a coherent initial state on the splitting probabilities. Finally, we study how a finite number of measurements modifies the splitting probabilities and broadens the resonances at special sampling times.

We describe a compact and simplified experimental setup for the production of ultracold strontium atoms. Thanks to its low-power oven and coil-free Zeeman slower design, the vacuum system has an overall length of only 40cm including oven, Zeeman slower and all-glass science cell. The oven has a power consumption of 14W at 460°C and produces a collimated flux of 3 10^10at/(s cm^2) at this temperature. The laser system employs master-slave laser architecture throughout and requires neither second-harmonic generation nor tapered amplifiers, reducing cost and complexity. The system has been in continuous use for more than a year.

We construct short triorthogonal codes for qudits of odd prime dimension by generalizing doubling, which combines a triorthogonal code with a code admitting a transversal phase gate, and raises the distance by up to two. This gives codes with parameters $[[28,1,4]]_3$, $[[37,1,5]]_3$, $[[72,1,6]]_3$, $[[118,1,8]]_3$, $[[33,1,5]]_5$ and $[[20,1,4]]_7$, each shorter than the cyclic, concatenated and Reed-Muller codes of the same distance, and a doubling construction of the $[[15,1,3]]_3$ code. When the columns of a generator matrix are regarded as charged points, triorthogonality becomes the vanishing of multipole moments up to octupole order, and doubling becomes a double layer of opposite charges; this picture explains why inputs with nontrivial coefficients can give shorter codes. We also show by exhaustive search that the shortest codes of distance three have length $11$ for $p=5$ and length $7$ for $p=7$. Combined with high-rate distance-two codes, the new codes reduce the cost of qutrit magic state distillation by up to an order of magnitude in regimes with high input noise.

A recent formulation of quantum belief showed that quantum retrodiction depends not only on the reduced density operator of the system of interest, but also on correlations with a hidden reference system, which leads to the notion of quantum belief equivalence. In this paper we formulate a multi-shot problem, where the extended posterior obtained after one update is used again as the prior for the next update. We first define a formal notion of $n$-shot equivalence and derive several propositions for arbitrary extended beliefs. We then argue that the agent must also specify why the data obtained in different rounds concern the same underlying object. Through the quantum de Finetti representation, this narrows the one-copy belief to a special class: candidate-state ensemble belief. In that sector, we show that two beliefs are $n$-shot equivalent if and only if their $(n+1)$-th moments are equal. We also give a physical interpretation of this moment condition and illustrate it through the equivalence between Haar priors and projective-design priors at bounded update depth.

Coherent multidimensional spectroscopy probes interactions and dynamics of molecular systems through nonlinear optical signals. Quantum light excitation has been explored as a means of controlling these signals, raising the question of how excitation-light correlations affect the precision of molecular parameter estimation from the emitted signal. In this work, we show that photon-number correlations and two-photon coherence play distinct roles in encoding molecular information in the emitted rephasing signal. In the weak-emission regime and within the single Schmidt pair approximation, we derive a normally ordered information law in which the joint photon-number moment and the squared magnitude of the two-photon coherence weight the amplitude and phase sensitivities of the molecular response, respectively. For matched temporal modes and mean photon numbers in each input mode, two-mode squeezed vacuum enhances both weights relative to coherent excitation, whereas independent displaced squeezing preserves the amplitude weight but reduces the phase weight. The background population and its parameter dependence also affect the total quantum Fisher information, which therefore cannot be inferred from the coherent mean-field signal alone. We derive a leading-order bound on its enhancement over coherent excitation when the background population is nonnegative and common to the compared sources. These findings provide criteria for selecting excitation sources according to how the target molecular parameter affects the amplitude and phase of the response.

Controlling transition rates is a central objective across quantum optics, condensed-matter physics, and chemical physics, encompassing processes such as spontaneous emission, energy and charge transfer, spin relaxation, and chemical reactions. Although Fermi's golden rule provides a powerful framework for calculating such rates of weakly coupled transitions, conventional calculations require the interaction to be specified in advance; the range of rate responses attainable over a broader interaction space remains unknown. We formulate spectral-overlap golden-rule rates as quadratic forms of the interaction and derive rigorous bounds on rate modulation over a specified interaction space. As an example, application to energy transfer from a donor to a molecular vibration coupled to an optical cavity reveals that enhancement and suppression depend jointly on the interaction and cavity detuning, including continuous reversal of the rate response for a fixed interaction. The same approach may elucidate rate control for other golden-rule processes, including excitation-energy transfer, nonadiabatic electron transfer, nonradiative electronic transitions, vibrational and spin relaxation, and spontaneous emission.

This work revisits the debate on fractional uncertainty relations that arose a decade ago and tries to settle it. After a careful study of the position-momentum uncertainty product of the Lévy wave packet, a novel lower bound is proposed for uncertainty relations in fractional quantum mechanics. This bound is nearly linear in the Lévy index and is satisfied by exact, calculable solutions available in the literature.

In this work, we investigate the convergence rate of the quantum Blahut-Arimoto (BA) algorithm proposed for computing the coherent information of less noisy quantum channels. Previous work established exponential convergence under certain restrictive assumptions on the channel. Using a Taylor expansion around a positive definite optimizer, we show that, for an injective degradable channel whose degrading channel has a relative-entropy contraction coefficient strictly less than one, the algorithm converges at an exponential rate after sufficiently many iterations. We further verify this condition for qubit amplitude-damping (AD) channels in the relevant parameter regime. In addition, by analyzing the Bogoliubov-Kubo-Mori (BKM) metric on the Bloch ball, we derive an explicit characterization of the relative-entropy contraction coefficient of qubit AD channels. The proposed approach is further extended to calculate the relative contraction coefficient and the relative expansion coefficient of two qubit AD channels.

We present an error-controlled framework for the quantum simulation of non-Markovian open-system dynamics in Gaussian environments. For a system coupled linearly to a Gaussian environment with zero mean, the bath's influence on the reduced dynamics is completely determined by its two-time correlation kernel. This allows us to replace the microscopic environment with an equivalent bath that has the same kernel. On a finite simulation interval, a rank-$N$ approximation of the kernel yields an effective bath of $N$ bosonic modes with time-dependent couplings to the system. To encode these modes in qubits, we first truncate each mode to its lowest $d$ occupation levels. When stronger couplings lead to large occupations, we introduce coupling dilution, which replaces each mode with several more weakly coupled copies while preserving the bath correlation kernel. This distributes excitations across more modes and trades additional modes for smaller local dimensions. We derive explicit reduced-state error bounds and establish polynomial circuit width and depth in simulation time and inverse accuracy under stated spectral-decay and coupling-regularity assumptions, provided elementary unitaries admit polynomial-cost implementations.

The Fröhlich-Pizzo (FP) model is a quantum-mechanical model originally developed to describe the interaction between an atom and the electromagnetic field in the nonrelativistic limit $c\to\infty$. We show that an adaptation of the FP model based on the local algebras of a $U(1)$ chiral current captures essential features of the horizon-induced decoherence mechanism identified by Danielson, Satishchandran, and Wald (DSW) in the limit of large holding time $T$. Our analysis suggests that the effective dynamics of the system undergoing decoherence in the DSW setting retains non-Markovian features. Our approach also offers a glimpse into the possible role of quantum events in the dynamics underlying horizon-induced decoherence.

We investigate spin-resolved momentum distributions and phase vortices in multiphoton electron-positron pair production within a modified two-level model. This model retains the diagonal spinor inner-product terms neglected in the adiabatic approximation, thereby inducing spin-resolved transverse asymmetries in the momentum distribution. For a circularly polarized pulse, the handedness determines the winding direction of the quantized vortices, whereas for a linearly polarized pulse, the phase distribution exhibits nodal lines rather than quantized vortices. For two time-delayed circularly polarized pulses, the time delay introduces a relative phase that governs the multiphoton interference, which in turn drives the vortex evolution in each spin configuration. These results demonstrate that pulse polarization and time delay enable coherent control over vortex topology in pair production.

We theoretically investigate the interplay of topology and localized non-Hermiticity in a finite Su-Schrieffer-Heeger chain characterized by non-Hermitian potentials at its boundaries. By tuning the boundary gain and loss parameters, we exploit the finite-size hybridization of two mid-gap topological edge states to analytically derive the exact coordinates of boundary-induced exceptional points (EPs), $Γ_{\rm EP}=\pm i v^{N}/w^{N-1}$, at which these states undergo coalescence. We demonstrate that dynamically encircling these boundary EPs facilitates a robust, chiral edge state-transfer protocol. Depending on the orientation of the encircling loop, this protocol allows a topological edge state localized at one boundary to be either transferred to the opposite edge with perfect fidelity or returned to its starting position through a double switching process. Importantly, since the non-Hermiticity remains strictly confined to the boundaries, this chiral transport occurs without affecting the energy spectrum of the bulk bands. These results establish a minimal framework for a large-scale topological chiral switch that is experimentally verifiable and capable of being controlled through boundary non-Hermitian driving.

Dense ensembles of nitrogen-vacancy (NV$^-$) centres in nitrogen-rich diamond dephase on the electron spins of the substitutional nitrogen (P1) centres. If the paramagnetic nitrogen is instead converted into NV$^-$ centres, the laser that initializes the sensor also pumps the bath into $m_s$ = 0, a state with no moment along its own axis. Using cluster-correlation-expansion (CCE) calculations, combined with an exact solver for probe-bath exchange and with no adjustable parameter, this paper asks whether such an optically polarized NV$^-$ bath dephases a sensor more slowly than a P1 bath of the same density. The answer is set by the field. In a field along [111], three quarters of the bath centres lie off the field axis, and the moment of their $m_s$ = 0 state along the field grows from 0.04 at 25 G to 0.46 at 300 G and 0.81 at 800 G. At 25 G the polarized bath is therefore nearly silent: at $10^{17}$ cm$^{-3}$ the dephasing time $T_2^*$ of a separately addressed $^{15}$NV$^-$ probe is 112 us, six times the 18.1 us of a P1 bath, and still 2.4 times at 90 % polarization; an ensemble measurement gains a factor of two. At 300 G the advantage over P1 shrinks to 1.4, and at 800 G the polarized bath dephases faster than P1. The field dependence of every bath, P1 included, follows the mean moment of its centres along the field. For the Hahn echo, exchange with on-axis bath centres and bath relaxation ($T_1$ = 6 ms) limit the gain to 1.2 times the P1 value at 25 G. Optical polarization of an NV$^-$ bath at low field therefore offers dephasing times beyond the P1 limit of nitrogen-rich diamond.

A quantum computer could recover the key of any Ethereum account whose public key appears on chain. We prove that no sidechain or bridge that leaves Ethereum's rules unchanged can protect such accounts: their funds must move into a contract whose release condition relies only on quantum-safe primitives. We design \emph{PQ-Vault}, a custody system for unmodified Ethereum combining this vault, a quantum-safe proof-of-stake sidechain whose checkpoints carry compact certificates, and an optimistic dispute protocol. We give the first security proof of compact certificates against quantum attackers and a matching attack: with classically chosen parameters, the guarantee falls from 128 to about 60 bits, and a simple rule restores it. We show that a common seed-update rule in hash-chain proof of stake lets an attacker steer chosen slots and profit from splitting its stake, and give an election whose steering gain and inclusion delay are provably bounded against quantum attackers. Since compressing certificates with a pairing-based SNARK breaks quantum security, we use fraud proofs that need a single signature check. For 65,536 validators, a certificate is 0.8 MB, 260 times smaller than all signatures, and verifies in about 20 ms; the vault accepts a checkpoint for about 420,000 gas.

Kelvin waves carry energy along vortices, but their resonant interactions contain information that is absent from the linear spectrum. We identify a geometry that exposes this information on a vortex surface in four spatial dimensions. Perpendicular incoming waves cancel the complete local-area four-wave coupling, leaving the finite nonlocal interaction mediated by the surrounding fluid. This interaction restores conversion at generic wave-number ratios, yet changes sign and vanishes at a selected ratio while momentum and frequency remain exactly matched. Matching to Gross-Pitaevskii (GP) theory, including the microscopic core response, establishes a zero of the full coupling at every sufficiently small nonzero wave number, with ratio tending to $λ_*\simeq1.469$. Finite-grid GP coefficients exhibit a sign reversal for the same resonant quartets. Separate coherent-mixing calculations and weak-probe spectra connect the coupling sign to the generated-wave phase and the ordering of reflection-even and reflection-odd modes. The resulting suppression removes a leading channel for changing propagation directions without changing the paired wavelengths. These results isolate a nonlinear effect of the surrounding flow that local tension misses, providing a microscopic benchmark for vortex-wave theories and a starting point for studying angular redistribution beyond the Kelvin spectrum.

The solution of combinatorial optimization problems by means of quantum annealing is based on the preparation of an equally superposition state. Such superposition is crucial to the associative memory problem of correctly recalling patterns. In this paper, we study the alignment of the amplitudes of stored states in memory using the proposed auxiliary Hamiltonian, which is switched off at the end of evolution. The results of the algorithm execution were obtained both by numerical modeling and by the perturbation theory method, which made it possible to obtain the dependences on physical parameters in explicit form. As examples, systems of two and three qutrits, represented by spins S=1, are considered. Since the Hamiltonian is expressed in a univer-sal form through projectors onto states stored in memory, it can be used for other quantum sys-tems (platforms).

A circuit parameter can change measured features without changing their projected Gaussian kernel. We characterize this lost dependence and distinguish recovery by metric design from nonlinear feature expansion. With analytic feature coefficients, a fixed finite data basis affinely independent on the input domain, a fixed positive definite metric, and fixed bandwidth, the coefficient Gram matrix determines all-input kernel equivalence, global coordinate inactivity, and generic differential rank. An exact four-qubit family exhibits a sharp boundary: diagonal metrics give rank two, dense metrics reach but cannot exceed three, and no fixed affine expansion crosses this ceiling. One appended nonlinear scalar coordinate suffices for rank four and is minimal when the original features are retained. A single pairwise product achieves this with an explicit nondiagonal metric; a scalar sum of two products achieves it with a diagonal metric. Both use existing ideal local means. Exact certificates establish ranks in 54 selected circuit/readout settings. Matched finite-shot comparisons show that minimal representation size need not give the best sensitivity among the tested designs. Under a factorized measurement distribution, conditional product estimation cannot increase variance at a fixed design. Execution audits further separate kernel identifiability from compiled cost.

