Papers

The ergotropy, or unitarily extractable work, of a quantum system naturally splits into incoherent and coherent contributions, respectively set by population inversion and coherences in the energy eigenbasis. We show that this split makes the coherent ergotropy of a Mach–Zehnder qubit sensitive to path predictability that the output interference fringes do not reveal. We send the path qubit, prepared as a thermal quantum battery, through two quantum-controlled interferometers built from the same elements, a fixed beam splitter and a beam splitter coherently controlled to be present or absent, differing only in the order in which these two act. The two arrangements share identical visibility, stored energy, and incoherent ergotropy at every point in the parameter space. Yet, for work extracted from the output battery alone, placing the controlled beam splitter first never yields less coherent ergotropy, and at fixed visibility and interferometric phase the difference is governed by the path predictability that this ordering creates. The same expression reappears as a purity deficit on the beam-splitter controller, so the work advantage comes with a Landauer bound on the cost of locally resetting the controller that is never larger at the same temperature. We further examine the effects of decoherence on the battery and consider a relativistic realization in which a Wigner rotation correlates the particle's spin with its path. Tracing out the spin decoheres the battery and allows the two arrangements to exhibit different coherent ergotropies even in regimes where their non-relativistic counterparts coincide. These results show that interference visibility is not a complete measure of the coherence available as work.

We analyze fork-grating generation of electron vortex beams beyond the ideal single-mode approximation. The incident beam is described as a paraxial Gaussian ensemble with finite transverse momentum spread and a first electromagnetic Hartree phase accumulated before the grating. Within Fresnel propagation we derive an analytical expression for each diffraction order and determine the corresponding orbital-angular-momentum statistics. The mean OAM of a selected order remains fixed by the topological rule, $\langle L_z\rangle_m=mp\hbar$, while its variance is set by the residual transverse momentum spread of the beam prepared at the grating. For the Gaussian mixture, the transverse purity is $\mathcal P_{\perp,m}=[1+2(\Delta L_{z,m}/\hbar)^2]^{-1}$. The observed annular profile is governed by a separate propagation-dependent blurring scale, so a beam can retain well-defined mean OAM while having low transverse purity or a partially filled vortex minimum. Within the radial phase-screen approximation, the Hartree self-field modifies the propagated profile while preserving the full-plane OAM moments and transverse purity.

Polynomial excitations consisting of creation and annihilation operators are studied. Subsystem entanglement is proven produced and preserved by such manipulations. NPT entanglement already present between any two subsystems of a general pure or mixed multipartite Gaussian state is preserved under all polynomial excitations. Nevertheless, these excitations can create NPT entanglement between initially separable subsystems, implying that the number of NPT entangled pairs cannot decrease. Polynomial excitations of a wide class of initially separable pure states are considered. For these states, the method reduces the infinite-dimensional positivity problem to a finite-dimensional one: after partial transposition, NPT entanglement is equivalent to a corresponding bilinear representation matrix not being positive semi-definite. Furthermore, using symplectic diagonalization and spectral decomposition, an explicit transformation is constructed between the Fock-space and position representations. It is applied to quadratic excitations of a three-mode mixed Gaussian state. The behavior of the NPT entanglement is tracked between subsystems as a function of a parameter $\kappa$, which tunes the non-locality of the excitation, and quantum negativity is evaluated. Under a chosen quadratic Hamiltonian, the resulting unitary time evolution maintains NPT entanglement for long intervals, interrupted only by short periods of PPT states. Finally, a closed analytical expression is derived for the covariance matrix of a general quadratic operator for an arbitrary number of degrees of freedom in phase space. Our framework directly connects mathematical foundations, theoretical modeling, and experimentally feasible implementations.

