Papers

We analytically study the time evolution of the expectation values of observables in periodically kicked many-body quantum systems. Starting from an initial state, we compute both the transient and the long-time properties of the observables. Our derivation explains the criteria and the mechanism that lead to the infinite-temperature statistical average of observables at long times, irrespective of the initial state. When the criteria are violated, the observables oscillate with time. These oscillations are subharmonic and robust to small perturbations, suggesting the emergence of a discrete time crystal phase. We demonstrate these features explicitly in periodically kicked nonintegrable spin chains. For a spin chain with two kicks per cycle, we show that the kicked chain can exhibit an ergodic or a discrete-time crystal phase for the same kicking strengths, depending on the initial state preparation. We complement our time-evolution study of observables with the spectral form factor of these kicked models.

Let $H$ be a finite simple graph. A one-particle continuous-time quantum walk on its line graph $\ell H$ has one mode for each edge of $H$. This paper is a corrected and reorganized account of that setting. We first record the matrix encoding of an edge-amplitude vector, its Schur state. The encoding is necessarily complex symmetric if it is to be complex linear and to retain the global phase, and it is normalized by $1/\sqrt{2}$. It is unitary for the Frobenius inner product and is closed under a canonical tensor lift to the categorical product of graphs. The tensor lift also pins down the convention. Among all unimodular phase variants the symmetric choice is the only one that survives, and every relaxed variant reduces to a sign. We then replace the labelled tensor-power description by the bosonic and fermionic Fock spaces over $\ell^2(EH)$, and assemble the standard free-particle apparatus in the form used afterwards. This covers the occupation-number basis, the second-quantized line-graph Hamiltonian, permanent and determinant formulae for many-particle transition amplitudes, and the one-particle reduced density matrix. The one graph-theoretic input is the even-Eulerian criterion, which is the zero-sum $2$-flow criterion of Wang and Hu, recalled here with a short proof to fix conventions. Its translation through the incidence identity gives a real equimodular full-support $-2$ eigenmode of $A(\ell H)$, and hence bosonic condensates of energy $-2N$ that are uniform over the edges of $H$. The fermionic case is stated separately so that the Pauli constraint is explicit.

Quantum low-density parity-check (QLDPC) codes offer a promising route to scalable fault-tolerant quantum computation, but their performance under iterative decoding is strongly influenced by short-cycle structure and other harmful subgraphs in the associated Tanner graphs. This paper develops an algebraic framework for constructing and analyzing (Q)LDPC codes from dyadic and quasi-dyadic matrices-translation-invariant $2^\ell \times 2^\ell$ binary matrices specified compactly by a signature row and forming a commutative ring with recursive block structure. Leveraging this structure, we relate cycles in lifted Tanner graphs to tailless backtrackless closed walks in the protograph and derive efficient, implementable methods to enumerate and control short cycles (notably $4$-, $6$-, and $8$-cycles). We introduce dyadic-aware PEG-style construction algorithms that use forbidden sets of shifts to maximize attainable girth when possible and otherwise minimize the multiplicity of the shortest cycles at the target girth. Motivated by error-floor phenomena, we further characterize and explicitly enumerate absorbing sets in key dyadic layout boundary cases, identifying configurations that induce abundant $(a,0)$-absorbing sets. Finally, we propose CSS-oriented dyadic constructions that satisfy commutation constraints by design and demonstrate via belief-propagation simulations that reducing short-cycle multiplicity can yield substantial decoding gains even when girth cannot be increased.

In non-relativistic mechanics, the total (orbital) angular momentum (AM) of a spatially-distributed system can be decomposed into intrinsic and extrinsic contributions. In relativistic quantum mechanics, intrinsic AM is typically associated with spin, which can be described using the Pauli-Lubanski four-vector. Here, we develop a unified formalism that combines the main features of both approaches and describes the intrinsic AM of a relativistic wavepacket, including both spin and orbital contributions. Our approach is based on the "expectation Pauli-Lubanski vector" constructed from the expectation values of the wavepacket's momentum and AM. Equivalently, it defines the intrinsic AM relative to the wavepacket's energy centroid. In contrast to the conventional Pauli-Lubanski formalism, the zero-mass singularity does not occur for the expectation Pauli-Lubanski vector. Consequently, the intrinsic AM of a wavepacket may have an arbitrary orientation with respect to its momentum, even for massless particles. We illustrate the general theory with a number of examples of relativistic wave beams and packets carrying spin and orbital AM.