Selecting an effective quantum compiler configuration requires coordinated decisions over both hardware targets and compiler settings, with the ultimate goal of improving circuit execution fidelity. Existing SOTA approaches typically decompose this problem into two sequential stages: a device is chosen first, after which compiler options are tuned on that device through RL-based search. This bottom-up strategy can be fundamentally limited by its initial device decision, since a poorly matched backend may constrain the best fidelity achievable regardless of how effectively later compiler options are optimized. In contrast to classical compiler tuning, where the search space is often prohibitively large, the configuration space of quantum compilers remains manageable enough to support exhaustive search. Consequently, rather than repeatedly searching from candidate configurations, one can derive reusable configuration knowledge from offline oracle results and apply it directly to new circuits. In this paper, we introduce a top-down configuration-selection paradigm and build QuOPTBench, an exhaustively searched benchmark containing oracle configurations for 268 quantum circuits. We first study whether LLMs can directly infer suitable configurations and evaluate ten representative LLMs. The results reveal that vanilla LLMs remain far from the oracle. We then employ an LLM to extract transferable rules from sampled circuits governing configuration selection. Using these rules together with predictors trained on the enumerated configuration data of the sampled circuits, we design QuTOP, a rule-guided ML framework that performs fast configuration selection without iterative online search. Across our evaluation, the distilled rules consistently strengthen LLM-based selection, while QuTOP provides the strongest overall balance between solution quality and selection latency among the baselines.

Quantum Fisher information (QFI) is a fundamental quantity in quantum information and quantum mechanics, and evaluating it in various physical systems has become an important research topic. However, its evaluation in large systems still faces many challenges. Hereby we propose an ancilla-based protocol for evaluating the QFI of large systems and establish the conditions under which this protocol can ``perfectly'' evaluate the QFI in theory. As a demonstration, the protocol is applied to quantum circuits to evaluate the QFI of the Greenberger-Horne-Zeilinger state.

Quantum circuit optimization is a key step toward the efficient execution of quantum algorithms. Template matching has emerged as one of the dominant approaches for simplifying quantum circuits, yet it confronts the intrinsic challenge of accommodating gate commutativity. The state-of-the-art template-matching algorithm relies on a directed acyclic graph (DAG) representation. While this DAG-based technique handles gate commutativity satisfactorily, it fails to preserve the local connectivity inherent to quantum circuits, thereby leading to relatively high matching complexity. In this paper, we introduce a hypergraph representation (HG), a commutativity-aware representation that collapses commuting gates into a single super-node while retaining all local connectivity. This enables matches to be extended locally without revisiting the rest of the circuit, with incremental updates limited to the immediate neighborhood. Experimental results demonstrate that our HG matcher achieves 11--606x speed-up over the DAG-based implementation in Qiskit (Iten et al., 2022) on both random and arithmetic benchmarks, while maintaining the same optimization quality. The acceleration increases with circuit size, confirming that preserving locality and connectivity is the key to scalable quantum circuit optimisation.

We derive sufficient criteria that guarantee convergence of open quantum system dynamics to a unique long-time state independent of the initial conditions. We refer to this behavior as complete relaxation. Focusing on systems described by Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equations on finite-dimensional Hilbert spaces, our approach uses only elementary mathematical arguments. For autonomous systems, we recover three previously derived relaxation criteria, which can be expressed as algebraic conditions on the Lindblad operators and the Hamiltonian entering the GKSL equation. For periodically driven systems, we obtain a new criterion involving a similar algebraic condition and a local continuity requirement on the time-dependent GKSL generator. This result implies an earlier criterion for complete relaxation formulated in Ref. [J. Phys. A 52, 43LT01 (2019)]. We also discuss implications of our approach for periodically modulated classical master equations, as well as extensions to driven systems without a periodicity constraint.

A ligand can adopt multiple conformations within the same binding site, and these conformations can interact differently with the surrounding protein. Multiconformer modeling must therefore determine which candidate conformations to retain and what occupancies to assign to them. An established automated approach uses mixed-integer quadratic programming (MIQP) with hard occupancy and conformer-count limits for this selection. Here, we reformulated conformer selection as a quadratic unconstrained binary optimization (QUBO) problem with finite penalties and discrete occupancies. We solved the QUBO using a quantum-classical hybrid solver. We compared this workflow with the MIQP-based qFit-ligand workflow across 83 paired X-ray ligand entries using the same experimental inputs and the same qFit-ligand processing protocol. For each entry, both final models were evaluated against the same composite-omit map generated from the common input structure before the two workflows diverged. Quantum-qFit produced higher ligand-region real-space correlation coefficients (RSCC) in 62 entries 74.7% and lower occupancy-weighted torsional strain in 66 entries 79.5%. Similar directional trends remained in the 28 entries with matched final conformer counts. The molecular Electron Density for Individual Atoms score (EDIAm) decreased in most entries. This result shows that higher regional map agreement did not necessarily correspond to stronger atom-level density support. Overall, the results show that the conformer-selection formulation can change which ligand states are represented from the same experimental data and provide a QUBO framework for studying multiconformer ligand selection.

Quantum Multi-Programming (QMP) enables the simultaneous execution of quantum circuits from multiple users on a single quantum chip in cloud quantum computing services. However, QMP is vulnerable to crosstalk attacks, in which a malicious user deliberately induces crosstalk to disrupt other users' computations. As a countermeasure, prior work has proposed the use of buffer qubits, which remain idle and are allocated between quantum circuits to suppress the effect of crosstalk. Nevertheless, to the best of our knowledge, such countermeasures have not been publicly reported in production quantum cloud software. In this paper, we extend the QMP of OQTOPUS, open-source software that is already in production use for operating real quantum computers, with a buffer-qubit-based circuit allocation method. Experiments on a real device characterize the attack effect in terms of energy relaxation and dephasing, showing that observable degradation appears in dephasing characteristics of qubits adjacent to the attacker circuit. Based on this result, we release the proposed method as part of OQTOPUS and confirm that the buffer qubits are correctly reserved around the allocated circuits.

Motivated by a recent experimental work $[\href{https://arxiv.org/abs/2608.20327}{\text{arXiv:}2608.20327}]$, we theoretically investigate the nature of phase transitions in a trapped dipolar quantum gas upon tuning the contact interaction strength and dipole orientation. Using extended Gross-Pitaevskii simulations including thermal and quantum effects, we map the phase diagram comprising unmodulated superfluids, triangular droplet arrays, and stripe states. We further characterize the order of the transitions separating them through imaginary-time hysteresis analysis. The unmodulated-to-modulated transition evolves from discontinuous to continuous with increasing dipole tilt before becoming discontinuous again at large tilts. The degree of continuity is further affected by particle number, temperature, and confinement. While continuous behavior generally correlates with the emergence of stripe states, this correspondence is not systematic, and finite-size effects also influence the continuity of the transition. The triangular-to-stripe transition is found to be discontinuous at small contact interaction strengths and becomes increasingly continuous upon approaching the unmodulated-to-modulated phase boundary. Our results reveal a tunable transition order in finite dipolar quantum gases and provide guidance for its experimental investigation.

Quantum batteries can outperform their classical counterparts through collective quantum effects, yet the conditions enabling such advantage remain unclear. Using a generic class of free-fermionic chargers we prove that global operators are insufficient for scalable superextensive charging and that a cumulative hierarchy of many-body operators is required, with the structure of the battery determining the degree of advantage. This is obtained by relating the charging power to the norm of the commutator between the battery and charger Hamiltonians and deriving an upper bound only capturing noncommuting terms. Moreover, we revisit the concept of participation number and propose an effective definition that accounts for the relative strength of the contributing terms, correlating it with the charging power scaling. Not limited to quadratic Hamiltonians, our results establish cumulative locality as a key resource for quantum charging advantage.

We prove a complete modified logarithmic Sobolev inequality with a system-size-independent constant for Chen--Kastoryano--Gilyén Gibbs samplers on one-dimensional spin chain at every fixed positive temperature. The result holds for Hamiltonians with bounded finite-range interactions, including noncommuting and spatially nonuniform interactions. It yields trace and diamond mixing times of order $O(\log N+\log(1/ε))$. The proof establishes complete spatial entropy factorization and absorbs quasi-local errors as conditional relative entropy at the original joint state and reference. The static estimate also yields a system-size-independent CMLSI for the single-site Petz heat-bath and regularised heat-bath dynamics.

We study the minimum persistent memory required to distribute a graph state through a quantum switch. Specifically, consider a central switch that assists $n$ remote users in distributing a graph state, using independently generated user-switch Bell pairs. Since Bell-pair generation is probabilistic, different links generally succeed at different times. When a Bell-pair is generated, the qubits may need to be stored in memory while waiting for other links to succeed. Recently, new protocols have been proposed to reduce this storage overhead by processing and releasing some switch qubits before all Bell links are available. However, these protocols do not characterize the minimum persistent switch memory required at each stage. Moreover, the local-cover method in the state-of-the-art Piecemaker protocol is computationally expensive for general target graphs. In this work, we characterize the minimum persistent switch memory required after any subset of users' Bell links are generated and processed. We then develop an online stabilizer-transition protocol that attains this limit, which can be implemented in polynomial time in the number of qubits $n$. Remarkably, this optimal protocol can provide substantial memory reductions over existing heuristic approaches. In particular, for the path graph $P_n$ over $n$ users, Piecemaker protocol requires at least $\lfloor n/2\rfloor$ qubits of peak persistent memory for \textit{every Bell-links generation order}, whereas under the order $(1,2,\ldots,n)$, our protocol requires only one persistent switch qubit. Finally, the same stabilizer-transition framework also provides a direct forward construction for sequential graph-state generation using the minimum number of quantum emitters, equal to the maximum of the height function.

Quantum low-density parity-check codes now reach encoding rates up to 50% at useful distances. Their checks however are long-range group actions, not local neighbourhoods, and that connectivity has so far been supplied by neutral atoms. Silicon spin qubits offer the same primitive --- coherent transport of qubit blocks --- through electron shuttling, and on microsecond rather than millisecond timescales. They however travel along fabricated tracks rather than free space: permutations an atom array obtains by moving tweezers must here become collision-free motions on a physical lattice. We here present the first code and spin-qubit hardware co-design. We build an architecture whose geometry mimics that of a family of non-abelian groups, broad enough to host codes of excellent parameters: a hierarchy of nested conveyor-belt loops on a plain square lattice of shuttling tracks, in which every group multiplication becomes a rigid, globally controlled motion of whole qubit trains. We call it NeST, for Nested Shuttling Tracks. A code search over the family returns rate-20% mitten codes up to $[[1400,280,\leq 28]]$, and circuit-level simulations including shuttling dephasing give thresholds above $10^{-3}$ with sub-$50μ$s stabiliser cycles, two to three orders of magnitude faster than neutral-atom implementations. Via extrapolations, we estimate that this largest code may reach a logical error probability per qubit per round of $10^{-14}$, assuming a ten-fold improvement on early shuttling demonstrations, with other physical errors at p=0.1%. Logic is compatible with NeST too: for the [[150,30,10]] code we build a code-surgery gadget in which every qubit again moves only by rigid belt motions, at no qubit cost and a 29% increase in gate layers. This demonstrates that ultra-low-overhead fault tolerance and a fast clock speed are not competing goals, and that silicon spin qubits can supply both.

We demonstrate a hybrid quantum-classical approach for exploring ground-state manifolds of maximum independent set problems, in which quantum hardware supplies the initial solutions and an entirely classical post-processing algorithm expands them, increasing the solution diversity of quantum hardware measurements by up to several orders of magnitude. Quantum optimization devices, while capable of generating high-quality solutions, can suffer from fundamental sampling limitations. This is particularly problematic for applications that strongly depend on a large variety of uncorrelated optimal solutions. We apply the Houdayer cluster update algorithm to systematically expand quantum-generated solution sets through classical post-processing. We validate our approach on a test bed of 43 problem instances from QuEra's Aquila analog annealing device, achieving diversity amplification factors, defined as the increase in the number of distinct solutions at a given set size, of up to 11923x with a median of 24.3x across different problem scales and hardness parameters. Because exact ground-state degeneracies are known for these instances, the recovered fraction of the manifold can be measured rather than bounded: post-processing recovers a median of 21% of the ground-state manifold, and provably all of it for six instances. We also demonstrate that, in some cases, the classical post-processing can discover independent sets larger than those found by the quantum hardware, thus improving on solution quality and not just diversity. While the method is non-ergodic and cannot guarantee complete manifold coverage, it consistently discovers a larger number of high-quality, and in some cases strictly better, configurations than quantum sampling alone. This work demonstrates how simple classical post-processing can enhance the utility of quantum optimization results.

Long-range interactions in many-body quantum systems give rise to a wide range of dynamical phenomena, from collective dynamics well described by integrable mean-field models with symmetric all-to-all couplings, to fast scrambling of quantum information from disordered long-range interactions. Here, we investigate scenarios in which both regimes emerge within a single deterministic, translation-invariant XY spin model with long-range couplings. We consider a sparse powers-of-two (PWR2) graph, where each spin interacts with a logarithmic number of neighbors, and a power-law-decaying model. By altering the initial state via local perturbations on a completely symmetric state, we show that the dynamics changes from collective to scrambling as witnessed by bipartite and multipartite entanglement measures. We characterize this collective-to-scrambling crossover using Lyapunov exponents in the semiclassical regime, and show that the spectral properties of the coupling graph adjacency matrix provide a very efficient tool to predict the onset of fast scrambling. Our results offer a unified framework for controlling the switch between collective and scrambling dynamics in a setup accessible in experiments with neutral atoms in cavities or in tweezer arrays.

Trapped-ion, neutral-atom, and circuit QED quantum computers naturally enable coupled qubit-boson simulations. Boson-fermion interactions arise in quantum field theory, where renormalization is required to obtain finite results. We study one of the simplest examples of a coupled fermion-boson system, the static Yukawa model, on the QSCOUT trapped-ion system. We use similarity renormalization to express the same physics in terms of effective particles described by different values of the renormalization parameter $s$. This enables us to map data taken in the window of bosonic occupancy that is experimentally accessible to larger occupancies of distinct effective particles. We use this to study strongly coupled, high-occupancy regimes despite limited readout ranges. Using a trapped-ion qubit-boson device on Sandia National Laboratories' QSCOUT platform, we demonstrate the time evolution of the static Yukawa model.

Identifying the quantum signatures of classical chaos remains a central question in quantum physics, and quantum scrambling provides a new perspective on this correspondence. We study two distinct limits of the same model to examine how the correspondence between chaos and scrambling changes across different regimes. The thermodynamic-limit anisotropic Dicke model exhibits a close correspondence between chaos and scrambling, whereas this correspondence breaks down in the large-frequency-ratio limit of the anisotropic Rabi model (ARM). The contrasting chaotic behavior in the two limits originates from the different numbers of classical degrees of freedom, whereas their similar scrambling behavior stems from eigenstate delocalization. This implies that, in the large-frequency-ratio limit, eigenstate delocalization alone is insufficient to qualify the ARM as a classically chaotic model. This finding suggests that identifying chaos in quantum systems requires jointly considering the classical degrees of freedom and eigenstate delocalization.