Variance squeezing of a V-type atom interacting with a dissipative cavity is investigated. First, the influence of atomic initial state parameters on the variance squeezing is explored. The results show that the atomic variance squeezing switches alternately between Sx and Sy as the initial state parameter alpha sweeps from -pi to pi. The two squeezing intervals are symmetric about alpha = pi/4, each with a width of pi/2. For alpha = pi/14, only the Sx component can generate variance squeezing and will eventually disappear with time evolution due to unavoidable environmental noise. Then, the influence of system parameters on the variance squeezing is also studied. It is found that, the optical variance squeezing depth of Sx is determined solely by the atomic initial parameters and is independent of the system parameters. Both weak cavity-environment coupling and atom-cavity detuning can significantly enhance the robustness of the Sx variance squeezing. The SGI parameter has an extremely weak influence on variance squeezing. These results are beneficial for high-precision quantum communication applications.

Dissipation dilution has driven a revolution in the quality factors ($Q$) of top-down nanomechanical resonators. Yet it has not been leveraged for van der Waals (vdW) materials. Here we report quality factors up to $372{,}000\pm37{,}000$ in monolayer MoS$_2$ drums at 4 K, nearly an order of magnitude beyond the previous best for any vdW material at this temperature, enabled by a clean, polymer-free exfoliation technique. We develop a dissipation-dilution model for circular drums and analyze the contributing intrinsic and extrinsic dissipation mechanisms. The MoS$_2$ monolayer exhibits a dilution factor of order $1,000$, establishing sub-nanometer-thin resonators as ultimate dilution materials. The intrinsic quality factor, however, is limited by surface losses at atomic thickness. Conversely, multilayer drums show a lower dilution factor but a high intrinsic quality factor, on par with established top-down materials of similar dimensions, both resulting from the increased thickness. A two-level-system analysis of the temperature-dependent damping confirms this bulk-versus-surface picture and provides first insight into its microscopic origin. Our results identify dissipation dilution as the governing mechanism for high-$Q$ mechanical vdW resonators. Combined with strategies such as soft clamping or stress engineering, they establish atomically thin resonators as a platform for ultrahigh-$Q$ quantum transduction and sensing.

Photo-detection is a fundamental component of experimental photonics, yet theoretical models often treat detectors solely in the photon-number basis, neglecting other relevant degrees of freedom such as spectral characteristics. We present a complete quantum process model for physically realistic photodetection that incorporates both photon-number effects and frequency-dependent detector response, described through explicitly derived Kraus operators in the operator-sum representation. This formalism accommodates realistic inefficiencies, models detection within finite spectral windows, and can be directly substituted for idealized models in quantum optical analyses. The model leads to identifying the suitable detection window of the detectors relative to the spectral distribution of incident photons and conversely, in order to maximize the observability of quantum effects.

We report Zeus-256, a room-temperature nitrogen-vacancy (NV) diamond processor with 256 simultaneously active processor-level logical qubits arranged in a 16 x 16 array. Each logical qubit combines an NV electron-spin ensemble with nuclear-spin memory and ancillary resources. OpenQASM 2.0 circuits are transpiled into RFSoC-controlled microwave, radio-frequency, optical, timing, measurement and bus-configuration sequences. An optically programmable proprietary protein-chromophore layer with an internal metastable-triplet spin mediator provides a reconfigurable biomolecular quantum bus for local and long-range interactions. Benchmarks cover QFT, GHZ entanglement, Grover search, arithmetic, variational, neural-network, graph-state and Shor-family circuits. Factor recovery is reported for 11 integers of 8-84 bits, with 10 attempts per instance; the 84-bit endpoint uses 256 qubits and 40,250,342 reported gates, with a reported execution time of 551.694 ms. Bell-CHSH measurements yield S = 2.8008 +/- 0.0446. Three-qubit Grover search returns the marked state in 958 of 1,024 shots (93.55%), compared with an ideal reference of 94.53%. A separate 30,000-shot population-and-parity protocol yields fixed-phase GHZ+ fidelity of 99.8960%, an estimated standard error of 0.2885 percentage points and a conservative physical 95% interval of [98.2342%, 100%]. Timing metrics are partial and do not establish quantum advantage. Scaling to 9,984 processor-level logical qubits is an engineering target, distinct from the demonstrated register.