Long-range (LR) quantum spin systems offer promising advantages for quantum information processing and sensing. Here, we investigate parameter estimation in an long-range XX spin model coupled to a reservoir, which gives rise to an effective long-range RT-symmetric non-Hermitian iXY Hamiltonian. The interactions extend up to a tunable coordination range and decay algebraically with distance, enabling a direct comparison between long-range and short-range (SR) regimes. Focusing on the estimation of the transverse magnetic field and anisotropy parameter, we initialize the system in a fully polarized state and analyze the resulting dynamical quantum Fisher information (QFI). We show that, with suitable tuning of the system parameters, both the time and system-size scaling of the QFI are enhanced in the LR regime relative to their SR counterparts. Moreover, the non-Hermitian LR model can exhibit superior dynamical QFI compared with the corresponding Hermitian model, demonstrating a genuine metrological advantage induced by the interplay of long-range interactions and non-Hermitian effects. In contrast, we establish a no-go result at the critical magnetic field: when the probe is prepared in the lowest-energy eigenstate, the QFI scaling remains identical for the Hermitian and non-Hermitian cases.

Entropic uncertainty relations $H(A)+H(B)\geqslant \gamma$ give a nonzero lower bound $\gamma$ to the sum of the Shannon entropies $H$ of the outcome probabilities of incompatible observables $A$ and $B$. They are better than the variance-based uncertainty relations because they only depend on the Born statistics of the outcomes and not on the outcomes themselves, and because bounds $\gamma$ typically are state independent. Here we provide a state-independent lower bound $\gamma_s$ that is better than the textbook Maassen-Uffink bound and, in the limit of the parameter $s\to 2$, becomes asymptotically tight for all $A,B$. The bound can be extended to Renyi entropies. After the submission of this paper, we found out that the main results presented here were already on page 6 of https://quantum-journal.org/papers/q-2018-03-30-59/pdf/

We present a statistical framework for extracting spatially resolved entanglement directly from an ensemble of marginal (one-body) wavefunctions in Time-Dependent Quantum Monte Carlo (TDQMC). Treating the guide waves as a statistical mixture in Hilbert space, we show that the Gram matrix acts as a covariance operator whose spectrum coincides with the Schmidt spectrum. The associated functional standard deviation closely tracks the von Neumann entanglement entropy both globally and locally via walker partitioning, providing a physically transparent real-space diagnostic of quantum correlations without requiring construction of the full many-body wavefunction. Applications to one-dimensional two-electron bosonic and fermionic systems (helium atom and hydrogen-like molecule) demonstrate excellent agreement with strict conditional-wave results for opposite-spin electrons. For same-spin fermions, TDQMC's statistical treatment of exchange symmetry avoids the unphysical negative local entropies that arise from naive ln(2) subtraction, yielding spatial profiles that remain positive throughout. The method establishes a direct bridge between classical ensemble statistics and quantum entanglement measures, offering a computationally efficient real-space diagnostic tool for mapping the spatial distribution of correlations in many-body systems.

We study the Mpemba effect in a pair of linearly coupled harmonic oscillators, one of which is parametrically driven and coupled to an independent thermal bath. Using the covariance-matrix formalism, we derive the relaxation dynamics under both Gaussian white noise and Lorentzian colored noise, including single-channel and dual-channel noise embedding. We characterize relaxation through the Frobenius distance to the steady state and through the projection onto the slowest mode of the dynamical generator. Our results show that parametric driving provides the primary control knob for anomalous relaxation: as the drive approaches the stability boundary, the Mpemba crossing time decreases systematically. Colored noise further enhances the effect, with dual-oscillator Lorentzian noise producing a stronger reduction in the crossing time than single-oscillator noise and enlarging the parameter region where the Mpemba effect occurs. Nevertheless, the slow-mode structure of the drift matrix remains the dominant mechanism, while the influence of colored noise is secondary and mainly quantitative. We show that the Mpemba crossing time decreases as the system approaches the parametric stability boundary and that Lorentzian colored noise enlarges the region in the parametric and coupling strength plane where the Mpemba effect is observed.