Early studies on the Dicke model linked superradiance to quantum chaos, whereas later anisotropic Dicke and Rabi studies reached apparently conflicting conclusions. We resolve this tension by distinguishing global chaos from local instability. Along the isotropic Dicke path, a sweep at fixed low excitation energy crosses both the superradiant boundary and a nearby chaotic window, explaining the reported correlation. However, the anisotropic Dicke model can be chaotic in the normal phase and regular in the superradiant phase, making superradiance neither necessary nor sufficient for global chaos. A fidelity out-of-time-order correlator (FOTOC), in contrast, probes the local stability of the stationary point selected by the initial wave packet. The superradiant transition destabilizes the origin, whereas a change in anisotropy can restore its stability and create displaced saddles. Wave packets centered at these saddles exhibit exponential FOTOC growth even on a classically regular Dicke energy shell with Poisson statistics. This local sensitivity also enables quantitative spectroscopy: combined with the topology of stationary points and local density of states relations, FOTOC dynamics reconstructs the absolute amplitudes of spectral singularities in both models without fitting the density of states.

Structured light provides a route to controlling quantum materials not only through its polarization, but also through its spatial profile and orbital angular momentum (OAM). We develop real space theories of a Weyl semimetal driven by a vortex beam and show that optical OAM generates highly localized Floquet vortex states with pronounced circulating photocurrents. Exploiting cylindrical symmetry, we derive a Bogoliubov-de Gennes-like radial equation that resolves the states by angular momentum and reveals their evolution between the light-dressed Weyl cones. For Laguerre-Gaussian beams, the spatially varying drive produces strong hybridization between localized vortex states and bulk states. We complement this continuum description with a Wilson-lattice formulation that retains the full two-dimensional spatial structure and enables direct calculation of local photocurrents. Both approaches consistently identify OAM-induced vortex states localized around the beam axis. The lattice calculation further shows that these states support substantially stronger circulating current densities than the more extended surface states, with the largest current densities associated with the most strongly localized, low-angular-momentum vortex modes. Our results establish optical OAM as a tunable control parameter for creating and manipulating localized current-carrying states in Weyl systems and provide a real-space framework for studying photocurrents generated by spatially structured light.

Phase transitions (PTs) in quantum many-body systems offer a powerful route to manipulate the performance of quantum batteries (QBs). Here, we investigate an anisotropic Dicke QB with Kerr nonlinearity, focusing on the role of PTs in the charging process of the QB system. By analyzing how the Kerr nonlinearity reshapes the cavity level-spacing structure, we find that multiple near-degeneracies emerge at specific nonlinearity strengths. Away from the region of multiple near-degeneracies, the stable stored energy is governed primarily by the ergodic-nonergodic transition (ENET), whereas within this region it is controlled by first- and second-order dissipative phase transitions (DPTs). We employ Liouvillian spectral theory to quantify the critical slowing down associated with the DPTs, and use the Wigner function to characterize the properties of the cavity field in the vicinity of criticality. We optimize the charging process via reinforcement learning (RL) and reveal the physical mechanism underlying performance enhancement from the perspective of ergodic and nonergodic phase dynamics. Our results offer a feasible pathway for manipulating and optimizing quantum battery performance based on intrinsic PT behaviors.

We give a bounded-error quantum polynomial-time algorithm for finding hidden parabolic subgroups of $\mathrm{GL}_n(R)$ over any effectively presented finite chain ring $R$. We call auxiliary group elements or subgroups used to extract information through oracle queries \emph{probes}. For chain length at least two, elementary abelian socle probes first recover the complete flag modulo the maximal ideal. When the residue field has size $q\ge3$, we reconstruct the flag recursively, lifting rank-one terminal members one digit at a time. The intermediate digits reduce to abelian hidden subgroup problems, while the final digit is a finite-field multiple-shift problem solved using learning from subset and Fourier sampling. For $q=2$, where distinct flags can have the same stabilizer, we instead lift the conjugate parabolic subgroup through the congruence filtration. A final linear system determines it modulo normalizer directions. The algorithm outputs generators with probability at least $1-ε$ in time $\mathrm{poly}(n,\log|R|,\log(1/ε))$. Consequences include $\mathrm{GL}_n(\mathbb{Z}/N\mathbb{Z})$ for every $N\ge2$ and, with an explicit maximal-order presentation, $\mathrm{GL}_n(\mathcal{O_K}/N\mathcal{O_K})$ for number fields $K$.

We advance the compact dressed Hamiltonian (CDH) framework to simulate the dynamics of open quantum systems strongly coupled to structured bosonic environments. The CDH approach combines reaction-coordinate mapping with a polaron transformation, incorporating strong system-environment hybridization into a dressed representation before truncating the collective bosonic mode. As a result of this truncation, dynamical features are captured with substantially fewer states than in the original representation. The residual environment is treated using a weak-coupling Markovian quantum master equation. We benchmark the method for spin-boson-type models including a single spin, coupled spins, and spin ensembles, considering both resonant and off-resonant regimes and weak to strong system-bath coupling. Comparisons with hierarchical equations of motion and converged reaction-coordinate calculations demonstrate that the CDH representation systematically approaches the reference dynamics with a compact Hilbert space, accurately reproducing oscillation frequencies, relaxation behavior, and long-time populations over a broad parameter regime. The method further captures cooperative phenomena, including bath-mediated interactions, synchronization between spins, and signatures for collective emission. Beyond efficient time propagation, the CDH framework provides direct access to the spectrum and eigenmodes of the Liouvillian. We demonstrate that slow dynamical modes converge rapidly in the CDH representation, enabling identification of relaxation timescales without fitting time-dependent observables. As a whole, the CDH framework provides an efficient and physical description of strongly coupled open quantum-system dynamics.

Photonic and qubit-based (digital) approaches to quantum computing are largely regarded as separate paradigms. This article aims to bridge these paradigms by developing a method for mapping quantum-optical systems onto qubit-based quantum circuits. The key ingredient enabling this mapping is the introduction of a truncation of the Fock space describing single-mode optical states. Within this framework, representations of basic photonic operations are developed, including the phase-rotation operator, the displacement operator, the squeezing operator, and the beam splitter. Explicit quantum circuit constructions are provided for Fock-space truncations of dimension $N=2$ and $N=4$. We discuss benchmarking of the implemented operations and identify the regime of applicability and the limitations of the proposed method. The presented results can be used to simulate quantum optical circuits on qubit-based quantum computers, with special relevance to Gaussian Boson Sampling in the low-photon-number regime. To demonstrate the practical applicability of this approach, we complement the theoretical framework with a Python-based quantum programming tool CO$Φ$ that compiles Blackbird quantum-optics programs into qubit-based OpenQASM circuits using a truncated Fock-space encoding. The compiler is available on GitHub at https://github.com/Quantum-Cosmos-Lab/cophi.

Cloud-accessible quantum computing has made heterogeneous Quantum Processing Units (QPUs) available through provider platforms that differ in qubit technology, calibration state, queueing behavior, and pricing model. This heterogeneity makes execution management a quantum-engineering concern: a quantum circuit may be executable on several backends, but the resulting cost, latency, fidelity, and reproducibility depend on backend selection and on how measurement shots are allocated. This paper presents the Quantum Broker, an open-source and provider-agnostic framework for Quality-of-Service-aware quantum execution management. The framework operationalizes shot-wise distribution by exploiting the statistical independence of quantum measurement shots to dispatch a single circuit across multiple heterogeneous QPUs according to user-defined constraints and optimization objectives. It combines a modular execution architecture, interchangeable backend-profiling strategies, and the Quantum QoS Specification Language (QQSpec), a declarative language for expressing QoS requirements. Dispatch planning is supported by two solver backends: a mixed-integer linear-programming (MILP) solver, and a nonlinear dual-annealing solver. Experiments on benchmark quantum circuits and noisy simulator backends show that the Quantum Broker can produce feasible QoS-aware dispatch plans under heterogeneous backend conditions and can improve QoS satisfaction with respect to single-backend and naive multi-backend baselines. The results also expose a practical trade-off between planning time and dispatch quality, with the nonlinear solver producing higher-quality allocations at increased computational cost. Overall, the Quantum Broker provides an extensible execution-management layer for engineering portable, reproducible, and QoS-aware quantum software over fragmented quantum cloud infrastructures.

Clean, interacting, periodically driven systems are believed to thermalize to featureless, infinite-temperature states that preclude the formation of stable ordered states. Here, we show stable quantum order, distinct from prethermal order, and its phase transitions in the ground state of the average-energy operator. Decomposing the time evolution into geometric and average-energy dynamics, we apply Geometric Floquet theory to identify the Floquet ground state. We derive a general variational principle to compute the Floquet ground state in large interacting periodically driven systems, and use it to develop a matrix product state algorithm. In driven nonintegrable chains of more than 100 interacting spins, our numerical simulations exhibit a gapped, area-law entangled Floquet ground state in extended parameter regimes; the ground-state manifold can support both dressed equilibrium order (e.g., Floquet antiferromagnets) and inherently nonequilibrium order (e.g., ground-state time crystals). This quantum order is protected by a finite average-energy gap, which closes at phase transition points upon changing model parameters. We decompose Floquet phases of matter into their equilibrium and nonequilibrium elements: whereas the Floquet ground state at any fixed time is a representative of an equilibrium phase of matter, the nonequilibrium content is entirely produced by the drive holonomy and is geometric. Finally, we identify quasilocal counterdiabatic driving as a mechanism for the stability against heating of gapped Floquet ground states in nonintegrable quantum systems, and argue why Floquet ground states evade the Eigenstate Thermalization Hypothesis. Our work enables the study of interacting nonequilibrium matter deep into the many-body regime, and lays the foundations for the engineering of strongly correlated ordered quantum states.

The resource theory of coherence quantifies the quantum properties of states and their role in quantum information processing. Extending coherence theory to ensembles, the natural objects in quantum communication, remains an active research direction, with their operational potential still being explored. In this work, we establish a maximally coherent ensemble in every finite dimension: the continuous ensemble of pure states distributed according to the normalized Haar measure attains the tight upper bound on basis-free relative entropy ensemble coherence. We then prove that ensemble coherence bounds the effective informational advantage of postselective measurements over the Holevo quantity for two equiprobable pure states. Finally, for the qubit B92 QKD protocol, we show that the coherence of Alice's ensemble upper-bounds the secret key rate in the asymptotic regime. These results give ensemble coherence a quantitative operational meaning in quantum communication and cryptography

We investigate the dynamics of two bosons in a tilted one-dimensional optical lattice with both standard and density-assisted tunnelling. The relative sign of the two tunnelling processes strongly affects the Bloch dynamics, leading to distinct reinforcing and competing regimes. We examine how the tunnelling processes generate correlations and find that, in the absence of onsite interactions, the early-time entanglement growth follows the same scaling with the density-assisted tunnelling amplitude. Finite onsite interaction changes this picture by breaking the symmetry between the reinforcing and competing regimes and enhancing the correlation differently in two regimes. This shows how the interplay between the two tunnelling mechanisms can change dyanmics and entanglement in a controlled few-body setting. Particularly, at equal tunnelling amplitudes, the doublon and singlon sectors decouple completely for arbitrary onsite interaction, lattice tilting, and initial state.

Practical security analysis of Coherent-One-Way (COW) quantum key distribution requires optical-device modeling, finite experimental statistics, and security inference to be treated consistently without conflating assumptions. We present a modular observable-level simulation framework organized through the pipeline θ_phys -> p -> O -> S_j(O), in which physical source, channel, receiver, and detector parameters determine detector-resolved event probabilities, a finite-block layer applies an effective dead-time treatment and generates aggregate detector counts, and interchangeable security evaluators act on the same observable record. The framework is verified against analytical optical, virtual-state, and finite-key relations and evaluated against reported experimental COW-QKD operating points. The Kato finite-key calculation reproduces the refined experimentally reported secure-key rates most closely at intermediate distances, with deviations of -1.5% at 50 km and -10.3% at 75 km. Monitoring bright-port decoy counts agree within 0.9-2.4%, while remaining distance-dependent dark-port residual identifies the principal model-sensitive observable of the present physical description. Applying Kato and Azuma-Hoeffding concentration treatments to identical detector records isolates the effect of finite-key statistical inference and shows substantially tighter Kato phase-error bounds for rare-event monitoring records studied here. Holding the Kato evaluator fixed, joint optimization of coherent-state mean photon number mu and receiver splitting fraction t_B increases model-predicted secure-key rate by 7.4-20.2% relative to optimization of mu alone with t_B = 0.3. The framework therefore provides a common computational interface for experimental reproduction, controlled security-model comparison, model-based protocol optimization, and modular adversarial stress testing in COW-QKD.

We design a hybrid quantum-classical computational workflow, combining density functional theory and dynamical mean-field theory, to investigate the electronic properties of CaCuO2, a parent structure of high-temperature cuprate superconductors. Our approach uses a quantum algorithm as an impurity solver that is based on variational quantum compressed time evolution to compute the time-dependent Greens function on an IBM Heron quantum device. Utilizing error mitigation techniques and a Lehmann representation fitting procedure, we extract the density of states from the signal in the accessible time regime. Despite the significant challenges rooted in the residual imprecision of currently accessible NISQ devices, we successfully resolve the characteristic features of the spectral function. However, we find that the required numerical accuracy for full DMFT self-consistency exceeds current hardware capabilities, indicating that practical real-material DMFT applications will necessitate post-NISQ hardware developments.

Geometric phase gates with addressed laser radiation are widely used in trapped-ion quantum computers to drive high-fidelity entangling gates on an arbitrary qubit pair of a larger ion chain. Such programmable connectivity exploits the collective phonons to mediate the desired interaction, while simultaneously achieving robustness to their thermal fluctuations by a careful calibration of the gate time with respect to the laser and vibrational-mode frequencies. Crosstalk errors can arise when the spectator qubits, which should ideally remain idle during the gate, are partially driven by the laser fields. The minimal crosstalk, which is set by the laser beam size on the spectator ions, can be achieved when the addressing beams propagate perpendicular to the ion chain. However, this results in exciting the radial phonons, and can complicate achieving high-fidelities as the ion chain grows due to the so-called spectral mode crowding. In this work, we present the theoretical description of a scheme recently implemented by Faorlin et $al.$. This scheme overcomes these complications by engineering addressable state-dependent forces along the ion-chain with laser beams that propagate perpendicular to it through the use of structured light gradients. In this way, one can excite the axial phonons and avoid the spectral mode crowding, while simultaneously minimizing the crosstalk. We present a detailed derivation of the entangling gate scheme, together with analytical closed-form expressions for the leading contribution to the gate error caused by thermal motional fluctuations and dephasing noise. Our results confirm that such fluctuations account for up to 93$\%$ of the error budget under the operating conditions of the gate implemented by Faorlin et $al.$. We identify target parameters to reduce the motional error from the reported $10^{-3}$ to the $10^{-5}$ level.