We present a fully autonomous model of a mechanical Maxwell demon engine that converts heat absorbed by a qubit into population inversion in an attached quantum battery. A damped mechanical oscillator acts as a pointer that incorporates the essential demon function of information acquisition about the qubit state and subsequent feedback into the system dynamics, replacing external measurements and control operations. This is achieved by means of a Holstein-type Hamiltonian, which makes the pointer's equilibrium position depend on the qubit state and thereby induces a state-dependent resonance shift. The mechanism enables a selective energy transfer to an attached spin system that acts as the quantum battery. We derive both local and global Lindblad master equations for the coupled system and identify the parameter regimes in which the engine operates efficiently. The figure of merit is the resulting steady-state population inversion of the battery, quantified in terms of ergotropy. Based on these results, we discuss the necessary conditions for practical implementations of the demon engine on realistic experimental platforms.

Quantum devices can lose the resource needed for a specified function without entering a fixed failure subspace. We propose a resource-based reliability framework for this situation, quantifying the remaining task-relevant resource relative to a stated ideal capacity. The resource measure is selected through its operational connection to the task and the allowed operations. We develop this approach for a trusted quantum random-number generator and a calibrated two-port interferometer. Relative-entropy coherence determines the optimal asymptotic yield of standard coherent qubits under incoherent operations for the former, while logarithmic $l_1$ coherence quantifies the fringe resource of the latter and determines its calibrated correct-port probability. An exactly solvable multi-spin spin-boson model illustrates how environmental records affect these resources at the same isolated-spin dephasing strength. Collective noise preserves coherence within magnetization sectors for product inputs, but enhances the decay of Greenberger-Horne-Zeilinger branch coherence. Finite-record simulations connect the resource definitions to measurement counts and show that increasing the sample size reduces statistical fluctuations without eliminating bias from an incorrect many-spin noise model. The resulting framework provides a task-specific route to reliability assessment when a fixed failure projector is insufficient, while keeping retained resource capacity distinct from a classical survival probability.

Quantum computers are approaching the early fault-tolerant regime. Verifying the next generation of quantum hardware requires joint emulation of the quantum processor, hardware noise, and classical control and decoding logic. We introduce the Programmable Pauli Virtual Machine (PPVM), an open-source framework for digital twins of quantum processors. PPVM unifies Pauli propagation and generalized tableau simulation under a common abstraction within a single virtual machine. Its bytecode supports arbitrary classical control flow, with measurement-conditioned feed-forward available in the generalized tableau backend. For neutral-atom hardware, we derive independent and correlated atom-loss channels and integrate them into both backends. We demonstrate loss-aware magic state distillation on over a thousand physical qubits and integration with classical decoding through Bloqade QEC Studio.

Quantum error-correction code and circuit construction is an active field of research, motivating automated methods for identifying equivalent designs. We develop and evaluate automated strategies for deciding whether two descriptions of quantum error-correction codes are equivalent under specified transformations. We formalize permutation equivalence for stabilizer and CSS codes and local-Clifford equivalence for stabilizer codes within a unified framework that separates physical from representation freedom. We develop three decision strategies (group-action search, isomorphism-based methods, and constraint solving), together with invariants and signatures for preprocessing. The empirical evaluation shows that no paradigm dominates across equivalence notions, code families, and parameter ranges. We therefore combine their complementary strengths in input-dependent hybrid checkers following a staged Refute-Refine-Decide architecture. Mean hybrid runtimes remain below 10 s for most evaluated structured-code cases with $n \leq 37$; for inequivalent code instances with $n=144$, they are about 310 s for permutation and 16 s for local-Clifford equivalence.

Spatiotemporal optical vortices (STOVs) are structured light featuring a phase singularity in the spatiotemporal domain, exhibiting unique topology that couples spatial and temporal dimensions. To date, amplification of STOVs remains unexplored, and their wavelength tunability is limited by available light sources. In this work, we present the theoretical analysis and experimental demonstration of optical parametric amplification (OPA) of STOVs. The pulse energy of the STOV signal is enhanced by a factor of 60, while its spatiotemporal structure is robustly preserved. The generated idler inherits the phase-conjugated STOV topology with the opposite topological charge, governed by simultaneous conservation of energy, linear momentum, and spatiotemporal orbital angular momentum. The intrinsic wavelength-conversion capability of OPA further provides a route towards spectrally tunable STOV generation, spanning from visible to near-infrared wavelength regimes. This work paves the way toward further development of multi-stage amplification architectures, facilitating applications of wavelength-tunable spatiotemporally structured light at ultrahigh intensities.