Finite-time quantum thermal machines require diagnostics beyond average work and efficiency, because microscopic engines operate in regimes where fluctuations, incomplete thermalization, and coherence are equally important. Here we develop a measurement-backaction-free (coherence-preserving) fluctuation diagnostic for an engineered qubit Otto engine coupled to an actively maintained population-inverted hot channel. The engine is analyzed using a dynamic Bayesian network (DBN) reconstruction of the unmeasured coherent cycle, yielding work, heat, power, and normalized efficiency-proxy fluctuations without imposing the projective dephasing inherent in two-point energy measurements. The inverted channel is treated as an active reduced-model resource; accordingly, all reported power and efficiency enhancements represent gross working-medium advantages, not net device efficiencies. In the full-thermalization limit, population inversion enhances extracted work and output power while opening a stability sector with markedly reduced relative power fluctuations. When finite-duration isochores are implemented, this gross enhancement reorganizes into a structured operating landscape with distinct high-power, high-efficiency, and low-relative-noise sectors, whose boundaries are governed by the competing timescales of nonadiabatic driving and thermalization rates. A direct comparison reveals that DBN and conventional two-point measurement predictions diverge precisely in coherence-rich regimes, identifying where a backaction-free reconstruction is essential. A coherence-sensitive analysis further shows that the positive-temperature reference operates optimally in an almost decohered region, whereas the inverted high-efficiency branch remains aligned with the dominant post-hot-bath coherence ridge. These results provide a reduced-model benchmarking framework for engineered qubit thermal machines.

The application of quantum reinforcement learning (QRL) to real-time control systems faces significant challenges regarding hardware latency, noise susceptibility, and learning convergence. This work presents an end-to-end investigation of a minimal hybrid quantum-classical agent applied to the CartPole benchmark, addressing the gap between idealized simulation and execution on a physical superconducting quantum processing unit (QPU). We demonstrate that a single-qubit agent acts as an effective learning model, solving the environment in substantially fewer episodes than a comparable classical actor-critic network even when the training of the hybrid agent is restricted to use parameter-shift for its quantum circuit component. To connect learning to deployment constraints, we map the inference-time trade-off between control-loop rate and measurement shot budget to provide guidance for an eventual real-time control demonstration. The resulting performance matrices show that both inference control frequency and shot count strongly affect balancing stability: higher inference frequencies consistently improve performance, and increasing the shot budget lowers the minimum inference frequency required to achieve near-maximal balancing. These results highlight the importance of finding an optimal medium between shot count and control frequency and developing circuits that are e.g. initial-state invariant. Lastly, we address the critical bottleneck of control latency on NISQ hardware by bypassing the standard high-level software stack and programming the Zurich Instruments readout electronics directly via command tables. These results quantify some of the current boundaries of quantum-assisted control and provide a start for achieving the tens-of-hertz throughput required for real-time closed-loop control feedback.

We present a time-resolved digital quantum simulation of cosmological particle creation in a de~Sitter–radiation FLRW transition. Instead of compiling only the final Bogoliubov transformation into a one-shot circuit, we discretize the conformal-time evolution and implement the dynamics as a Trotterized sequence of short-time circuit blocks. This formulation gives access not only to the late-time particle number, but also to the build-up of fixed-basis pair occupation during the non-adiabatic transition. Using a four-qubit single-excitation encoding for a momentum pair $(+\mathbf{k},-\mathbf{k})$, we compare matrix-Trotter evolution, noiseless statevector simulation, finite-shot Qiskit Aer simulation, and a shallow $N=1$ IBM hardware implementation. The simulator results are consistent with the analytic sudden-transition benchmark $n_k=1/[4(k\eta_e)^4]$ in the controlled single-excitation regime. The IBM experiment demonstrates execution of the shallow circuit block, but exhibits a residual hardware error of order $10^{-2}$, indicating that quantitative hardware reconstruction of the particle spectrum remains beyond current NISQ performance.