The five-qubit Absolutely Maximally Entangled AME$(5,2)$ state, whose every pair of qubits is maximally mixed so that all its information lives in non-local correlations, could in principle serve as a single shared quantum networking resource for teleporting two unknown qubits in parallel (each via its own Bell measurement and Pauli correction). Nonetheless, its hardware implementations remain scarce despite its theoretical importance. Here, we demonstrate parallel teleportation based on a five-qubit absolutely maximally entangled state, AME$(5,2)$, on the superconducting processor ibm_pittsburgh. We construct three-qubit Clifford decoders that extract two Bell pairs using three logical two-qubit gates for each of 60 inequivalent sender-receiver assignments. Using parallelization and classical Pauli frame post-processing, we retain reference-receiver entanglement on both channels after three teleportation rounds. With XY4 dynamical decoupling and the lowest-cost decoder, the final entanglement fidelities are $0.704\pm0.028$ and $0.680\pm0.022$, where uncertainties are pointwise $99\%$ confidence-interval half-widths over eight trials. Their lower bounds exceed the separability threshold of $1/2$. The decoder with lower circuit depth generally retains higher mean fidelity, and XY4 generally improves on XX. These results establish a hardware demonstration of two-channel entanglement transmission through repeated AME-assisted teleportation and provide compact decoding circuits for reconfigurable multipartite communication.

We review and analyse quantum information-theoretic approaches to black hole evaporation that purport to bring us closer to a resolution of the black hole information paradox. Our focus is on the Page-time paradox and on the contribution of the Hayden-Preskill model to understanding information release under the assumption of unitary evaporation. In this model, the black hole is taken to be a finite-dimensional quantum system whose dynamics can be represented by a quantum circuit, and its information-processing and communication abilities are studied. We identify the assumptions underlying this modelling and highlight two key features, fast scrambling dynamics and entanglement as a resource, that underpin the information release in the model. We argue that this reasoning exemplifies a broader change in how information is used in black hole physics, in which quantum information theory now provides a useful operational modelling framework. This application avoids earlier philosophical objections insofar as it is not based on epistemic ignorance and does not regard information as a substance. This line of reasoning has become central to the debate and, as such, warrants greater attention from the philosophy of physics community.

The quantum marginal problem, concerned with the compatibility of local and global properties of a multipartite quantum system, is arguably one of the fundamental questions in quantum theory. In this article we introduce a novel family of inequalities bounding the allowed local spectra of a pure tripartite state. The number of inequalities in this family grows with the dimension of the system. Most importantly, the inequalities hold for arbitrary dimensions. For equal local dimension at most 4, they generate the complete set of eigenvalue inequalities.

The growing demand for high-capacity, fast-charging, and durable rechargeable batteries has intensified the search for advanced electrode materials, with two-dimensional materials offering large surface-to-mass ratios and short ion-diffusion pathways. Here, pristine and Co-doped Janus HfSSe monolayers were investigated as anode materials for Li-ion and Na-ion batteries using first-principles density functional theory. Pristine HfSSe was found to be dynamically stable and exhibited a 0.85 eV band gap, while Co substitution shifted the Fermi level toward the valence-band region. Adsorption of the first Li or Na layer induced metallic behavior, thereby improving charge transport. Co doping strengthened alkali-metal binding, with the most favorable Li and Na adsorption energies changing from -2.6125 and -1.9800 eV to -3.7405 and -3.0529 eV, respectively. Co doping created electron-deficient sites that enhanced Li/Na binding. Co-doped HfSSe accommodated up to four Li layers and three Na layers, increasing the theoretical capacities from 555.43 to 776.19 mAh/g for Li and from 370.29 to 582.14 mAh/g for Na. The average open-circuit voltages were 0.62 V for Li and 0.29-0.30 V for Na, with minimum migration barriers of 0.2153 and 0.1044 eV, respectively. These results identified Co-doped Janus HfSSe as a promising anode material for Li-ion and Na-ion batteries.

We investigate photon-to-axion-like-particle (ALP) conversion in a finite, linearly polarized laser pulse for a single ALP field with simultaneous scalar-type and pseudoscalar-type couplings to photons. Varying the collision angle between the strong pulse and the probe provides a continuous kinematic scan of the resonant ALP mass. For fixed kinematics in this setting, the scalar-type and pseudoscalar-type ALP conversion amplitudes interfere coherently, making both the photon-to-ALP conversion probability and the polarization rotation depend on the difference between the probe polarization angle $α$ and the coupling angle $θ_g$. Conversion is maximal at $|α-θ_g|=90^\circ$, where the polarization rotation vanishes, while the rotation magnitude peaks at $α-θ_g=45^\circ$ modulo $90^\circ$, where conversion is half-maximal. These complementary polarization-angle dependences provide polarization-resolved signatures of mixed scalar--pseudoscalar photon couplings.

We show that several potential-energy functions based on the exponential function $e^{-αr}$, $α> 0$, are either equivalent or identical to the Tietz potential. Some of those potentials exhibit redundant parameters that can be removed without affecting their performance for the description of the vibration-rotation spectra of diatomic molecules.

In single-shot Bayesian multiparameter quantum estimation, measurement incompatibility can increase the minimum joint quadratic loss by at most a factor of two relative to the bound obtained by optimising each parameter separately. Using the generalised Barnum--Knill inequality, we establish the same bound for a wider class of additive losses generated by positive score functions, showing that this limitation extends beyond the standard quadratic setting. To illustrate this result, we consider a broad family of periodic losses, including the sine loss sometimes employed in interferometry, and derive the corresponding incompatibility bound for Bayesian multiphase estimation with arbitrary prior knowledge. We further extend the framework to unbounded losses, such as absolute losses; this also recovers the case of quadratic losses.

We study how the one-dimensional deformation suggested by nonadditive $q$-calculus can be extended to a rotationally covariant quantum model and what observable consequences follow from this extension. We choose a radial extension about a distinguished center in which only the radial derivative is deformed, while tangential derivatives retain their ordinary form. Within this model, we construct self-adjoint frame-momentum operators and derive a rotationally invariant uncertainty bound with a correction proportional to the mean distance from the center. We then adopt a non-negative kinetic Hamiltonian built from these momenta and derive the leading harmonic-oscillator energy shifts for weak deformation. The energy corrections split the levels with different orbital angular momenta that are degenerate in the undeformed oscillator, while preserving the degeneracy associated with rotational symmetry.

We theoretically introduce a quantum-circuit synthesis protocol to realize any $n$-qubit transformation $U\in U(2^n)$, up to a diagonal. The resulting circuit is directly native to and optimal in gate count and depth for systems where bitstring-conditioned rotations with tunable angle and axis, $C^{(n-1)}R(θ,φ)$, form the set of native operations. Subsequently, we suggest how this protocol can be implemented in a few-mode superconducting circuit, and experimentally demonstrate the method for the smallest nontrivial case, i.e., for two qubits. We report an average gate fidelity of 97.6 % for Haar-random two-qubit unitaries up to phase shifts in the computational basis. Importantly, these results suggest that multimode devices, such as those in the multimon or multiunimon families may become competitive with qubit-array networks for general-unitary implementations for qubit counts as low as three.

The exact multi-resolvent hierarchy of dense many-body spectra encodes higher-order spectral-weight correlations, but closing it predictively for interacting Hamiltonians remains a challenge. We introduce the multi-resolvent self-consistency (MRSC) equations, which separate an exact algebraic hierarchy from an approximate finite-parameter closure. The exact Feshbach geometric identity organizes r-resolvent cumulants into a ladder over irreducible vertices Gamma^(r), and the projected hierarchy expresses those vertices as functionals of the cumulants. The closure works in finite parameters: a connectivity basis organizes a general Hamiltonian's seed into class amplitudes, and a causal r-fold Stieltjes representation with a moment-field identity reduce moment matching to a finite-dimensional problem closed at a predictive fixed point. On the free-fermion benchmark the tested exact identities are reproduced and the Faddeeva closure is recovered at r=1. In a blind test on the interacting Ising chain, with the exact two-resolvent data withheld, the Hamiltonian-derived closure predicts the tested probes to 0.35%-0.97%. At the observable level the exact two-resolvent sector supplies a sign-correct, energy-resolved correction to the single-resolvent baseline for the off-diagonal eigenstate-thermalization-hypothesis (ETH) variance, of order one relative to it. Closure errors organize hierarchically: a level-by-level deficit decomposition, anchor measurements of the isolatable terms, and an explicit propagation bound. The same moments further yield a diagnostic chain for the window conditions of local rotational invariance -- an exact drift-kernel identity, a proven single-state identifiability boundary, and a transferability census over couplings and realizations -- a finite-order framework, not a proof of universal emergence.

Thin-film spontaneous parametric down-conversion, due to the relaxed phase-matching condition, generates photon pairs that are extremely broadband in frequency and angle and highly entangled in time/frequency and position/momentum. Here we show that it also provides a very broad orbital angular momentum (OAM) spectrum, which, in contrast to the case of bulk crystals, is decoupled from the frequency spectrum. To demonstrate it experimentally, we generate photon pairs in a $7~μ\mathrm{m}$-thick lithium niobate film and compare them with those from a $500~μ\mathrm{m}$-thick periodically poled lithium niobate crystal under identical pump conditions. The thin-film source exhibits a substantially broader OAM spectrum, with the azimuthal Schmidt number almost 9 times larger than that of the bulk source. On this highly entangled state, we perform quantum-state tomography in selected two- and four-dimensional OAM subspaces, demonstrating high-purity maximally entangled states. These results highlight thin nonlinear films as a promising platform for high-dimensional quantum-state generation with weak spatial--spectral coupling.

The Unruh effect links acceleration to thermalization, providing a relativistic setting for anomalous quantum relaxation. We demonstrate a {\it relativistic} strong quantum Mpemba effect in the Unruh thermalization of a two-level detector coupled to a massless scalar field. For a fixed pair of isospectral initial states, relaxation curves that never cross in inertial motion exhibit a Mpemba crossing above a threshold acceleration. At a higher, precisely tuned acceleration, the initially farther state has zero overlap with the slowest decay mode and relaxes with a faster asymptotic exponential rate. We identify how competition between transition and dephasing channels governs the relaxation spectrum, where sufficiently strong longitudinal coupling enables acceleration to switch the relaxation bottleneck between population and coherence modes. We derive the spectral-switching condition and construct isospectral preparation protocols that eliminate slow-mode contributions within their physical domains. These protocols reveal how coherence can suppress or enhance slow-mode overlap at fixed purity, depending on the underlying spectral structure. Our results establish acceleration as a control parameter for anomalous quantum relaxation, connecting relativistic quantum dynamics with nonequilibrium thermodynamics.

Optimal approximate state conversion is a fundamental task in quantum resource theories, yet existing solutions are largely tailored to specific distinguishability measures and resource theories. We show that every optimal approximate-conversion problem in the three paradigmatic majorization-based quantum resource theories of non-uniformity, bipartite pure-state entanglement, and pure-state coherence reduces exactly to one of only four elementary taut-string constructions. This holds for problems generated by Schur-convex spectral distances and by a broad family of quantum divergences satisfying a natural reduction property with respect to the corresponding equivalence group. The resulting framework encompasses a broad class of physically relevant distinguishability measures, including the trace distance, all unitarily invariant norms, quantum relative entropy, maximal quantum $f$-divergences, and the $α$-$z$ Rényi relative entropies. The increment vector of the corresponding taut string completely determines both the optimal approximation error and a canonical optimal state. Our results establish a common geometric framework for approximate quantum resource conversion, revealing that a broad class of seemingly different optimization problems is governed by the same taut-string geometric principle.

The measured logical error rate of a quantum low-density parity-check (QLDPC) code depends on the decoding algorithm. We develop a framework that certifies non-degenerate maximum-likelihood (ML) decoding outcomes on individual sampled shots under circuit-level noise, providing a common reference for comparing decoders and codes. Upper and lower bounds on the minimum correction cost in the true and competing logical classes establish success, failure, or an undecided outcome. Branch-and-bound search refines these intervals while retaining valid bounds under resource limits. Counting the outcomes bounds the empirical ML logical error rate, with interval width equal to the undecided fraction. Results for two bivariate bicycle codes show that best-first ordered statistics decoding (BF-OSD) tracks the non-degenerate ML benchmark closely while leaving some ML-correctable shots.

Ions possess both center-of-mass motion and internal states, rendering trapped-ion optical clocks susceptible to perturbations of both degrees of freedom, which results in systematic shifts and fluctuations with motional and relativistic origins. We develop a quantum theory that connects these effects to filter functions determined by the employed pulse sequences and show how the interrogation can be tailored to suppress or enhance specific perturbations. Our treatment includes laser frequency noise and motional effects such as recoil and Doppler shifts, micromotion and excess micromotion, as well as state-dependent trap imperfections and accelerations, e.g., caused by Stark shifts. We further account for relativistic effects including time dilation and the mass defect, and show how the same framework can be applied to hypothetical dark-matter signals. By considering ensemble-averaged phases and their variances, we characterize both systematic shifts and fluctuations, while asynchronous operation relative to the Paul-trap drive allows motional fluctuations to average down between runs. Our results provide a unified framework for characterizing and controlling the systematic and statistical contributions that determine the trueness and precision of trapped-ion optical clocks.

The Fer expansion writes the propagator of a driven quantum system as an ordered product of exponentials, each generated by the time integral of an effective Hamiltonian that governs the evolution left over by the previous factors. It can be stopped after finitely many factors whenever this leftover evolution is known in closed form, for instance when the effective Hamiltonian commutes with itself at all times, or precesses about a fixed axis with constant angular velocity. For $\mathfrak{su}(2)$, in any representation, from a qubit to a spin of any size, we resum the Fer recursion into a closed map on curves in $\mathbb{R}^3$. We prove that, for a real-analytic drive, in both cases the expansion stops beyond the first factor only trivially, when the first exponential is already exact.

We show that, starting from the same state, optimal driving can sometimes reach a colder (or hotter) target in the same amount of time while dissipating less energy, or equivalently dissipate the same amount of energy in a shorter time. We study this counterintuitive phenomenon in the slow-driving regime of an open quantum system, where we name it Near-Equilibrium Anomalous Tradeoff (NEAT). We establish necessary conditions for its occurrence and show its underlying geometric origin. While NEAT is reminiscent of the well-known Mpemba effect, the two phenomena are distinct in general. We demonstrate NEAT in an exactly solvable qutrit model, as well as for d-dimensional birth-death dynamics with independently controlled energy levels. Finally, we show how NEAT can improve the performance of Carnot engines.