Trotterization is a widely used algorithm for simulating quantum evolutions and consists of approximating a target unitary through a local linear decomposition of its generator that is repeated over $N$ steps. We introduce {scheduled trotterization}, a variable-weight modification in which the coefficients of the local linear decomposition are allowed to change from step to step. Using the geometry of the Lie group of unitary operators, we express the global endpoint error as a product of transported local defects, whose leading terms are obtained by two applications of the Baker-Campbell-Hausdorff formula, one inside each local step and one between different transported defects, separating the internal Trotter error from the external accumulation error. While we recover recent tighter bounds on the global approximation error when the weights are held fixed, the new framework allows us to propose a weight-varying schedule that significantly decreases the global error. For exact infinitesimal synthesis, we prove that this improves the usual fixed-weight $O(N^{-1})$ behavior to $O(N^{-2})$, without changing the basic pulse skeleton. We also extend the framework to imperfect infinitesimal synthesis, as arises in quantum gate synthesis problems, where admissible coefficients may only approximate the desired local corrections. In this case, the error is controlled by a local covering parameter measuring the quality of the available coefficient set. Numerical experiments for random $\SU(2)$ targets further support the predicted theoretical improvements. The results suggest a novel perspective for the analysis of Trotter errors, which can be treated as schedulable quantities to be coherently canceled at the endpoint.

Quantum mechanics and general relativity are remarkably successful, yet their joint predictions remain beyond direct experimental reach. Photonic interferometers operating in a gravitational field offer a promising route to test this regime: gravitational redshift differentiates photon propagation between vertically separated arms, leading to a predicted phase shift and reduction in interference visibility. These effects are minute on laboratory scales, motivating existing proposals to consider large interferometer areas to accumulate them geometrically. Indeed, such schemes typically require kilometre-scale optical paths to produce appreciable interferometric signals. Here, we propose a strategy that replaces geometric accumulation with spectral enhancement by coupling the two interferometer arms to optical scatterers based on ultranarrow atomic transitions. These transitions serve as local spectral references: gravitational redshift changes the photon's detuning from each resonance, producing large differences in reflection amplitude and hence substantial visibility loss and interferometric phase shift already for centimetre-scale height differences. We quantify the experimental requirements and assess the feasibility of implementation with current or near-term technology. Our proposal thus opens a route to tabletop optical tests of the interplay between quantum mechanics and general relativity.

The distance of a quantum code is a fundamental metric that dictates its error-correction capability. While quantum low-density parity-check (qLDPC) families such as Bivariate Bicycle (BB) codes offer a promising pathway to low-overhead fault-tolerant quantum computing, computing their distance is challenging. Current exact solvers and even search heuristics that provide a distance upper bound suffer from severe computational bottlenecks, restricting the discovery of optimal codes. In this paper, we construct a dataset of BB codes with corresponding distance upper bounds obtained through high-budget heuristic searches. We introduce BB-Net, an attention-based neural network architecture for predicting the distance of BB codes. It achieves 96.39% accuracy on the reference distances in the test set, compared with 94.86% for state-of-the-art heuristics with a budget of up to $10^{4}$ times more computational runtime. On a subset with certified exact distances, BB-Net achieves 98.94%. By relieving the distance-calculation bottleneck, BB-Net enables faster screening of large code spaces, particularly in ML-driven search pipelines, and thereby can accelerate the discovery of novel quantum error-correcting codes, an important capability for advancing scalable fault-tolerant quantum computing. Our code is publicly available: https://github.com/NadavSc/BBNet

