Papers

We develop Interval Algebraic Quantum Field Theory (IAQFT), a finite-precision operational formulation of algebraic quantum field theory (AQFT). Physical experiments provide only finitely many observations at finite resolution and therefore determine regions of compatible states rather than uniquely specified point states. IAQFT represents this information by quantum parcels—non-empty convex weak$^*$ open regions of state space—with observational parcels determined by finitely many finite-precision expectation constraints. Exact AQFT states remain indispensable mathematical objects and are recovered under appropriate parcel refinement. We establish reduction to exact states, measurement update and no-signalling, and formulate locality through compatible parcel nets. In finite dimensions an exact Jacobian formula for invertible Lüders updates gives a volume-contraction criterion. Spacelike vacuum correlations and strict CHSH violations persist throughout sufficiently small observational parcels. Reeh–Schlieder cyclicity becomes finite-precision local reachability, while parcel equivalence of vacuum refinements implies vacuum GNS equivalence and hence does not evade Haag-type obstructions. Tomita–Takesaki modular automorphisms act on parcels, measurement update is modularly covariant, and modular conjugation induces a duality between normal parcels of an algebra and its commutant. State-dependent modular correlations are continuous under predual-norm variation of faithful normal states; shrinking parcels with vanishing KMS defect recover a KMS state. Bisognano–Wichmann yields a parcel formulation of the Unruh effect, recovering the exact KMS relation and Unruh temperature under refinement. Finally, limiting projection faces and their conjugation actions recover the Murray–von Neumann factor classification.

We study the metrological properties of a continuously monitored Kitaev chain in the presence of imperfect detection. The system is conditioned on a no-click record, while each emitted fermion is registered only with probability $0\leq q\leq 1$. Because the conditional dynamics remains Gaussian, the steady state is fully characterized by the fermionic correlation matrix. This allows a direct evaluation of the quantum Fisher information and of the mean Uhlmann curvature. For perfect detection, the monitored steady state retains a singular critical structure and the quantum Fisher information with respect to the chemical potential becomes super-extensive. For any $q<1$, imperfect detection introduces a finite smoothing length that rounds the singularity and restores extensive scaling. The detector efficiency behaves instead as a compatible mixed-state estimation parameter, as signaled by the vanishing mean Uhlmann curvature. These results show that incomplete trajectory information destroys the metrological enhancement associated with monitored criticality through a mechanism that differs from ordinary thermal smearing.

Full-counting statistics (FCS) provides a systematic framework for characterising current fluctuations in quantum transport, quantum optics, and open quantum systems. We introduce QuantumFCSjl, an open-source Julia package for efficient and flexible numerical FCS calculations. The package defines currents through monitored jump operators and weights, allowing particle, electric, and heat currents to be treated within the same workflow. It implements a recursive cumulant algorithm with dense, sparse, and iterative solver backends, making it suitable for models that are challenging for direct dense methods. We demonstrate the package on photon counting in a driven-dissipative Jaynes-Cummings system near the blockade-breakdown phase transition and on heat-current fluctuations in a non-linear circuit-QED heat engine. These examples show how higher cumulants reveal intermittency between bright and dim emission, antibunching, and provide probes of thermodynamic uncertainty relations. Benchmarks against an existing FCS implementation show substantial speed-ups.

We study the dynamics of open quantum systems driven by an external time-periodic force. Combining Floquet theory and the time-convolutionless projection operator technique we derive a time-local quantum master equation which exactly takes into account the periodic driving, while treating the system-environment interaction within second order in the coupling strength without performing the Markov approximation. The resulting equation of motion for the reduced density matrix is called Floquet time-convolutionless master equation. Employing the example of the driven spin-boson system, we demonstrate that this master equation is capable of describing strong non-Markovian effects, while yielding the Floquet-Lindblad master equation in the Markovian limit. A characteristic feature of memory effects in such driven dissipative systems is the emergence of sharp peaks of the trace-distance based non-Markovianity measure as a function of the driving amplitude, which can be traced back to quasienergy crossings leading to almost decoherence-protected subspaces through a quasienergy-induced dissipative decoupling mechanism.

We formulate a compact dynamical representation of quantum-information diagnostics for time-dependent two-mode bosonic systems in terms of the Bogoliubov ratio $\lambda_k(\eta)=\beta_k(\eta)/\alpha_k(\eta)$. For vacuum-evolved pure Gaussian pair states generated by a Hermitian quadratic Hamiltonian, $\lambda_k$ obeys a closed complex Riccati equation. After one partner mode is traced out, the reduced-state spectrum is determined by $q_k=|\lambda_k|^2$, from which the purity, linear entropy, Rényi-2 entropy, and von Neumann entropy follow directly. These Gaussian results are mathematically equivalent to those obtained from the standard density-matrix or covariance-matrix formalism; the advantage of the ratio representation is a compact separation between model-dependent dynamics and universal state diagnostics. Writing $\lambda_k=\sqrt{q_k}e^{i\theta_k}$ further exposes how pair production drives radial growth, whereas frequency rotation and detuning act through the phase and can suppress coherent squeezing accumulation. We also establish an exact extension to non-Gaussian $SU(1,1)$ sectors. For a lowest-weight Fock seed with conserved number difference $d$, the same ratio equation governs the evolution, while the reduced spectrum becomes a negative-binomial distribution determined by $(q_k,d)$. The Gaussian formulas are recovered at $d=0$. Cosmological perturbations and a chirped-pulse optical parametric amplifier illustrate the common dynamical mechanism and its information-theoretic consequences.