We establish sufficient conditions for two-way local quantum-channel stability in classical $\mathbb Z_2$ lattice gauge models with spins on $m$-dimensional cells of a $d$-dimensional lattice. Each interaction multiplies the spins on the boundary of an $(m+1)$-cell. This family, defined on the full spin Hilbert space without a Gauss-law constraint, includes the Ising model at $m=0$ and the magnetic sector of the toric code at $m=1$. The low-temperature proof combines two ingredients: locally indistinguishable flat sectors and extended magnetic defects of dimension $d-m-1$. For $1\le m\le d-2$, sufficiently weak local classical perturbations at sufficiently low positive temperature preserve equivalence to the canonical flat ensemble. No internal or gauge symmetry is required of the perturbation. For weak noncommuting perturbations, we prove the same conclusion in a smaller sufficient window by reducing the diagonal probabilities to a weak classical interaction and recovering the coherences with a local channel. The conversion channels use product ancillary inputs, have polylogarithmic causal radius, and achieve any prescribed inverse-power whole-system trace-norm error. Sufficiently high-temperature states are instead two-way equivalent to a product state. Independent finite-dimensional onsite systems can be included with weak local couplings. An optimized covariance between two distant neighborhoods of parallel $m$-tori is nonincreasing under one-way local conversion and invariant under two-way conversion. Its values $\mathcal F_m=1$ and $0$ distinguish the proved low- and high-temperature domains without a protecting symmetry. These sufficient domains do not determine the full phase diagram.

Quantum amplitude estimation offers a theoretical quadratic speedup over classical Monte Carlo methods for financial derivative pricing. However, extending gate-based algorithms to path-dependent barrier options has historically been hampered by sequential path discretization, where tracking price paths across $d$ monitoring dates incurs a linear escalation in qubit footprint and gate depth ($\mathcal{O}(d)$), posing severe coherence challenges for near-term quantum processors. In this work, we present a constant-depth quantum pricing framework that fundamentally eliminates the temporal dependency of barrier monitoring. Leveraging the Brownian reflection principle and Girsanov theorem, we project the continuous supremum dynamics onto a static bivariate joint distribution of the terminal price $S_T$ and running supremum $M_T$. This allows decoupling dynamic boundary checks into a static bivariate oracle comprising two parallel comparators and a dual-controlled rotation gate. We prove this architecture reduces circuit depth and comparator complexity from $\mathcal{O}(d)$ to an invariant $\mathcal{O}(1)$, while supporting discrete monitoring via zero-quantum-cost boundary corrections. Transpilation benchmarks for daily monitoring ($d = 252$) show our framework slashes physical CNOT count by 98.59% (from 2262 to 32) and compresses two-qubit depth by 98.02% (from 1514 to 30 layers). Under a realistic 127-qubit IBM Eagle noise model, the shallow circuit achieves a 7.84% relative valuation error with M3 readout mitigation. Finally, the framework seamlessly extends to nonlinear exotic payoffs lacking analytical solutions, establishing a noise-resilient pathway toward practical quantum advantage in computational finance.

Unstructured meshes are widely used in modelling and simulation in Computational Fluid Dynamics (CFD) due to their geometric flexibility. However, they require an efficient block encoding circuit describing the system. Here, we present a new block encoding methodology for unstructured mesh solvers based on decomposing the system matrix into a sum of 1-sparse matrices. This block encoding is engineered to reduce subnormalisation even in the absence of structure by hiding the contribution of large matrix elements behind others. We investigate three methods of 1-sparse decomposition. Our circuit constructions can optionally take advantage of limited matrix bandwidth and repeated values. For example we consider digitisation (reduced precision), where the number of multiplexed rotation gates is equal to the number of non-unique matrix entries. We evaluate our methodologies using 2D and 3D CFD matrices for unstructured aerofoil meshes, structured cavity, and duct meshes, with and without matrix preconditioning. Our results show that we are able to achieve a block encoding with a near constant subnormalisation factor as the number of matrix preconditioning infill levels increases. This significantly reduces the subnormalised condition number and, in one case, reduces the degree of the QSP polynomial approximation to $1/x$ by 100,000. Reduced precision digitisation is shown to become more effective as the number of preconditioning infill levels is increased and, in one case, reduces the number of multiplexed rotations from 2,785,576 to 546 whilst maintaining an infidelity of $2.6\times10^{-5}$ relative to the classical solution. The effect of digitisation on QSVT solutions is demonstrated using 2D and 3D unstructured mesh aerofoil cases. Due to its flexibility and automatic applicability, we believe our 1-sparse decomposition block encoding can offer benefits to other quantum applications.

Dipolar Bose--Einstein condensates (BECs), i.e., BECs with long-range dipole-dipole interactions (DDI), exhibit extraordinarily rich physics and serve as a versatile experimental platform for exploring exotic quantum states of matter. Within the mean-field framework, a dipolar BEC can be described by the Gross--Pitaevskii (GP) model with a DDI term. Its stationary states consist of the ground state, which minimizes the GP energy functional under the normalization constraint, and excited states, which are higher-energy critical points that typically correspond to constrained saddle points. Excited states encode collective excitation modes and play a key role in the dynamical stability and quantum phase transitions of cold-atom systems. However, in contrast to the extensively studied ground state, they remain far less explored numerically, especially in dipolar systems. In this work, we develop a numerical method based on the constrained gentlest ascent dynamics (CGAD) that systematically computes excited states of dipolar BECs by stably targeting constrained saddle points with any prescribed Morse index. Specifically, a semi-implicit sine-pseudospectral discretization with an orthonormalization correction step is adopted, and the nonlocal DDI terms are evaluated efficiently and accurately via the nonuniform fast Fourier transform (NUFFT). The resulting scheme is applied to one-, two-, and three-dimensional dipolar BECs, enabling a detailed numerical investigation of their excited states. Remarkably, our simulations reveal that excited states can persist even in regimes where the ground state of the condensate becomes mean-field unstable. This work provides a computational framework for studying excited states in dipolar quantum gases and offers insights for future theoretical and experimental investigations.

Using contour-integral representations of the permanent and of the Hafnian, we turn the computation of their moments for random matrices into a replica calculation, analogous to that of the moments of the partition function of a mean-field spin glass. For the $2k$-th moment of $N\times N$ matrices with independent entries, the dominant saddle point is replica symmetric for $k>2$, and we obtain in closed form the exponential growth rate, the prefactor and the first $1/N$ correction, in agreement with exact enumerations. The growth rate depends only on whether the entries are real or complex; higher cumulants affect only the prefactor and the $1/N$ term. At $k=2$ the replica-symmetric solution becomes unstable, separating a power-law bulk of the distribution from a large-deviation tail, which we compute. The results apply to boson sampling with single photons and with squeezed light.

Atmospheric turbulence and channel loss represent the primary limiting factors in ground-to-satellite quantum communication systems, yet their joint impact remains insufficiently characterized across diverse operational conditions. In this work, we develop a comprehensive and open atmospheric channel model for quantum optical links along ground-to-satellite paths, integrating altitude-dependent molecular and aerosol absorptions. The model is validated with available data from missions such as Micius and Hispasat, including a secondary viability assessment for a hypothetical Starlink-based quantum communication network, where we evaluate the predicted channel behavior in terms of single-photon transmittance and power balance, alongside the channel capacity of the link for uplink and downlink exclusively. Our comparative analysis demonstrates the ability of our channel model to predict real data under simple atmospheric behavior assumptions, which offer practical guidelines for the design and optimization of future quantum satellite missions.

Concatenation of quantum repeater nodes has been proposed as a means to distribute entanglement efficiently across future long-distance networks. Here, we demonstrate a trapped-ion repeater node that establishes photonic entanglement over a 17 km fiber traversing a city, moving beyond laboratory-only prototypes. The node comprises two atomic ions coupled to an optical cavity. First, a detailed characterization is performed of the long fiber channel and of ion-photon entanglement distributed across it. Next, a repeater-node protocol is implemented, achieving entanglement between a local photon and a remote photon with a Bell-state fidelity of $81.6^{+1.9}_{-1.4}\%$. These results demonstrate that trapped-ion repeater-node technology can operate over existing city-scale fiber infrastructure and represent a step toward distributed quantum repeater networks.

High-fidelity entangling gates are essential for quantum information processing. In transmon circuits, higher excited states provide additional pathways for engineering interactions within the computational subspace. Here we demonstrate controlled-Z (CZ) gates that exploit two noncomputational states, $\ket{02}$ and $\ket{20}$, through selective Floquet coupling. The nontrivial parametric modulation can activate both auxiliary transitions from $\ket{11}$ while suppressing the leading exchange between $\ket{01}$ and $\ket{10}$. Based on this approach, we develop two gate protocols: a nonadiabatic round trip through a bright auxiliary superposition and adiabatic evolution along a zero-energy dark state, both achieving average gate fidelities above $99.99\%$ in numerical simulations. Control of the modulation phase further extends the bright-state protocol to conventional and unconventional geometric CZ gates. Effective-model simulations show that unconventional control improves tolerance to residual $ZZ$ coupling and static qubit-frequency offsets relative to conventional control over the parameter ranges examined. Simulations including neighboring spectator qubits show that the original nonadiabatic bright-state and adiabatic dark-state CZ protocols retain high gate fidelities. This framework offers new routes toward the experimental realization of CZ gates and their geometric implementations.

We theoretically investigate narrowband nonreciprocal transmission in a Doppler-broadened five-level M-type atomic medium. After Doppler averaging, the M-type system retains a narrow near-resonant electromagnetically induced transparency window that is narrower than that of a standard three-level $Λ$ system. This spectral narrowing is associated with the decreasing separation between the two inner dressed states as atomic velocity increases. The transparency window exhibits pronounced direction-dependent transmission, with high forward transmission and strong suppression in the reverse direction. The transparency linewidth and forward-backward probe transmission can be controlled via two independent driving fields, while the central transparency frequency is kept essentially unchanged. The resulting narrowband nonreciprocity supports high forward transmission together with strong suppression in the reverse direction, which is suitable for frequency-selective optical filtering and nonreciprocal optical transmission in thermal atomic media. Our scheme with these specific features is geared towards enabling compact vapor-cell-based nonreciprocal devices for quantum network applications.

Symmetry-protected ground-state crossings can produce exact first-order transitions (FOTs) even at finite $N$, in contrast to continuous transitions governed by soft-mode criticality. We establish exact Juddian ground-state crossings for arbitrary finite $N$ in the one- and two-photon anisotropic Dicke models and identify a common two-channel structure: the eigenvalues of the coupling matrix set the local normal-state instability thresholds, whereas its determinant fixes the exact crossing. Despite this common structure, the resulting FOTs have distinct fates determined by the bosonic response. In the one-photon model, the overlap between coherent Juddian branches vanishes in the thermodynamic or infinite frequency-ratio limits, asymptotically suppressing the FOT cusp. In the two-photon model, squeezed Juddian states lose normalizability at spectral collapse, thereby terminating the physical FOT line at finite $N$. Although the cusp strength tends to zero as the endpoint is approached, the terminating FOT retains a collective spectral signature: the different-parity gap is predicted to close with an $N$-dependent exponent $μ_N=(2N+3)/4$, one greater than the cusp termination exponent. By contrast, the same-parity soft mode retains $N$-independent square-root scaling and governs the critical response. Thus spectral collapse can terminate an exact finite-$N$ FOT while preserving its collective imprint in the parity-resolved spectrum.

We propose an approximate classical algorithm for estimating quantum circuits' transition amplitudes, $\langle Ψ_f | \hat{U} | Ψ_0 \rangle$, based on Monte Carlo sums over bidirectionally sampled Feynman paths. The algorithm generates Feynman paths, i.e., sequences of intermediate computational basis states, by combining information from random walks initiated at both the input and output states, $Ψ_0$ and $Ψ_f$, respectively. It further combines this bidirectional approach with Multiple Importance Sampling, a powerful variance reduction technique that avoids variance peaks caused by divisions by the very low sampling probabilities associated with hard to reach paths. Empirical data demonstrate the superior convergence rate exhibited by the bidirectional algorithm over a unidirectional, forward-only sampling approach. This superiority is due to the effectiveness of the proposed algorithm in finding and weighting paths with non-zero amplitude in an extremely sparse path space. Sum of paths algorithms exhibit very favourable space complexity. Monte Carlo replaces exhaustive enumeration of the exponentially large path space by stochastic sampling, the computational cost being determined by the variance of the estimator. This work demonstrates these two features by presenting results on very large quantum circuits, with up to 4096 qubits.

We show that quantum systems on non-amenable lattices, whose boundaries constitute an extensive fraction of the system, host novel forms of bulk ordering with no Euclidean counterpart. Combining boundary-retaining iDMRG with an exact symmetry-fixing duality, we investigate $p<5$ state clock models on the coordination-3 infinite Cayley tree. We find that between the ordered and disordered phases lies an emergent intermediate phase with bulk order induced by an arbitrarily weak boundary field rather than by conventional spontaneous symmetry-breaking. This establishes boundary-sensitive order as a distinct quantum ordering mechanism defying Landau's spontaneous symmetry-breaking paradigm. The intermediate phase realizes a bulk-boundary correspondence in which the unpolarized boundary selects a specific ordered bulk state.

We develop quantum algorithms for optimal control over a prescribed finite time interval (finite horizon), focusing on continuous-time linear-quadratic regulation (LQR). This foundational control problem often requires solving a nonlinear matrix Riccati equation, which can be costly for large systems and long control durations on conventional classical solvers. We instead work directly with the state-costate optimality equations, reformulating the LQR problem as a multiple-shooting linear system. Importantly, we prove a condition-number bound for the system that is independent of the horizon, under stabilizability and detectability assumptions. By incorporating the initial and final conditions into a single linear system, we can solve the subsequent linear system more efficiently with a quantum linear systems subroutine. For a given initial state, our quantum algorithms return classical estimates of the optimal cost and the optimal control inputs at a selected time, without constructing a Riccati solution operator. Given sparse-matrix block-encodings, an initial-state preparation oracle and a fixed number of control inputs, the query and gate complexities scale polylogarithmically with system size and control duration, provided that sparsity, relevant norms, and stability parameters are bounded. The dependence on the target error is inverse-linear up to logarithmic factors. We establish the required bounds uniformly in system size and duration for a family of damped mass-spring chains with two endpoint controls. Numerical experiments support the analysis.