Discrete time crystals are non-equilibrium phases of matter with spatiotemporal order and a response that breaks the time-translation symmetry of a periodic external drive. Interactions, spatial disorder and correlated random driving can in theory stabilize this order. In experiments, however, coupling to the environment limits the time crystal lifetime. Here we use stochastic local bit-flip error correction to prolong the time-crystalline response of a driven, spatially disordered two-dimensional Ising model on a superconducting quantum processor, using a repetition code with distances three and five on a honeycomb lattice with up to 68 physical qubits. Even though ancilla qubits, midcircuit syndrome measurements and decoding increase the required quantum and classical resources, the stochastic drive increases the memory decay time by a factor of up to two. At late times we observe that recovery stabilizes spatial order across the lattice. The spin-configuration distributions explain this separation, as recovery suppresses disagreeing bonds while broadening occupies completely reversed states. Syndrome measurements without correction accelerate the memory decay, demonstrating the importance of conditional correction. Our results show that local bit-flip error correction can preserve time-crystalline memory over more drive cycles than the bare dynamics.

Scalable long-distance quantum gates are essential for distributed quantum computation and scalable quantum networks. We propose an efficient scheme for implementing an $n$-qubit fan-out gate $C^n$ (also known as a controlled-NOT-$\cdots$-NOT gate) across spatially separated parties. Our protocol requires only a pre-shared $n$-qubit Greenberger-Horne-Zeilinger state, $n$ local controlled-NOT (CNOT) gates, and feed-forward operations, thereby reducing both the CNOT and Hadamard gate counts by $(n-2)$ when compared with the standard decomposition-based approach. We further develop two optical architectures to implement the heralded and post-selected $n$-photon fan-out gates, respectively. These schemes require fewer single photons resources and achieve higher success probabilities than their decomposition-based counterparts, representing significant improvements. The results indicate that our approach is experimentally feasible and pave the way toward practical long-distance quantum computation.

We study coherent classical shadows protocols for an unknown $d$-dimensional quantum state of rank at most $r$, allowing an arbitrary joint measurement on all available copies. For observables with operator norm at most one and centered squared Frobenius norm at most $F$, we study the minumum number of copies $T$ needed for the protocol to successed with propbability $1 - \delta$. We prove a lower bound on $T$, that depends both on $\delta$ and the number $M$ of post-measurement observables. Denoting $\ell=\max\{\log(2M),\log(1/\delta)\}$, we show that $T=\Omega\left(\min\left\{\frac{\sqrt{rF\ell}}{\varepsilon},\frac{(F\ell)^{2/3}}{\varepsilon^{4/3}}\right\}+\frac{\ell}{\varepsilon^2}\right)$ under the mild assumption $\log(2M)\lesssim d\min\{r,F\}$. The lower bound nearly matches the known upper bound and matches the conjectural strengthening of the known upper bound. The proof is inspired by the framework of the proof of the lower bound for Boolean Hidden Matching. We develop a Gaussian-lift noise kernel that transfers forward and reverse Gaussian hypercontractivity to the Grassmannian, allowing us to bound the distinguishing advantage in an auxiliary game with a revealed query observable. We use Schur–Weyl structure and posterior moment bounds to control arbitrary coherent measurements on the source side.

Maximum compatibility provides a criterion for phylogenetic reconstruction in which the objective is to retain a maximum set of mutually compatible characters. For binary characters, pairwise compatibility can be represented by a weighted graph whose vertices correspond to characters and whose edges connect compatible pairs. A leading algorithm by Cherry [BMC Bioinformatics, 18(1):127, 2017] uses this representation to identify maximum compatible character sets as maximum weight cliques. We formulate the problem as maximum weight independent set enumeration on the complement graph and use deterministic postprocessing to map sampled bit strings to maximal feasible solutions. To explore the prospects of quantum computational advantage, we further construct bespoke correction-in-the-loop Quantum Approximate Optimisation Algorithm instances and find that traditional Lagrange multiplier choices may not be optimal for the enumeration problem on noisy devices. We also introduce lossless graph reductions with reconstruction rules that preserve the complete set of optimal solutions. Our results indicate that graph reduction and sampling can be effectively combined to address the enumeration bottleneck in maximum compatibility phylogeny, while retaining exact reconstruction when the residual optimum set is completely resolved. We enhance Cherry's approach to maximum compatibility by introducing graph reduction techniques and quantum sampling. Our classical benchmarks show a clear difference between finding one optimum and recovering the optimum set in practice. We demonstrate the utility of our methods on graphs constructed from SARS-CoV-2 sequences.