The quantum approximate optimization algorithm (QAOA) has emerged as a promising candidate for demonstrating quantum advantage on noisy intermediate-scale quantum (NISQ) devices. While various QAOA parameterization schemes exist, ranging from the original single-angle approach to the more expressive multi-angle quantum approximate optimization algorithm (MA-QAOA) and automorphic-angle quantum approximate optimization algorithm (AA-QAOA), each presents distinct trade-offs between expressiveness and classical optimization complexity. In this work, we introduce the $k$-interaction-angle quantum approximate optimization algorithm ($k$A-QAOA), a parameterization scheme that groups cost function terms by their $k$-body interaction order, providing a natural middle ground between parameter efficiency and solution quality. This approach is particularly well-suited for combinatorial optimization problems defined on hypergraphs, where multi-body interactions naturally arise in applications such as Boolean satisfiability and resource allocation with multi-party constraints. We benchmark $k$A-QAOA against standard single-angle quantum approximate optimization algorithm (SA-QAOA), MA-QAOA, and AA-QAOA on two problem classes: 3-uniform cyclic sign-alternating hypergraphs and random coefficient hypergraphs. Our results demonstrate that $k$A-QAOA achieves approximation ratios comparable to MA-QAOA while requiring significantly fewer function evaluations, thereby reducing quantum resource consumption.

We investigate entanglement dynamics in bipartite systems governed by inhomogeneous Hamiltonians of the form $H = H_L + H_R$, where $H_{L/R}$ acts only on the left or right region and is homogeneous within each region. Focusing on the XX chain and the transverse-field Ising chain, we derive analytical formulas for the entanglement entropy between the two regions in the hydrodynamic limit of long times. In this regime, fermions incident on the interface undergo scattering, generating entanglement between reflected and transmitted modes. The resulting quasiparticle picture is controlled by the transmission coefficient, which we obtain analytically by solving the stationary lattice Schrödinger equation. Due to the bounded dispersion, strong inhomogeneity suppresses both transport and entanglement growth. We benchmark our analytical predictions against numerical simulations in paradigmatic setups. Finally, we extend the analysis to the interacting XXZ chain using tDMRG. The numerical data show qualitative agreement with the quadratic case: entanglement growth remains suppressed in the strongly inhomogeneous limit. Notably, however, entanglement continues to increase even when transport is suppressed, at least at intermediate times.

This textbook is drawn from notes for a two-semester graduate course in quantum mechanics. It begins with the most constrained quantum system, and recovers the rest of the subject by relaxing those constraints one at a time. The starting point is a single qubit, the smallest nontrivial Hilbert space with the strongest possible restriction on its dynamics, made concrete by a Bloch cube whose six faces are the cardinal states of a spin-1/2 system. Tensor products admit many qubits; lattices give them a place to live; time evolution sets them in motion; the continuum limit produces wavefunctions; three-dimensional angular momentum, the hydrogen atom, and perturbation theory follow; Lorentz invariance promotes the lattice of spinors to the Dirac equation; and the renormalization group asks how theories at different scales relate. Each chapter loosens one feature of the qubit while keeping the others fixed, so that the standard apparatus of graduate quantum mechanics arrives as a sequence of controlled generalizations rather than as separate topics. Discrete-to-continuous transitions recur at four scales: in Hilbert-space dimension, in real space, in time, and in coupling. The book closes by reimposing one of the original constraints, returning to a two-level system that is now a logical qubit protected by quantum error correction, with the fault-tolerance threshold appearing as an unstable RG fixed point and supplying the reason a logical qubit, independent of its underlying hardware, can exist at all.