Machine learning is widely regarded as a promising application in which quantum computing could offer a computational advantage. However, general quantum machine learning models with provable guarantees on performance, trainability, and efficient inference remain limited. In this work, we introduce quantum Hamiltonian embeddings, a supervised learning framework in which a classical training dataset is encoded into a single effective, parameterized Hamiltonian. Training optimizes the parameters of this data-dependent Hamiltonian, whose approximate ground state defines the classification rule. Once the ground state has been approximated using a quantum algorithm, inference can be performed either classically using a classical representation of the learned state, or with a quantum representation of the state. We establish efficient methods for gradient estimation and prove favorable generalization guarantees. Furthermore, under standard cryptographic assumptions, we show that Hamiltonian embeddings can realize hypothesis functions beyond the reach of efficient classical algorithms. We then demonstrate the framework at scale on IBM Heron processors using a standard benchmark dataset. Together, these results establish Hamiltonian embeddings as a new framework for quantum machine learning, combining theoretical guarantees with a path for experimental investigations at scale on quantum hardware.

Counterdiabatic (CD) driving suppresses the excitations of fast protocols by adding an auxiliary Hamiltonian, but in many-body and topological systems the exact CD term is generally non-local and multi-body. We study this obstruction for Thouless pumping in the Rice-Mele model, first without and then with interactions. For noninteracting fermions, the exact CD term of the pump is non-local, but the variational framework of Sels and Polkovnikov yields accurate nearest-neighbor approximations. For the spinful Rice-Mele chain with onsite and nearest-neighbor repulsion, in the regime where the competition of the two interactions stabilizes quantized pumping, this approach fails: the infinite-temperature variational action only penalizes the CD amplitudes, and the resulting two-parameter nearest-neighbor term does not prevent the pump from breaking down when the cycle time is reduced from $50/t$ to $2/t$. We trace the failure to the structure of the exact many-body gauge potential, whose amplitude for each hop depends on the interaction energy that the hop costs. Resolving the nearest-neighbor currents by this energy, and fixing the coefficients with a ground-state-weighted action, gives a local ansatz with 14 coefficients that keeps the interacting pump quantized for cycle times $T=2/t$ and $T=1/t$, with an accuracy per site that does not degrade between rings of 8 and 12 sites.

Correlated decoding improves matching and clustering surface-code decoders by reweighting one decoding subgraph conditioned on the other's correction. We show that standard reweighting can cause correlated decoders to fail on size-$(d-1)/2$ fault configurations that a distance-$d$ code should correct, reducing error suppression deep below threshold. Under circuit-level noise, a single first-pass edge can discount several correlated edges, even though their joint occurrence requires additional independent faults, so the decoder favors an over-discounted correction. Regularizing the reweighting rule restores the nominal distance scaling and a clear correlated-decoding advantage.

We benchmark the Iterative Redecode Scheme (IRS) on fast transversal Clifford circuits, achieving high-accuracy correlated decoding using local memory-style detectors and decoders. On a deep random Clifford benchmark, IRS yields approximately $4\times$ lower logical failure rates than the ghost protocol at $d=11$ with matched buffers, and $15\times$ lower rates than logical observable matching (LOM). In three-block GHZ preparation, IRS achieves $2\times$ lower logical error rates than reliable logical Pauli-product decoding with matched initialisation, improving to $25\times$ at $d=19$ with $\lceil d/2\rceil$ full initialisation rounds. We place IRS, which builds on Wan et al.'s scheme, within a broader propagation-assisted local (PAL) framework, where local decoders exchange messages rather than decoding a global hypergraph. IRS alternates local minimum-weight perfect matching (MWPM) on memory-equivalent detector error models (DEMs) with Pauli-frame propagation and detector updates across transversal CNOT layers, seeking local error estimates consistent with the global detector record. Prior-informed DEMs account for probabilities of propagated errors missing from the memory-equivalent model, improving initial decoding and reducing logical error rates. Zero-weight physical Pauli mechanisms enable inference and propagation of initially indeterminate stabilizer outcomes. Error rates saturate after a few iterations even for deep, adversarial alternating-tCNOT circuits, allowing iteration caps with negligible loss of accuracy. We find syndrome-extraction buffers of order $\lfloor d/4\rfloor$ sufficient for distance-dependent error suppression in the demanding regimes studied. The approach extends to other local decoders and CSS codes; for repeated logical $S$ gates, IRS achieves approximately $4$ to $10\times$ lower logical error rates than LOM, depending on initialisation.

We determine the exact quantum communication and entanglement-distribution capacities of three fundamental bosonic channels, namely thermal loss, thermal amplification and additive Gaussian noise, assisted by operations that completely preserve positive partial transpose (PPT). These operations are more powerful than local operations and classical communication (LOCC), but cannot generate distillable entanglement on their own. For thermal loss, the unconstrained capacity coincides with the Pirandola-Laurenza-Ottaviani-Banchi (PLOB) bound throughout the non-entanglement-breaking regime. The corresponding upper bounds are also attained for thermal amplification and additive noise. We extend these results to energy-constrained communication, establishing exact capacities for all three channels at every prescribed mean input energy. Our results solve a class of bosonic capacity problems under PPT assistance and establish exact benchmarks for determining whether the same communication rates can be achieved via LOCC alone.

We derive a general Gorini-Kossakowski-Lindblad-Sudarshan master equation for two co-located, uniformly accelerated two-level detectors weakly coupled to scalar fields in the Minkowski vacuum, retaining coherent and dissipative contributions for arbitrary orientations, field masses, and spacetime dimensions. For equal orientations, we determine stationary states and their entanglement for two couplings to massless fields in four dimensions: symmetric coupling yields acceleration-dependent concurrence, whereas rotating-wave coupling gives acceleration-independent concurrence.

We investigate quantum-state texture during the thermal relaxation of an anisotropic spin-$1/2$ Heisenberg dimer subject to a longitudinal magnetic field and a Dzyaloshinskii-Moriya (DM) interaction. Starting from local transverse and longitudinal couplings to a bosonic bath, we construct a global weak-coupling Lindblad equation, identify its transition channels, and discuss the applicability and limitations of the secular approximation. The Gibbs state is obtained explicitly in the local spin basis, revealing that the DM coupling controls both the modulus and phase of the single-excitation coherence by modifying the energy splitting and rotating the chiral phase. For heating and cooling protocols, we compare rugosity, fidelity-based texture, and trace-distance texture with coherence, vector spin chirality, and purity. The relaxation dynamics separates population thermalization from the decay and precession of deliberately prepared energy-basis coherence. Their combined contribution to local coherence produces DM-dependent texture overshoots and, during cooling, damped oscillations and sign changes of the coherence quadratures. These transients differ from the evolution of coherence magnitude and purity, while trace-distance texture weights them differently from the overlap-based quantifiers. Calculations at reduced dissipation preserve the texture maxima within the secular model. The results identify a phase-sensitive diagnostic of relaxation.

This is a set of detailed notes that are part of a Ph.D. Course on Quantum Control delivered at the Department of Chemistry of Seoul National University in 2014. Part of this course was also taught in the Department of Chemistry of the Friedrich Schiller University Jena. It focuses on quantum optimal control and quantum optimal control algorithms based on the gradient and extended gradient methods.

Accurate modelling of chemical reaction rates requires precise correlated energy differences. Quantum computing offers a potential route to their determination, but extracting energies from quantum-prepared states can demand prohibitive sampling. We demonstrate measurement-efficient correlated energy estimation using an electronically challenging H$_2$DBB--Ru model derived from a Ru-functionalized hafnium metal-organic framework relevant to radiodynamic and photodynamic therapies. The mixed estimator combines a quantum-prepared target with sparse multiconfiguration references and recovers ground-state corrections using magnitude-only compute-uncompute measurements. Analytical variance estimates predict 1.6 mHa precision with a few hundred shots, about 100 times fewer than the single-determinant formulation and three orders of magnitude fewer than optimized Hamiltonian-term sampling. With approximate targets, it reaches comparable accuracy using simpler state preparation than direct expectation-value estimation. Emulator and trapped-ion experiments on Quantinuum Helios validate the approach up to (10,10), including a 50-qubit circuit combining AI-assisted state preparation with error detection, providing a measurement-efficient route to correlated energy differences for challenging chemical problems.

Quantum annealing generally samples degenerate ground states with nonuniform probabilities. This unfair sampling depends on how the driver Hamiltonian couples these states near the end of annealing. For combinatorial optimization problems with a cardinality constraint, the penalty method and constrained quantum annealing (CQA) differ in these couplings. The transverse-field driver of the penalty method does not directly couple feasible ground states, whereas the fully connected XY driver of CQA couples pairs of them related by a single spin exchange. We investigate how this difference affects ground-state sampling, using closed-system simulations of random graph bipartitioning instances together with degenerate perturbation theory. For the instances studied, the conditional ground-state distribution of penalty-based quantum annealing approaches that of CQA at sufficiently large penalties and long annealing times. This convergence can be explained by the effective Hamiltonian of penalty-based quantum annealing, in which virtual single-spin flips to infeasible states generate a second-order interaction proportional to the CQA driver projected onto the feasible ground-state manifold, which is the leading term of the effective Hamiltonian of CQA. In the numerical simulations, the Jensen--Shannon divergence between the conditional ground-state distributions of penalty-based quantum annealing and CQA decreases approximately as the inverse square of the penalty-to-objective energy ratio, consistent with the perturbative analysis. This correspondence between the effective Hamiltonians extends to equal-weight fixed-magnetization constraints under the same perturbative conditions, providing a common mechanism for sampling bias in the two implementations.

We study tunneling between two identical, smooth, compactly supported potential wells in a constant perpendicular magnetic field, with the coupling and magnetic field fixed and the well separation tending to infinity. For a sufficiently small positive magnetic field, we prove lower bounds on the hopping coefficient and on the splitting of the two lowest eigenvalues outside a set of separations of density zero. If the well centers are separated by $2d_1$ and the magnetic field strength is $bλ$, the lower bounds have the form $e^{-bλd_1^2-Cd_1^{1+δ}}$ for every fixed $δ\in(0,1)$. No radial or reflection symmetry of the single-well potential is assumed. The proof combines the explicit Landau resolvent kernel with a complex analytic estimate for logarithmic averages of the hopping coefficient.

The primary pathway to the investigation of exceptional points (EPs) in open quantum systems has been the use of Markovian master equations. However, recently it has been realised that they can arise in settings that show non-Markovian behaviour. The main approach in this direction has been the use of pseudomodes, which allow the influence of a structured environment to be replaced by new damped auxiliary modes. In this work, we use a Heisenberg-equation approach which relies on the reaction-coordinate formalism to obtain exact analytical dynamics. First, we show how our method considerably simplifies the analysis compared to the use of master equations. Second, we utilise it to discuss non-Markovian revivals in systems with second and higher-order EPs, showing that the notion that EPs demarcate the onset of revivals is not generally true. We then utilise our results to discuss the dynamical effects of higher-order non-Markovian EPs, deriving bounds on the number of revivals and investigating enhanced asymptotic relaxation near higher-order EPs. Finally, we investigate non-Markovian EPs with engineered reservoirs and show how they can be utilised to control the rate of irreversible information loss.

An important aspect of many linear optical quantum computing architectures is probabilistically generating small dual-rail qubit entangled states, or seed states. While many schemes to achieve this have been discovered, attention has been primarily focused on minimizing input resources and maximizing success probability rather than establishing a detailed understanding of linear-optical error performance. In this work, we develop a framework for resolving sensitivities to physically distinct errors in linear optical state generation, allowing us to identify precise ways in which these errors affect the properties of the output state. We use this framework to identify seed state generators in which destructive many-photon interference prevents detector loss and detector noise from causing a falsely successful heralding event. We show that this effect suppresses errors, for example cutting the effective loss on the output of particular Bell state generators in half relative to a standard scheme. We also present a new Bell state generator in which both detector loss and detector noise do not affect the quality of the output Bell state to first order, and a 4GHZ generator with >75% higher success probability than a standard circuit. In addition we provide some useful identities, bounds and invariants for studying linear optical seed state generation.

The formulation of quantum measurements compatible with relativistic causality is obstructed by the tension between the locality of observable algebras and the dynamical state transformations induced by measurement processes. We develop a local measurement theory for quantum cellular automata, lattices of finite-dimensional quantum systems with a causal reversible dynamics evolving in discrete time steps. Measurement processes are described by localized completely positive maps and organized into operational measurement protocols, finite non-adaptive sequences of local instruments distributed across the causal cone induced by the automaton local dynamics. Each protocol induces an effective measurement on the initial time slice, whose support is constrained by the causal structure generated by the automaton. Non-local measurement effects therefore arise through causal propagation and composition of local operations, rather than from primitive non-local interventions or instantaneous collapse prescriptions. We establish the corresponding spatial support bounds and characterize the resulting measurement architecture. As an explicit example, we construct a two-step protocol for a one-dimensional nearest-neighbour qubit automaton which, for suitable automaton parameters, realizes a Bell-basis projective measurement on two neighbouring sites after coarse-graining of the local outcomes. Away from this point, the same protocol generates a continuous family of deformed Bell measurements whose entanglement and stabilizer Rényi non-classicality can be quantified explicitly. The framework thus provides a causally consistent operator-algebraic mechanism for synthesizing spatially extended quantum measurements from strictly local operations.

In hyperon-antihyperon production through electron-positron annihilation, quantum steering provides a stricter test of nonclassical spin correlations than entanglement. We determine when steering survives angular averaging and optimize angular selections to reduce the sample size needed to resolve it. In the specified production-frame spin convention, we show that windows symmetric about 90 degrees with even production-angle acceptance yield phase-independent Bell-diagonal states. Applying the necessary and sufficient criterion for steering under arbitrary dichotomic projective measurements determines the exact boundary for this family and reveals a steering region missed by the three-setting Cavalcanti-Jones-Wiseman-Reid (CJWR) criterion. For positive production parameters and uniform full-range acceptance, the steering threshold is $α\simeq0.36065$. We derive the covariance of weak-decay angular moments, construct fixed linear witnesses, and optimize the angular window. For $J/ψ\toΛ\barΛ$, steering survives full-range averaging. The statistical model predicts that, after separately optimizing the two angular selections at nominal $z=5$, the required full-range pair sample decreases from $8.61\times10^4$ for CJWR to $2.80\times10^4$ for the projective witness, a 67.4% reduction. This advantage persists under the production-acceptance and analyzing-power variations studied.