We investigate the ergotropy of tripartite Greenberger-Horne-Zeilinger (GHZ) and W states in the quantum atmosphere of a Schwarzschild black hole, focusing on how the extractable work is redistributed under Hawking-induced thermalization. We find that the two classes of multipartite entanglement exhibit qualitatively different ergotropy structures. For GHZ states, the ergotropies associated with different accessible subsystems organize into two degenerate families, whereas for W states they obey a linear averaging relation with no counterpart in the GHZ case. Under symmetric gravitational thermal corrections, the two GHZ families remain separated by a constant energy gap that is independent of the radial position. We further show that the Hartle-Hawking constant $D_{HH}$ and the normalized radial distance $r/r_h$ play competing roles in the evolution of extractable work: increasing $D_{HH}$ suppresses its recovery toward the asymptotic Hawking limit, while increasing $r/r_h$ enhances the ergotropy accessible to the observers. These results show that the redistribution of extractable work in a black-hole environment is governed not only by gravitationally induced thermalization but also by the structure of the underlying multipartite entanglement, providing a thermodynamic signature that distinguishes GHZ- and W-type quantum correlations in curved spacetime.

Noise characterisation not only enables error mitigation but also provides valuable information about the intrinsic performance of a quantum device, identifying dominant error contributions and bounding noise stability well beyond the aggregated calibration data. Deploying such methods on a specific hardware topology must combine efficiency and accuracy, assess noise stability, and validate the reconstructed noise model. Here we develop and implement these methods on a superconducting processor with square-lattice topology. First, we revise the cycle-benchmarking protocol and reduce the bias arising from unlearnable degrees of freedom via a regularised cost function. Second, we extend a previously developed tensor-network tomography method to match the device layout and show how its accuracy can be improved by repeated layer execution. Both methods allow approximate sublayer noise models to be extracted from parent ones. Using noise characterisation as a tool, we map the noise structure, track drift, and validate the adequacy of the learnt noise models against experimentally observed noisy estimations in benchmark physical and chemistry circuits. These results inform further improvements in the underlying technology and provide estimates of the size of noise-mitigated circuits that the device can support.

We present a Python-based program that combines maximally localized Wannier functions-based first-principles electronic structure with the nonequilibrium Green's function formalism to enable efficient simulations of scanning tunneling microscopy (STM). The workflow builds upon standard density functional theory packages to construct compact transport Hamiltonians that preserve the properties of realistic materials. Superconductivity is incorporated via an effective pairing potential within the Nambu-spinor formalism, while coupling to the STM tip and substrate electrodes is treated using the wide-band limit approximation. Within this formulation, transport quantities such as current-voltage characteristics and differential conductance are evaluated in a closed analytical form. This avoids explicit numerical energy integrations and enables rapid spectroscopic calculations over broad parameter spaces. The framework provides a unified and computationally efficient approach for modeling superconducting hybrid nanostructures with spin-orbit coupling, magnetic textures, and spin polarization. Representative applications in spin chains, two-dimensional and molecular magnets on a superconductor demonstrate its robust capabilities for both simple model systems and realistic ab initio molecular structures relevant to modern STM experiments.