Strong light-matter coupling gives rise to polaritons - hybrid excitations whose mixed photonic and matter character enables control over optical, electronic and chemical properties. This Feature Article surveys the main architectures supporting polariton formation, including photonic microcavities, plasmonic nanostructures, open cavities and metasurfaces, and outlines how inorganic semiconductors, organic aggregates and hybrid systems access strong and ultrastrong coupling. Key phenomena such as coherent dynamics, vibronic interactions, dark-state reservoirs and polariton-mediated energy and electron transport are discussed, together with the experimental and theoretical tools used to study them. We highlight examples where strong coupling modifies charge transport, energy flow and chemical reactivity, and we summarize emerging regimes, including intermediate and dark-strong coupling, that broaden the landscape of hybrid light-matter physics.

Collective strong coupling of molecular ensembles to optical cavities opens a route to modifying matter through genuinely collective electronic correlations. Yet even in the absence of a cavity, Coulomb correlations are notoriously difficult to describe, and cavity coupling adds transverse correlation channels extending over the entire molecular ensemble. Here we show that this seemingly intractable problem admits a controlled description by spin glass theory, i.e., by the analytically solvable spherical Sherrington-Kirkpatrick model. Our results predict two collective correlation phases, a paracorrelated phase and a spin-glass correlation phase, beyond the conventional uncorrelated molecular regime. These phases reveal an entropy-driven localization-delocalization mechanism that transfers molecular electronic states into collectively degenerate cavity-dressed states. Analytic calculation suggest that this collective correlated state can either remain insulating or even turn metallic if the entropic occupations favor a fractional filling. Our work reveals cavity-mediated electron correlations as a microscopic mechanism for emergent phases in strongly coupled molecular ensembles.

We propose a family of low-rank, completely positive and trace preserving schemes for the Lindblad equation, a common model for open quantum systems. Low-rank representation is employed at two levels: the density matrix is factorized into the product of tall-skinny matrices, and the columns of these matrices are further represented using the tensor train (TT) format, also know as matrix product states (MPS). This two-level low-rank format fits naturally into our existing Kraus is King scheme (arXiv:2409.08898v2 [math.NA]) for the Lindblad equation, whose underlying operations are arithmetic on the columns of the tall-skinny matrices. We show how these operations can be performed efficiently in the TT/MPS format, with particular emphasis on density matrix rank-truncation. We conclude with extensive numerical experiments demonstrating the convergence of this scheme and its efficiency in simulating systems with up to $10^{19}$ degrees of freedom using only modest compute resources.

We demonstrate a paraffin-coated planar reflective multipass vapor cell for compact optical atomic magnetometry. The cell has an internal volume of $12 \times 12 \times 8~\mathrm{mm}^3$ and supports 20 optical passes with a total transmittance exceeding $65\%$, while maintaining a longitudinal spin-relaxation time of $^{87}\mathrm{Rb}$ longer than $1~\mathrm{s}$. The planar geometry provides spatially separated input and output beams, enabling compact optical integration. A single-cell free-induction-decay (FID) magnetometer reaches $10~\mathrm{pT}/\sqrt{\mathrm{Hz}}$ in the geomagnetic-field range, presently limited by current-source noise in the field coils. A two-cell differential configuration achieves a sensitivity of $\sim 28~\mathrm{fT}/\sqrt{\mathrm{Hz}}$ over the $1$–$15~\mathrm{Hz}$ band for bias fields of $0.3$–$0.7~\mathrm{G}$. These results establish that paraffin-coated planar multipass cells offer high optical depth, long coherence times, and an integration-friendly platform for ultrasensitive magnetometry.

We consider the Hamiltonian $H$ of a particle in one dimension with a position dependent mass for which we apply the recent strategy of the so-called abstract ladder operators, in the attempt to find its eigenvalues and eigenvectors. We don't assume that $H$ is self-adjoint, while we focus on the case of a factorizable operator. We show then that pseudo-bosonic operators play a relevant role in this analysis, and we construct bi-coherent states attached to these operators. Explicit examples are discussed.