Rydberg atom arrays (RAA) have been advocated as a promising avenue for the quantum simulation of different exotic quantum states. Numerical predictions for the ground state properties of this experimental platform can, however, be challenging in two-dimensional setups. In particular, faithfully treating long-range interactions is often crucial for distinguishing the fate of competing phases, but it usually comes at considerable cost. Projected entangled-pair states (PEPS), optimized via a sampling-based approach, have been shown to deal with such terms on the same ground as shorter-range ones. In this work, we employ these tools to investigate debated physical questions in different frustrated geometries of RAA, from the emergence of spin-glass physics on the Kagomé lattice to topological order beyond the PXP model on the Ruby lattice. By that, we contribute to establishing PEPS as well-suited tools for creating digital twins of RAA experiments.

In the resource theory of superposition relative to linearly independent, nonorthogonal reference states, golden states are known for two reference states and for special overlap matrices, and all of them are maximally coherent in the Löwdin basis. We clarify what decides their existence and their Löwdin structure. The robustness and the geometric measure of superposition are maximized by the same states, which overlap equally with every reference state; their maximal values are set by the ground-state energy of a classical $XY$ model on the overlaps of the dual basis. For every overlap matrix, these states, and only these, are golden under the maximal superposition-free operations, but they need not be maximally coherent in the Löwdin basis. For the Kraus-type free operations, we prove a necessary and sufficient criterion, Gram majorization, for converting pure states into targets with nonzero coefficients; it reduces to majorization for orthonormal reference states. It shows that golden states of these operations must be maximally coherent in the Löwdin basis, but that this does not ensure their existence: three reference states that are not orthonormal admit a golden state if and only if their overlaps have a common modulus $s$ and their Bargmann phase $Φ$ obeys $s\geq2\cos[(π+|Φ|)/3]$. Equal-overlap states also yield a complete family of superposition witnesses in the Löwdin basis, which show that white noise on the span of the reference states is a resource unless these states are orthonormal.

The establishment of metrics and control of fundamental noise sources in quantum sensing is a long-standing goal in quantum science and technology. We report on the observation of polariton-mediated optical noise in a thermal Rydberg atom vapor and demonstrate its active control and suppression using a radio-frequency field in Rydberg electrometry. The noise exhibits structured amplification and reduction across the Rydberg electromagnetically induced transparency resonance. This reveals a nonlinear slow-light feedback mechanism in which the polariton medium stores and releases probe-field energy. We show that the reference radio-frequency field used in Rydberg heterodyne receivers can also tune the medium into an operating regime where high electromagnetic-field responsivity coincides with reduced optical noise. This operating-point control enables optimization of the electric-field sensitivity within the constraints imposed by Rydberg-polariton physics. These results establish polariton noise as a previously unrecognized intrinsic noise source in thermal Rydberg vapors and the corresponding control method as a crucial aspect of continued efforts to achieve fundamental sensitivity limits in Rydberg electrometry.

While quantum technologies are rapidly evolving, near-term applications heavily rely on hybrid quantum-classical paradigms. Among these, the classical shadows framework has gained a lot of traction, not only for quantum information science, but also for the development and verification of quantum hardware. It allows to efficiently classically estimate many properties of quantum states from randomized measurements alone, a task that is otherwise intractable due to the destructive nature of measurements in quantum systems. There are, however, many properties of interest that are, due to their very problem formulation, not efficiently estimable. In this work, we identify a computational kernel occurring in estimators of polynomial functions, a class of problems that are in general computationally difficult to solve. We show that this structure allows a row-wise partition that, together with a custom SIMD vectorization, enables massive parallelization and can reduce the computational cost significantly. We show applicability and scalability of the approach on different tasks, and our results showcase that the approach allows high sequential throughput and close-to-ideal parallel scaling. The work thus provides a new way of identifying and exploiting structure in classical shadow estimators, resulting in practical advantages on inherently difficult problems.

Fault-tolerant (FT) quantum computation offers a pathway to quantum advantage, but its realization is hindered by its significant overhead. The partially FT "STAR" architecture reduces the cost of universal computation at the price of relaxing FT requirements for non-Clifford operations, increasing exposure to hardware noise. Therefore, maximizing its performance and applicability demands careful co-design with the underlying hardware. In this work we investigate the co-design of the STAR architecture with neutral-atom platforms, connecting the underlying atomic physics to logical error modeling and application-level performance. At the physical level, we identify a favorable noise bias in $^{171}\mathrm{Yb}$ Rydberg gates, and show how it can be enhanced through error-selective pulse optimization. At the logical level, we identify an intrinsic error suppression mechanism, yielding vanishing logical coherent noise in leading order. Detailed circuit-level simulations of surface code implementations show more than an order of magnitude reduction in logical error relative to previous estimates. As a concrete target application, we focus on the Fermi-Hubbard model with periodic boundaries, for which we design a simulation circuit particularly suited to early implementations. We quantify the resource tradeoff of partially and fully FT approaches to gate synthesis, with the former showing approximately an order of magnitude reduction in state-injection depth, and an even larger reduction in Clifford resources. Comparing with classical and fully FT approaches, we identify regimes where partial fault tolerance provides both lower overheads and lower error rates. In our estimates, this is accessible with moderate error rates $p\sim 10^{-3}$ and a few thousand qubits, underlining that for these types of problems, partial FT approaches provide a compelling pathway to early quantum advantage.

The contextuality degree of a set of Pauli contexts is the least number of contexts that every noncontextual $\pm1$ assignment violates. For the four-qubit hyperbolic quadric $\mathcal{Q}^{+}(7,2)$, with $135$ points and $1575$ lines as contexts, Muller et al. conjectured from heuristic searches that the degree is $315$ and that the violated contexts of every optimal assignment form a dual polar space $DW(5,2)$. We prove both conjectures. The lower bound has a short proof by hand: every doily ($GQ(2,2)$) of the quadric contains ten Peres-Mermin grids covering each of its lines four times, so every assignment violates at least three of its fifteen lines, and averaging over the doilies gives $1575/5=315$. The equality case is local: an assignment is optimal exactly when it violates one ruling of one grid in every doily. Using this as a SAT encoding, we show that there are exactly $240$ optimal violated sets, one orbit of $\mathrm{O}^+(8,2)$, each isomorphic to $DW(5,2)$. The same argument gives the first lower bounds $\lceil L/5\rceil$ for all quadrics with $L$ lines in $N\ge4$ qubits. The degree theorem is kernel-checked in Lean 4, and the completeness of the enumeration is certified by a DRAT proof checked by the verified checker cake_lpr.

We examined the energy-momentum relationship of the valence band of Cu$_2$O, which has gained interest as an emerging solid host for giant Rydberg states. Our findings reveal a nonparabolic dispersion, described using the rest mass (0.570 times the free electron mass) and rescaled light speed ($1.6\times 10^5$ m/s), which draws parallels with relativistic theory for high-energy particles. We propose a straightforward expression for the bound-state energies of Rydberg excitons with finite quantum defects, whose energy scheme deviates from the hydrogenic series. This formulation identifies relativistic kinematics as the physical origin of quantum defects, offering a streamlined basis for future studies on complex many-body correlations.

Utility-scale quantum technologies will not only require a well-performing quantum platform, but also classical control hardware that is scalable, efficient, and meets the design requirements set by the quantum system of interest. One approach is the application of silicon CMOS technology, a highly scalable and mature technology, to design application-specific integrated circuits (ASIC) that are optimized for the quantum system. In this work, we present two-qubit control of electron and nuclear spins in NV centres in diamond, using a cryogenic CMOS qubit controller integrated with a diamond quantum device in a cryostat. Using Gate Set Tomography (GST) we characterize the performance of the single-qubit gates on both electron- and carbon nuclear spins, and analyze the limiting noise processes. We use dynamical decoupling to engineer a two-qubit gate, and estimate $F_\text{2q,avg} = 95(2)\%$ for the electron-nuclear two-qubit gate fidelity. Our demonstration of cryo-CMOS-driven two-qubit gates is a key step towards highly-integrated quantum devices based on colour centres.

The Parity Architecture was originally introduced in the context of quantum optimization algorithms to overcome hardware connectivity constraints. Here, we show that its benefits extend beyond this role by identifying specific parity transformations that enhance the success probability of the Quantum Approximate Optimization Algorithm (QAOA) for optimization problems defined on hardware-native and sparse graphs. Numerical simulations suggest that this enhancement originates from the higher-order operators introduced by the Parity representation, which accelerate the propagation of correlations across the physical device. We investigate this mechanism for the Signed Max-Cut problem on 3-regular graph instances and demonstrate its practical relevance on IBM Heron quantum processors. QAOA parameters are first classically optimized on small training instances containing up to 14 vertices and subsequently transferred to larger instances executed on quantum hardware. We consider Signed Max-Cut instances of up to 40 vertices and find that, together with an error mitigation technique, the parity-based QAOA identifies the optimal solutions for all the considered 40-vertex instances, whereas the conventional QAOA fails under the same conditions.

A linear potential gradient can strongly suppress quantum dynamics, while interactions can activate resonant many-body processes whose higher-order structure remains largely unexplored. Here we uncover a systematic hierarchy of high-order interaction--tilt resonances in an interacting Stark chain, where the resonance order counts the minimal number of elementary exchange steps involved. These resonances manifest as long-lived coherent oscillations with order-dependent timescales. By isolating individual resonant channels and developing a microscopic effective description, we connect these dynamical timescales to the underlying many-body exchange processes and reveal a pronounced dependence on the initial-state structure. Our results provide crucial insights into high-order many-body resonances and show how commensurate interaction-to-tilt ratios generate a hierarchy of parametrically slow coherent many-body dynamics.

We introduce squeezing-type lower bounds for a hierarchy of variance bounds under specific unbiasedness constraints, which generalizes the quantum Cramér-Rao bound. Our construction directly extends standard squeezing coefficients to the corresponding generalized metrological sensitivities while retaining their experimentally accessible structure. We show how observables maximizing these bounds can be identified analytically within families of accessible observables. If arbitrary observables are accessible, the optimized squeezing-type bound recovers the exact generalized metrological sensitivity. These bounds provide efficient and experimentally viable characterizations of generalized metrological sensitivities that are especially relevant in finite-shot scenarios and in the transition from local to global parameter estimation.

Compact quantum neural networks have been explored for cloud-cover parameterization, but their predictive value depends on how physical knowledge is incorporated and which classical models provide the reference. We investigate an offline residual formulation that retains a fitted \XR\ cloud-cover estimate and learns a correction to its logit in transformed target space. Using released ICON/DYAMOND-derived data, we compare ten model variants in six- and eight-input settings, with three matched replicates and 10,000 training samples per replicate. All quantum circuits use local Z readout and noiseless exact expectation values. Under a common 30-epoch protocol, residual prediction reduced physical-space test mean squared error relative to direct QNN prediction by 54.3\% and 38.8\% for six-input XYZ and ZZXY circuits, and by 49.2\% and 38.9\% for their eight-input versions. Residual QNNs also outperformed the selected compact residual multilayer perceptron in every paired replicate. A larger, longer-trained Grundner-Q1 adaptation nevertheless achieved lower error: residual Q1 reached mean MSEs of 0.00778 and 0.00791, compared with 0.01124 and 0.01082 for residual XYZ. The results support residual prediction for compact simulated QNNs within the tested budget and establish a clear boundary set by stronger classical references. They do not establish computational quantum advantage or online climate-model skill.

Universal behavior at continuous phase transitions is encoded in long-wavelength fixed-point theories controlled by dimensionality and symmetries. It is a central question for which systems this universal behavior and the underlying long-wavelength description can be captured by a noninteracting theory allowing for analytical and accurate predictions. In this work we provide a systematic procedure for obtaining the best noninteracting fermionic description of a quantum phase transition through fermionic Gaussian states. We demonstrate the performance of our procedure for the interacting long-range transverse-field Ising chain. This formulation reduces the problem to a self-consistent Euler equation that yields a critical line in close agreement with independent numerical benchmarks, while its singular momentum structure provides analytic predictions for continuously varying critical properties. Yet exact diagonalization shows that Gaussian-state fidelity to the exact ground state is poorest, and non-Gaussianity strongest, near the transition. Thus, accurate predictions for critical properties can emerge from the Gaussian variational description even where its microscopic wave-function approximation is weakest.

Quantum machine-learning (QML) models are increasingly considered for security applications, yet their adversarial robustness in malware analysis remains insufficiently understood. This paper presents Q-MALDetect, a hybrid convolutional and variational-quantum detector for byte-image representations of x86-64 Executable and Linkable Format (ELF) binaries, and evaluates it under feature-space and a range of Grad-CAM-guided, executable-aware evasion attacks. The model achieves 97.2% training accuracy, but its robustness deteriorates as attack strength increases, with the strongest evaluated feature-space attack reaching a 78.7% attack success rate (ASR). Among executable-aware attacks, Grad-CAM-guided no-operation (NOP) insertion produces the highest conditional ASR of 32.9%. Dynamic adversarial training is the most effective evaluated defense, reducing feature-space ASR to as low as 5.0%, executable-aware ASR to 7.7%, and the sequential-attack ASR to 34.0%. In contrast, convolutional-autoencoder preprocessing increases executable-aware ASR to 39.7%, coinciding with a rise in Grad-CAM attribution mass within the mutable .text region from 35.2% to 45.7%. Ablation results reveal no monotonic relationship between qubit count and robustness, while the encoding interface modifies the learned attack surface without neutralizing the strongest attack. These findings demonstrate that the effectiveness of attacks and defenses depends strongly on the perturbation constraints and evaluation conditions. Reliable deployment of QML malware detectors therefore requires assessment against both feature-space and executable-aware attacks rather than reliance on clean accuracy or generic denoising alone.

Mixed quantum states can exhibit unconventional forms of symmetry breaking without pure-state counterparts. A prominent example is strong-to-weak spontaneous symmetry breaking (SW-SSB), which cannot be diagnosed by observables linear in the density matrix. Here, we experimentally resolve finite-size critical signatures of SW-SSB transitions on a superconducting quantum processor. We develop a measurement protocol that combines quantum measurements with classical processing based on the known dephasing channel to reconstruct nonlinear mixed-state correlators. Using only two measurement settings, the protocol reconstructs fidelity, Rényi-2, and linear correlators, as well as string observables. Applying this approach to matrix-product states subjected to power-law-correlated dephasing, we observe finite-size crossings and scaling collapses in nonlinear correlators, accompanied by decaying linear correlations. We further map the estimated SW-SSB transition points across initial-state and channel parameters. Measurements of linear and Rényi-2 string observables further reveal signatures of mixed-state symmetry-protected topological (SPT) phases, with a nonlinear string-order crossover aligned with an independently estimated SW-SSB transition point. Our results establish a quantum-classical approach to probing SW-SSB critical behavior and mixed-state SPT order.