The dynamical formation of a complete Bose-Einstein condensate and the asymptotic purification of trapped bosons coupled to a quantized radiation field are rigorously established. By tracking the macroscopic one-particle density matrix $\kappa_T$ through a nonlinear resonance cascade, it is demonstrated that radiative relaxation irreversibly depletes all excited trap modes, even when the initial macroscopic state $\kappa_0$ is genuinely mixed. Here $\kappa_T$ is an average, with respect to a de Finetti measure $\mu_0$, over mean-field particle-field orbits, so that the mixedness of $\kappa_0$ reflects a statistical ensemble of orbits. Under the assumptions of a non-vanishing initial ground state component and strictly positive downward Fermi-Golden-Rule rates, strong trace-norm convergence to a pure condensate is proven, $$ \lim_{T\to\infty} \| \kappa_T-|\chi_0\rangle\langle\chi_0| \|_{\mathfrak{S}_1(\mathfrak{h})} = 0 \, . $$ Furthermore, the von Neumann entropy of the macroscopic one-particle density matrix is shown to vanish asymptotically, $$ \lim_{T\to\infty}S[\kappa_T]=0 \, , $$ without any claim of monotonicity in $T$. Thus, any initially mixed, positive-entropy state ($0<S[\kappa_0]<\infty$) is purified to the ground state $|\chi_0\rangle\langle\chi_0|$. For the proof, we derive the Hartree hierarchy of the coupled system of bosons and photons from the finite-$N$ BBGKY hierarchy of the microscopic quantum many-body system, establishing trace-norm convergence in the mean-field limit as $N\to\infty$. The limits are taken successively; first $N\to\infty$, then the weak-coupling limit, and finally $T\to\infty$. Although the global particle-field evolution remains unitary, the macroscopic one-particle state converges to a pure state as energy and correlations are continuously radiated into the dispersive field.

Spin wave theory plays a central role in the analysis of low-energy properties of the quantum ferromagnetic Heisenberg model. In this work, we present a first step towards a rigorous justification of this approximation in the context of quantum dynamics in one dimension. According to spin wave theory, the evolution of a spin wave state should be well approximated by its free evolution with the appropriate energy of free quasiparticles called magnons. Our main result establishes this idea rigorously for a class of spin wave packets. We focus on spin-$\frac{1}{2}$ systems, and consider wave packets composed of two magnons. We argue our result is optimal with respect to the timescales.

Non-Hermitian dynamics possesses distinct left and right eigenstates, but their normalization freedom obscures a direct probabilistic interpretation. Starting from a globally Hermitian system governed by the standard Born rule, we generalize dynamical quantum phase transitions (DQPTs) from a reference state to a physical subspace. This generalization provides a clear probabilistic interpretation of left and right states: when each state is normalized to itself, their mutual overlap determines a directly accessible dynamical transition rate. We discuss the new phenomena governed by this emergent non-biorthogonal Born rule and further identify a class of exceptional-point DQPTs (EP-DQPTs), at which the eigenstates of the critical propagator coalesce. Our theory places the probabilistic interpretation of non-Hermitian quantum mechanics on the firm footing of Hermitian quantum mechanics.

Amplitude embedding lets a variational quantum model read many classical features with few qubits, but the model output is then only a quadratic form in the normalized input. Data re-uploading, which encodes the input repeatedly between trainable blocks, can be used to enrich such a model. Because every additional upload of an amplitude embedding repeats a costly state preparation, the gain that an upload buys has to be known before the gates are spent. This tutorial thus addresses the problem of explaining what data re-uploading adds to an amplitude-embedded model and how large the gain is. We express sequential re-uploading and parallel re-uploading with two copies in one notation and show that each upload raises the reachable polynomial order by two. Under one trainable circuit family and one budget of trainable parameters, simulation results show that re-uploading raises the test coefficient of determination from 0.689 to between 0.883 and 0.975 on targets of order four and from 0.337 to between 0.642 and 0.783 on targets of order six, on all ten seeds. On a quadratic target and on handwritten digits, one upload remains the best choice, and every additional upload lowers the gate error that the classifier tolerates. These results help designers match the number of uploads to the polynomial order of the task at hand.