Spectral functions measured with angle-resolved photoemission spectroscopy (ARPES) provide key insight to elucidate the band structure of materials. Comparison with theory requires computing dynamical one-point functions in some equilibrium state, which can be classically challenging. Their measurement on quantum computers poses multiple problems and comes with a large sampling overhead when standard techniques are used. We introduce an efficient way of measuring spectral functions on a quantum computer by directly modeling the interaction of the system with the environment involved in ARPES experiments. We develop quantum circuits whose local expectation values are proportional to the spectral function $A(k,\omega)$ for all momentum $k$ and a specific chosen frequency $\omega$. Although coming with a qubit and two-qubit gate overhead, our approach requires $O(N)$ times less sampling than previous approaches, translating into a factor $O(N)$ faster in runtime, and is particularly adapted to ion-trap quantum computers. The algorithm requires to implement a fermionic Fourier transform (FFT). We write out an efficient gate decomposition for generic radix-$n$ FFT and benchmark it on hardware for radix-$3$ on $27$ qubits. We finally demonstrate our algorithm on a Quantinuum System Model H2 ion-trap system, computing the spectral function on a one-dimensional system of $27$ sites, using $54$ qubits.

Direct fidelity estimation benefits from tailoring measurements to a fixed target, but the operator-aware shadow importance sampling (OASIS) method optimizes an outcome-wise linear-program surrogate rather than the exact worst-case variance over physical states. We propose an exact spectral replacement for arbitrary target states under the same non-adaptive single-copy measurement model. Specifically, we characterize unbiased linear estimators by a single operator identity, determine the state-wise optimal sampling law for fixed reconstruction coefficients, and convert the exact minimax problem into a semidefinite program. The resulting offline design and online estimator are presented as an algorithm and implemented with local Pauli measurements. Numerical simulations under depolarizing noise demonstrate that our exact spectral optimization outperforms the OASIS surrogate in terms of estimation variance.

Partial-transpose (PT) moments are among the most practically relevant nonlinear quantities accessible from local Pauli classical shadows, because they directly underpin mixed-state entanglement certification and recent PT-moment-based phase diagnostics. The online framework of Marso et al. rewrote the exact PT-moment statistic into a fixed-memory recurrence that updates a small collection of accumulated matrices after each new shadow snapshot. Its update cost is independent of the shot number, but each step treats the incoming partially transposed snapshot as a generic dense matrix. Therefore, the arithmetic cost scales cubically with the dimension of the Hilbert space. We show that the same estimator can be updated exactly in subcubic time per shot while retaining the same memory. The key point is that the accumulated matrices become dense, but the fresh partially transposed snapshot still factorizes into local factors. Right-multiplication by that factorized snapshot can therefore be executed by exact column-pair sweeps. For the second PT moment, we further optimize the process by utilizing a Pauli basis update.

Quantum stochastic master equations of jump type are formulated in a general way and connections with quantum/classical hybrid systems and quantum filtering theory are discussed. By introducing the notion of “typical trajectory", we show how to recursively construct the solution of the non-linear stochastic master equation (the conditional state). Moreover, by the notion of “exclusive probability densities" we can describe all the probabilities related to the jumps, in particular, the waiting times of the jumps and their probability distributions. This general formulation and the idea of hybrid system allow to unify and generalize different fields: evolutions under non-Hermitian Hamiltonians, unitary dynamics interspersed by quantum channels at random times, quantum renewal processes, continuous time open quantum walks, Lindblad rate equation, ...

Multipartite entanglement is the premier resource for quantum technologies. Yet, its exact quantification in the laboratory is notoriously challenging, typically requiring the full knowledge of high dimensional quantum states. Here, we construct observable bounds to multipartite entanglement for systems of arbitrary size, which are functions of the local and global state purities, and correlation functions. First, we derive experimentally accessible upper and lower limits to both the bipartite entanglement of formation and the squashed entanglement of bipartite systems, by leveraging cornerstone results of quantum information theory: the entropy strong subadditivity inequality and the Koashi-Winter monogamy relation. Then, we convert them into bounds to the entanglement up to degree k for arbitrary states, and to the genuine k-partite entanglement, by employing a recently proposed method. Finally, we analytically and numerically test these results, by bounding the multipartite entanglement of several relevant states and mixtures, including the important classes of GHZ, Dicke, W states, and random pure states.