Fresh qubits, not size, set how long a noisy quantum system can remember. With $k$ input qubits reinitialized per time step, the longest memory any reservoir can attain under depolarizing noise is $\exp[Θ(k)]$ time steps, whatever its size, dynamics, and input encoding. A universal upper bound and an explicit reservoir that attains the exponential scaling establish this optimal resource law. The bound depends on the dynamics only through the entropy that fresh qubits remove per time step, so it holds for any Markovian noisy dynamics without feedback, including measurement-free error correction.

Sidewall morphology is a potentially important factor influencing superconducting qubit performance, yet its quantitative characterization remains challenging due to the absence of standardized measurement protocols. In this work, we develop a scanning probe microscopy-based measurement framework for the quantitative characterization of superconducting qubit sidewalls. The framework introduces a refined root mean square lateral sidewall roughness descriptor and a new curvature-equivalent radius for quantifying vertical sidewall morphology. The descriptors and measurement procedures are applied to different components of qubit devices, forming the basis of a proposed sidewall characterization protocol. This provides a foundation for quantitative comparisons of fabrication processes across laboratories, enabling future investigations of correlations between sidewall geometry and qubit performance.

Classical methods for computing quantum expectation values often propagate observables in the Heisenberg picture. To remain tractable, these methods rely on approximations that discard operator components during evolution. Yet the magnitude of these components alone does not determine the resulting expectation-value error, which also depends on their subsequent evolution and the input state. We develop \emph{generalized Pauli propagation}, a common algebraic framework encompassing Pauli propagation, Lie-algebraic simulation, and Krylov subspace methods. Using weighted commutator graphs, we derive exact identities that relate approximation errors to the signed contributions of omitted and discarded operator components. Our central result establishes \emph{delayed observability}, identifying conditions under which these contributions vanish at low orders in propagation time. We use this structure to develop finite-order error estimates and state-dependent selection rules. We further prove that retaining the symmetry-preserving part of a weak perturbation eliminates first-order expectation-value errors under suitable symmetry conditions. By revealing how approximation errors affect the desired expectation value, our framework provides a basis for more informative error analysis and the development of readout-aware simulation strategies.

A quantum walk is a mathematical model and a quantum version of a random walk. For the past two decades, it has been studied from mathematical and physical viewpoints. It has many desirable properties. This paper reevaluates quantum walk from a quantum mechanical perspective, as Feynman essentially proposed it as a toy model in his path integral method. Then we demonstrate that the quantum walk model exhibits both particle-like and wave-like properties by showing reflection and partial reflection as a particle and interference as a wave. In particular, for an initial state supported at two sites $\pm\ell$, we explicitly derive the weak limit distribution of the Hadamard walk and show that the Konno distribution is modulated by the interference factor $2\cos^2(\ell k(x))$. The resulting interference profile is reminiscent of far-field (Fraunhofer-type) diffraction.

The Renormalization Group (RG) establishes relations between effective descriptions of physical systems at different scales; in Hamiltonian RG, these relations induce a flow in the space of Hamiltonians. In direct correspondence, we design an RG framework for quantum control by constructing a flow in the space of time-dependent Hamiltonians. A prescribed control subspace, selected to contain only experimentally accessible terms, forms the fixed-point manifold, while the flow preserves the target unitary and monotonically reduces the Hamiltonian weight outside this subspace. Exploiting the freedom in constructing the flow, we introduce flow-equation engineering to enhance the versatility of the framework for diverse control problems, including time-periodic and open-interval smooth protocols with prescribed endpoints. We provide two disparate applications to exhibit the utility of our approach: (i) Nonperturbative Floquet engineering beyond the regime of validity of high-frequency expansions, which we demonstrate by constructing an implementable time-periodic protocol for the Haldane model; (ii) Accessible fast-forward driving from unit-fidelity counterdiabatic evolution, which we showcase for large transverse-field Ising chains away from the adiabatic regime by compressing the long-range multibody adiabatic gauge potential into the original time-dependent Ising control schedules. Our control RG framework reveals a unifying perspective on Hamiltonian engineering and unitary quantum control, and can serve as an organizing principle behind seemingly disparate nonequilibrium quantum dynamics.

We investigate open-system charging protocols for Rabi and Dicke quantum batteries under direct incoherent pumping. The charging dynamics follows a Lindblad master equation, while effective non-Hermitian generators describe the conditioned no-jump mechanism. For a single Rabi battery, this pumping suppresses coherent energy backflow, broadens the high-energy charging window, and improves robustness against both timing errors and detuning. At the selected Rabi operating points, pumping also increases ergotropy and the extractable fraction of the stored energy. For finite Dicke batteries, direct incoherent pumping likewise stabilizes the charging dynamics. Across the finite-size scan, the strongest pump considered improves the peak stored energy and ergotropy per cell and near-peak timing robustness relative to the Hermitian reference. The maximum average charging power also increases, although this metric includes pump-assisted jump contributions. Equal-input comparisons show that the relative performance of common-cavity Dicke and independent Rabi batteries varies with the pump-input bound. Taken together, these results show that direct incoherent pumping provides a route to stabilized charging in Rabi and finite Dicke quantum batteries.

Quantum communication networks promise information-theoretic security but this security collapses if intermediate relay nodes are compromised, a risk that grows sharply when compromised nodes cannot be identified. We address this twofold: first, we show that multi-path routing provides quantifiable protection against unidentified compromised nodes. Second, we provide a comprehensive statistical and graph-theoretic analysis of network and node security under compromise, covering full and partial node compromise, optimal placement of additional edges via an iterative method, and comparative hacking-probability analysis across network topologies. Together, these results identify the topology and multi-path routing strategy that most improves security for a given network. We apply this framework to quantum key distribution across multiple network topologies, demonstrating a scalable route to secure, reliable quantum communication under realistic, unidentified adversarial threats, without relying on quantum memory.

Distributing quantum circuits across a network of quantum devices is a recent approach to improve the scalability of quantum computation. Entangled pairs of qubits distributed across network nodes are used as a communication resource for executing inter-node (remote) gates. However, establishing these entanglement pairs incurs significant latency, and doing so during the circuit's execution may lead to the decoherence of logical qubits. Instead, it may be beneficial to distribute certain entanglement pairs before the circuit is executed. Thus, we consider the problem of distributing a quantum circuit across a quantum network containing some pre-distributed entanglement pairs and seek to minimize the execution time of the circuit. We address this problem in three steps. First, given the quantum network and (optionally) a probability distribution over training circuits, we determine a set of pre-distributed entanglement pairs under a specified budget. Second, we compute a qubit-to-memory allocation that minimizes the expected execution time given these pre-distributed resources. Finally, we identify any additional entanglement pairs required during execution, generate them concurrently, and execute the circuit gates. We evaluate our methods on a broad range of benchmark circuits.

Thermal light exhibits intensity fluctuations or photon bunching that has been used as a source of entropy or temporally correlated light. However, its low spectral density limits its use in practical applications like LIDAR. One method of remedying this is optical amplification to boost its brightness. In this paper, we show that the normalized second order coherence function $g^{(2)}(τ)$ of a thermal light source is preserved after amplification. We then use amplified thermal light to demonstrate a LIDAR raster scan of a building at 1.3 km with a depth resolution of 2 cm.

Light curves reveal stellar variability and support studies of stellar evolution and cosmic distances. Reliable classification is therefore important for large time-domain surveys. We present HyQ-LC for ten-class stellar light-curve classification using 359 handcrafted features and 633,034 training objects. The main model combines a window multilayer perceptron (MLP) backbone with a nine-qubit readout using amplitude encoding and angle re-uploading. Both this hybrid and its pure-MLP control have 44,238 parameters. On a shared 20,000-object test set, the hybrid has macro-averaged F1 (Macro-F1) point gains of 0.8276 and 1.2393 percentage points over the pure MLP on two fine-tuning seeds. A separate fixed-fusion configuration achieves slightly higher Macro-F1 but lower accuracy than approximately budget-matched LightGBM. Its positive class-level differences are concentrated in CEP, RRC, and ROT, while the full-budget LightGBM reference scores higher on both metrics. All circuits are simulated classically. The comparisons retain existing validation-selected checkpoints and use the same test objects, with features, predictions, and recomputation code publicly available. The results identify point-estimate improvements over the tested controls while leaving the specific contribution of the quantum branch unresolved.

We present a fully quantum theory of time-resolved transient absorption spectroscopy, providing a general framework for describing the linear response of a nonequilibrium target to quantum probe fields beyond the semiclassical approximation. We elucidate how quantum correlations between probe-field frequency modes couple to coherences in the target and derive a simple expression for computing the resulting spectroscopic signals. We identify conditions under which quantum light can modify transient absorption spectra beyond the limits achievable with classical fields. Our work establishes a theoretical foundation for exploiting quantum light in ultrafast spectroscopy and suggests new routes for resolving dynamics in matter on timescales shorter than the duration of the probe pulse.

Satellite-based quantum links are a promising enabler of long-distance entanglement distribution, overcoming the exponential losses of optical fibers. In uplink architectures, entangled photons are generated at ground stations and transmitted to orbiting satellites, reducing space-segment complexity but introducing significant atmospheric and geometric losses. Single-satellite dual-uplink configurations are additionally limited by the requirement of simultaneous visibility between both ground stations and the satellite. In this work, we investigate a dual-uplink dual-satellite network architecture and compare its performance with the single-satellite scheme under identical physical assumptions. The proposed topology introduces an inter-satellite link (ISL) that decouples the ground-station separation from the atmospheric uplink geometry. A realistic channel model is employed, incorporating geometric attenuation, atmospheric turbulence, background noise, and Bell-state measurement efficiency. The overall success probability and practical fidelity are evaluated as functions of satellite altitude and ground-station separation. Our results show that while the single-satellite configuration is suitable for regional-scale networks, it becomes infeasible for large separations due to geometric constraints. The proposed dual-satellite architecture mitigates this limitation and significantly extends the achievable communication distance, representing a key step toward scalable quantum internet infrastructures.

In an earlier work, we showed that, in the interaction-dominant setting, coupling the conjugate variables of a subsystem to distinct environment modes drives the subsystem to a maximally mixed state. Here, we extend the study to the full quadratic dynamics of a single-mode subsystem coupled to a two-mode environment, and identify the phase-space mechanism responsible for the asymptotic behavior. By tracking the exact reduced Weyl characteristic and Wigner functions, we demonstrate that they lose their dependence on local phase-space coordinates on every fixed compact region. In free-particle model, this happens for all values of coupling, whereas in the harmonic oscillator model, it happens above a critical value of the coupling. Under a finite-volume and momentum regularization, this behavior corresponds to the reduced subsystem approaching a maximally mixed state.

Accurately characterizing molecular properties and reactivity often requires electronic-structure calculations across an ensemble of molecular geometries. Quantum algorithms that process such ensembles coherently could address this challenge, but they require Hamiltonian block encoding circuits that combine advanced factorization techniques with sublinear scaling in ensemble size. Here, we introduce SVD-THC, which extends tensor hypercontraction to sets of Hamiltonians defined at different nuclear geometries through a singular value decomposition of the ensemble. We use SVD-THC to construct a single multiplexed block encoding circuit for all geometries in an ensemble. We then evaluate the approach on ensembles generated by varying internal rotational coordinates in 1-bromo-2-chloroethane as well as in glycine and alanine dipeptides, corresponding to established model systems for peptide conformational landscapes, with up to 5,184 geometries. Across several resolutions of the internal-coordinate grids, the Toffoli complexity of the resulting circuits grows only weakly with the number of geometries, changing by at most 12\% over grids that differ in size by up to 576$\times$. In an energy-thresholding circuit, this yields 35--200$\times$ fewer Toffoli gates than slicing together single-geometry block encodings. This approach could help make coherent processing of molecular geometry ensembles a useful primitive for fault-tolerant quantum computing.

The use of entanglement in sensing is often motivated by improved sensitivity arising from non-classical correlations among probes. For static signals, however, this quantum advantage in Ramsey spectroscopy with $N$ probes is known to be highly susceptible to dephasing, which severely limits the possible gain from entanglement. In contrast, we consider sensing of signals that vary in time. Considering the simplest example of dephasing by classical white noise, we show that entanglement allows a large increase in bandwidth when estimating the frequency components of a time-dependent signal. Without sacrificing any sensitivity, entanglement allows for an increase in bandwidth by a factor of $N$. Alternatively, when interrogation times are limited by the signal bandwidth rather than by dephasing, the average estimation uncertainty over a fixed bandwidth is reduced by a factor of $\sqrt{N}$ compared with separable states.

Quantum states are ultimately responsible for numerous counterintuitive phenomena that defy classical intuition. As the development of quantum technologies accelerates, our ability to harness these quantum resources becomes essential. This review addresses a fundamental question. How do we quantify the quantumness of a state, and which specific traits distinguish it from its classical counterparts? We examine quantumness through both theoretical and operational lenses, providing a clear framework for state characterization. Ultimately, we demonstrate that certifying quantumness is not just a theoretical exercise. It is a practical necessity for identifying, and realizing quantum advantage in real-world applications.

Plasma simulations for magnetic-confinement fusion (MCF) involve high-dimensional kinetic dynamics, strong nonlinear coupling, complex geometries, and multiscale spatiotemporal behavior, imposing severe computational bottlenecks. While quantum computing offers a potential alternative for accelerating plasma simulation problems, its practical advantage for fusion research has not yet been demonstrated. We review existing quantum computing studies across kinetic dynamics, wave interactions, equilibrium, and macroscopic stability, evaluating their hardware implementations and operational bottlenecks. Current studies remain largely restricted to linearized equations, reduced models, or isolated computational subroutines, leaving a substantial gap from realistic fusion simulations. We summarize key problem characteristics, including high dimensionality, structured dynamics, and measurement requirements, under which plasma applications are most likely to yield a quantum advantage. Guided by these considerations, we highlight potential approaches and present a roadmap toward practical quantum advantage of simulating plasma in MCF.

This paper is a non-planar counterpart of the author's earlier work on planar contact structures and topological quantum computation. There the page is planar and all branch points are paired by disjoint liftable arcs, compatibly with the joint eigenlines of the Ising representation and with Calabi-Yau (CY) Stein fillings, those with vanishing first Chern class. Here the page has genus g and connected binding, presented as a simple degree-three cover of the disk. Every maximal system of disjoint liftable arcs has exactly g members and leaves two branch points unused. The half-twist interchanging the two points is not liftable, but its cube is, and lifts to the identity. An integral residue criterion supplies the CY test. A factorization localized on a contact connected sum is automatically CY. Unlike in the planar case, a CY factorization need not be the shortest. Once the fusion channels of the g pairs are fixed, Ising fusion determines the channel of the remaining pair, and braiding acts there only by scalars. Fibonacci fusion can leave that channel undetermined, and the powers of the cube then act by ten distinct relative phases on a single joint eigenspace, while the CY Stein filling stays fixed