We theoretically investigate single-photon coherent transport through a finite waveguide quantum electrodynamics (QED) array with spatially modulated emitter-waveguide couplings. By combining exact scattering calculations with spectral factorization and a semiclassical WKB analysis, we identify how the coupling profile controls the reflection bandwidth and its finite-size dependence. A Gaussian transverse displacement produces an exponential-of-Gaussian decay-rate profile that broadens the high-reflectivity window and suppresses the boundary-induced Fabry-Perot oscillations compared with a uniform array. The transmission zeros remain exactly degenerate at the atomic resonance for arbitrary positive coupling profiles at non-Bragg spacings. In contrast, the collective poles reorganize under the spatial modulation, redistributing their radiative widths and preventing individual subradiant resonances from terminating the reflection window. We further derive an algebraic 1/N scaling law for the contraction of the bandwidth toward its bulk value. The bulk bandwidth is determined by the largest local decay rate, whereas the finite-size correction increases as the profile becomes sharper, leading to an optimal profile width. These results establish spatial coupling engineering as a practical tool for designing broadband atomic mirrors in atom-nanofiber and circuit-QED platforms.

Any pair of sufficiently generic Hamiltonians on $\mathbb{C}^d$ generates the full unitary group, i.e., any $W\in U(d)$ can be synthesized to arbitrary precision by alternating between the two evolutions for suitably chosen durations. For any given pair of Hamiltonians, the minimal number of switches required to cover the entire group is at least $d$ and unbounded in general. Despite this, we show that it scales linearly in $d$ in expectation. Assuming that the two spectra are sufficiently generic, we derive constructive upper bounds on the minimal switching number as a function of the change-of-basis matrix between the two eigenbases. In particular, if this matrix has a column whose entries all have equal moduli, as for a complex Hadamard matrix, then $9d$ switches suffice to reach every unitary. To obtain these results, we construct a short exact representation of any unitary as a product of unitaries that are alternately diagonal in two given bases. All bounds are extended to non-generic spectra and bounded evolution times.

Level crossings, where two quantum energy levels intersect, are ubiquitous in quantum systems and play a central role in controlling quantum dynamics. In this study, we establish a framework that connects these level crossing structures to the ultimate precision limits of quantum metrology. By analyzing a Hamiltonian with the level crossings structure, we identify the conditions under which multiple parameters can be estimated simultaneously with maximal sensitivity near the level crossing point. We then construct a resource efficient sensing protocol based on unitary quench dynamics and Bayesian estimation, enabling high precision, low cost parameter estimation without requiring entanglement or complex control. We present a protocol whose estimation precision saturates the Holevo Cramer Rao bound, the tightest achievable precision bound in multi parameter estimation. Using the two level model and the two spin Ising model as illustrative examples, we demonstrate how the protocol can be applied to a system with level crossing Hamiltonian structure. Our findings reveal that level crossings serve as universal operating points for precision quantum metrology, offering a simple and scalable path toward practical multi parameter sensing across diverse quantum platforms.

Boson sampling with array of on-demand single photons (discreet variable Fock states) as resource states provides distinct advantages in complexity scaling compared to single photon resource states mimicked by the states (continuous variable) generated in nonlinear photonics. Recent progress in realization of regular ordered array of mesa top single quantum dots (MTSQDs) enabling on-demand generation of many photon resource states with high single photon purity and indistinguishability [1,2] has opened the possibility of implementing chip-scale Boson sampling with single photons. An important question towards scale up of such circuits is how the dephasing and decay timescale of individual on-demand single photons affect the final probability distribution of the N-photon entangled state. In this work we report a framework that provides direct link between the physical sources of decoherence to the outcome of multiphoton correlation measurements. We explicitly incorporate the symmetrization of the N-photon states while accounting for the shape of the individual wave packets and dephasing. Using this framework, we show predictive estimates of the probability of generation of a 4-photon NOON state using an optical circuit initialized with 4 identical single photon wave packets, mimicking the emitted photons from MTSQD single photon sources reported in [2]. Specifically, we show how the probability of generating various 4-photon entangled states depend on the two-photon interference visibility which is determined by the pure dephasing timescale in relation to the radiative decay timescale. The results provide quantitative guidelines to measure 4 photon and higher number of entangled photon states generated in an optical circuit with on demand single photon sources and provide a link between physical processes such as temperature and the output state of the quantum optical circuits.