High-fidelity circuit execution on noisy intermediate-scale quantum devices is bottlenecked by compilation pipelines that disregard complex, correlated noise. To address this, this methodology article proposes a quantum machine learning control (QMLC) framework for generative quantum circuit synthesis from gate-set tomography (GST) data that bypasses the traditional two-step pipeline of characterizing native quantum gates via GST followed by unitary decomposition algorithms. Instead, a generative concept space is directly learnt from GST data, enabling conditional synthesis of quantum circuits on a desired output distribution. Our approach tokenizes GST germ circuits and embeds them into a structured latent space using a curriculum-learning-motivated strategy, starting with short circuits and progressively incorporating longer ones with diverse output statistics. The embedded sequences are processed by a set-vision transformer with permutation-invariant pooling, producing k-seed vectors that represent the learned concept space of the quantum device. Aggregating data across multiple circuits makes this latent representation inherently context-aware, capturing the shared physical noise environment (e.g., crosstalk, drift) that isolated gate metrics miss. We propose an unconditional diffusion model to sample from the concept space. During inference, a user provides a target measurement distribution, and the model generates a corresponding circuit. To ensure fidelity and robustness, the output is denoised using a diffusion model that operates on the target conditional covariance matrix. This end-to-end framework is a step towards context-aware, hardware-native circuit synthesis directly from raw GST data, which offers a new paradigm for integrating quantum control and compilation. The QMLC framework is particularly suited for near-term quantum devices with complex calibration procedures.

In a strongly interacting Rydberg atom array, the dynamics are often constrained to the decoupled Hilbert subspaces, representing an intriguing paradigm for nonergodicity. By considering a variable detuning of the global Rydberg coupling, we show that, not only is the existence of these Hilbert subspaces dependent on the interplay of detuning and interaction, but they are also strongly fragmented, with the fragment dimensions exhibiting various scaling behaviors with increasing system size. The resulting constrained dynamics of the system are thus governed by the dimension and connectivity of these fragments. We then adopt an auxiliary fermion description to reveal the underlying emergent kinetic constraints for the subspace fragmentation and fragment-confined dynamics. Our results provide a systematic understanding of Hilbert-space fragmentation in Rydberg arrays, and shed light on engineering nonergodic many-body dynamics beyond the PXP model.

Barren plateaus (BPs) are conventionally characterized by suppressed gradient variance, but this aggregate description does not reveal how the loss of gradient signal is composed across Hamiltonian terms. We introduce a term-resolved framework that decomposes the second moment of the gradient exactly into pre-cancellation activity, sign organization, and their statistical coupling. A conditional random-sign model, which preserves termwise magnitudes while treating signs as independent and symmetric, provides exact references for organization and coupling. We apply the framework to a hardware-efficient ansatz (HEA) and a Hamiltonian variational ansatz (HVA) for the transverse-field and longitudinal-field Ising models. For the HEA, finite-size suppression of the second moment is carried almost entirely by decaying activity, accounting for 96.5-98.9% of the fitted log-slope across tested depths in both Hamiltonians, while organization shows no systematic scaling and coupling remains consistent with its random-sign reference. For the HVA, activity and organization instead grow with system size and contribute comparably to the second-moment scaling. A bias-corrected mean-gradient check is consistent with zero in every tested condition, so these results carry over approximately to the gradient variance. Microscopic sign-alignment analysis further shows sector-structured organization in the HVA, whereas the HEA exhibits only weak residual sign structure that does not accumulate into net signed organization. These patterns are reproduced across both Hamiltonians, providing a term-resolved characterization of BP-relevant gradient suppression beyond aggregate gradient statistics.