Multivariate time series forecasting (MTSF) predicts future values of multiple variables from historical data. While quantum neural networks have been increasingly applied to this task, they typically rely on fixed local measurements, which restrict their expressivity. We propose MTSF-ANO, a simple hybrid model for MTSF that integrates variational quantum circuits with adaptive non-local observables (ANO). On the four ETT datasets, MTSF-ANO ranks first or second in MSE in 17 of 20 settings, improving over the strongest baseline by up to 20% on ETTh1, and outperforms or matches its fixed local observable counterpart across all settings. Our ablations show how the quantum circuit design and ANO non-locality affect performance. These results suggest that ANO is a promising direction for quantum time series forecasting.

We explore the use of waiting-time statistics in a quantum electron shuttle for electric-field sensing. Electron shuttles convert nanomechanical motion into charge transport, showing a noise-broadened crossover between stochastic tunneling and mechanically assisted charge transfer. This allows investigation of how transport fluctuations encode electromechanical parameters. Using a single-level quantum shuttle in strong-Coulomb-blockade and high-bias regimes with a Markovian quantum master equation, we analyze stationary dynamics in phase space and waiting time distributions. By estimating the electromechanical coupling, proportional to the electric field, we evaluate the classical Fisher information in waiting times and compare it with the quantum Fisher information of the stationary state. We relate the metrological response to mean waiting time, variance, and Fano factor. Our results show that the crossover from tunneling to shuttling is characterized by enhanced fluctuations and increased parameter sensitivity, leading to a pronounced enhancement of the Fisher information.

We propose a fast laser pulse sequence for the generation of non-thermal Fock state mixtures of the motion of a trapped ion, targeted at displacement metrology beyond the standard quantum limit. Using a polaron-frame description of the ion-laser interaction, we identify a resonant operating point-zero detuning and a Rabi frequency matching the trap frequency-at which selective population trapping survives strong driving, enabling preparation speeds beyond the weak-driving limit of previous protocols without requiring ground-state cooling. We trace the residual infidelity at large Lamb-Dicke parameter $\eta$ to a single coherent process, the counter-rotating blue-sideband term neglected in the rotating-wave approximation, and show that it is suppressed by two routine calibrations: a percent-level refocusing of the pulse duration and a small compensating Bloch-Siegert detuning. Numerical simulations of the full sequence show that this refinement keeps the preparation error at or below the $10\%$ level up to $\eta\approx0.5$ and restores the displacement-sensing Fisher information that the uncorrected protocol loses at strong coupling, recovering up to 9 dB relative to the nominal sequence.

Problem 5 in Five Open Problems in Quantum Information Theory [PRX Quantum 3, 010101 (2022)], asks whether the two-ququart Werner state $\varrho(4,-\tfrac12)$ is two-copy distillable, where $\varrho(d,\alpha)=(I+\alpha F)/(d^2+\alpha d)$. We answer it in the negative. To this end, we show the following stronger statement: for all $C\in M_{d_1d_2}(\mathbb{C})$ of rank at most $r \le d_1 d_2$, $\mathrm{tr}_1(C)\|_F^2+\|\mathrm{tr}_2(C)\|_F^2 \le r\|C\|_F^2+\frac{1}{r}|\mathrm{tr}(C)|^2$. A result by Costa Rico on the equivalence of this inequality with two-copy undistillability at $r = 2$ then settles Problem 5: $\varrho(4,-\tfrac{1}{2})$ is not two-copy distillable. Furthermore, we show that $\varrho(d,\alpha)$ is two-copy undistillable for every $d\ge2$, if and only if $\alpha\ge-\tfrac{1}{2}$. Thus, the one and two-copy distillability regions of $\varrho(d,\alpha)$ coincide. These results have been found and written up with AI tools, pointing towards a structural change affecting the field of quantum information and computation.

We present an all-to-all quantum-level crosstalk characterization of a commercial 16x16 MEMS optical switch for multi-user quantum communications using SNSPDs, correlating experimental data with a theoretical impact analysis on the decoy-state BB84 QKD protocol.