Quantum autoencoders (QAEs) are learning architectures that compress quantum data into a low-dimensional latent state while preserving the information needed for reconstruction. We study blind single-copy compression of quantum states through a $k$-qubit bottleneck and investigate the minimal circuit width required to attain the information-theoretic optimum under average infidelity. Between the conventional architecture, which is narrow but nonuniversal, and fully general completely positive and trace preserving (CPTP) realizations, which are universal but overparameterized, we identify a balanced regime. We prove that for every distribution of pure $n$-qubit states, there exists a QAE with $k$ encoder ancillas and $n$ decoder ancillas that achieves the optimal fidelity over all CPTP encoder–decoder pairs. The encoder-side statement is sharp in that we construct source families for which every optimal scheme necessarily uses at least $k$ encoder ancillas, thereby determining the universal encoder threshold exactly. On the decoder side, we show that isometric decoders are optimal for several analytically tractable source families, but we also exhibit an explicit counterexample demonstrating that decoder isometry is not universally sufficient. Nevertheless, numerical experiments indicate that the performance gap is practically negligible.

Reservoir computing is a framework which is primarily used for temporal information processing, using the intrinsic dynamics of an underlying physical system. The framework, in a quantum setup, is implemented using ergodic dynamics associated with Hamiltonian models. The computational power of the reservoir is closely tied to this underlying dynamical nature, and to probe this further, we study the effectiveness of a reservoir that is made using structured brickwall circuits built from two-qubit gates. Here, the global ergodic nature of the circuit model results from the said arrangement, which has an important role in extracting useful performance with a minimal setup that is independent of an associated Hamiltonian. We focus on the nature of the gates used in this setup and evaluate the resulting reservoir performance, correlating the same with known results on the dynamical nature of the circuit in question. As a baseline, we analyse brickwall circuits composed of Haar-random two-qubit gates, before moving on to dual-unitaries, where tunable ergodic properties allow us to systematically investigate its relationship with reservoir performance. We further consider a class of non-random two-qubit gates obeying a specific solvability condition, wherein the associated dynamics surpasses the equivalent circuit made up of two qubit Haar random unitaries in terms of randomness. Finally, we consider examples of Krylov space analytics, which allow for a reliable prediction of effective circuit reservoirs for sufficient task performance. Using the introduced metrics we validate the reservoir for time-series prediction using standard synthetic data sets to evaluate the fading memory capacity and accuracy for prediction tasks. Our results indicate that structured quantum circuits would serve as effective models that yield better and efficient task performance in reservoir computing applications.

We present an atomistic quantum transport simulation framework based on the Non-Equilibrium Green's Function (NEGF) formalism to model impact ionization in semiconductor avalanche devices, with direct relevance to near-term quantum networking applications. Conventional descriptions of avalanche breakdown rely predominantly on semiclassical simulation methods, such as local ionization coefficients, semiclassical carrier trajectories, or Monte Carlo sampling, all of which implicitly assume weak correlations and mean-field electronic interactions. These assumptions break down in nanoscale, high-field junctions where carrier multiplication emerges from strongly non-equilibrium, energy-resolved scattering processes. Our approach formulates impact ionization as a multi-particle self-energy within NEGF, enabling a non-perturbative, energy- and atomic orbital-resolved description of carrier multiplication directly from the device spectral function. This formulation captures strongly inelastic scattering processes beyond semiclassical approximations and is implemented in a matrix-based real-space representation suitable for nanoscale device modeling. Using a model semiconductor structure under high electric fields, we demonstrate the emergence of carrier multiplication and analyze its dependence on energy-resolved transport and nonequilibrium charge distributions. The framework provides insight into microscopic mechanisms governing avalanche processes and their impact on device performance. Our results establish a transport baseline for self-consistent calculations of the impact-ionization self-energy and carrier multiplication. By resolving the available and occupied states that underlie avalanche onset, this framework provides a route toward predictive modeling of silicon single-photon avalanche detectors and avalanche photodiodes used in quantum-network receivers.