Quadratic unconstrained binary optimization (QUBO) has emerged as a powerful framework for medical computing problems. Binary decision variables naturally represent clinical choices, making QUBO formulations well-suited for quantum annealing hardware. However, a fundamental scalability challenge limits practical deployment: problem size grows rapidly with input dimensionality, creating computational bottlenecks that restrict applications to simplified scenarios. This paper addresses this challenge through hierarchical problem reduction, as demonstrated in medical image segmentation, where pixel-level QUBO formulations create over 65,000 variables for a 256x256 image, forcing existing approaches to downsample to 42x42 resolution and discard 97% of pixel information. A superpixel-based QUBO framework is proposed using simple linear iterative clustering (SLIC) to group pixels into perceptually meaningful regions, then formulate segmentation as QUBO over a region adjacency graph (RAG) combining min-cut and smoothness objectives. Validation on INbreast mammography breast cancer images demonstrates a 4.2% improvement in segmentation quality (mean IoU 0.76 vs 0.73) with 33 computational speedup (0.67s vs 21.97s) and a 97.3% reduction in problem size (1764 to 48 variables), all achieved while processing full-resolution images rather than downsampled versions. The reduced problem size also fits well within current quantum annealer connectivity limits, removing the embedding overhead that has historically blocked direct deployment of pixel-level QUBO segmentation on quantum hardware.

Pre- and post-selection (PPS) paradoxes are striking demonstrations of quantum nonclassicality. Logical PPS paradoxes, where inferences made with the Aharonov-Bergmann-Lebowitz (ABL) rule are exactly 0 or 1, are linked to contextuality. Non-logical paradoxes lack this strong signature. In this work, we analyse more general, non-logical PPS scenarios involving mixed pre- and post-selected states. We show that two such scenarios, the $N$-box and quantum pigeonhole paradoxes, require coherence of both pre- and post-selected states in the basis of the intermediate measurement. This is done by showing each paradox holds if and only if there is weak-value anomaly for a single, paradox-specific operator, together with the fact that weak-value anomaly requires coherence. This clarifies the role of different notions of nonclassicality in these scenarios, highlighting the required quantitative departures from (strictly) classical explanations provided by incoherent sub-theories of quantum theory.

Quantum computers are more widely available than ever, making the field more accessible and widespread. Practitioners are coming from a wide range of domains, conducting experiments and research using quantum computing approaches across a variety of problems. The current literature suggests that developers follow certain methodologies in quantum software development, often with a matching set of tools provided. Yet with the novel paradigm, there are areas that remain unaddressed in practices and tools. In this article, we go into the details of experiment tracking in quantum software development. We explain the basic concept of experiment tracking and detail how, in essence, quantum computing sets demands on tracking practices. Given the experimental state of hardware and the constantly evolving software, quantum execution must be monitored, marginal gains aggregated for the best outcome, and error sources detected. In our case study, quantum reservoir computing for chaotic time series data prediction with error mitigation, we present a detailed quantum software development process and describe how experiments can be tracked throughout development. We then generalize this knowledge into the broader quantum development process.

The development of techniques for simulating quantum systems using classical computers is a paramount task for two primary reasons: i) there exist configurations for which classical computers are remarkably effective and will continue to be so, and ii) exploring the limits of classical computation facilitates the identification of the regimes of competence for quantum computers. In this work, we present MPStab, a quantum circuit simulator based on a hybrid formalism combining stabilizers and tensor networks, recently introduced in Ref. [1]. We present the package, its core functionalities, and explore its performances in a few interesting simulation regimes.

Exact synthesis is a key infrastructure in quantum circuit synthesis and optimization, which provides optimal implementations of small circuit shards and is widely used as a circuit re-synthesis optimization kernel. However, existing quantum exact synthesis methods suffer from encoding overhead, memory bottlenecks, and poor parallel scalability. In this work, we introduce a parallel exact synthesis framework for CNOT and phase polynomial circuits based on the semi-tensor product (STP) theory of matrices that avoids these issues. The algorithm contains two stages: it first enumerates candidate circuit topologies, and then instantiates each topology by determining the control and target qubit of its partial gates via a STP-based circuit solver. In the second stage, circuit topologies are encoded as canonical STP expressions, and the CNOT gates are synthesized through right-to-left STP matrix factorization that progressively eliminates infeasible gate decisions. In the framework, topology enumeration and the subsequent solving process are independent across different topologies, and can be naturally parallelized. Despite the NP-hardness of the problem, our algorithm yields up to $12.8\times$ parallel speedup with 32 workers, whereas the parallel speedups of existing SAT-based methods remain below $5\times$ with the same worker budget. On randomly generated synthesis targets, the proposed algorithm is typically $100$-$1000\times$ faster than the SAT-based approach on small and moderately difficult instances, and remains competitive for more difficult instances. When integrated in a real-world circuit optimization workflow, our algorithm achieves a median speedup of $3.41\times$ on the QASMBench benchmark.

We propose a four-terminal, X-shaped chiral Majorana interferometer with a central floating superconducting island, enabling the direct detection of the non-Abelian statistics of Ising anyons via the linear-response DC conductance tensor in charge transport experiments. Here, Ising anyons are realizable as edge vortices nucleated at Josephson line junctions defining the superconducting island, where both edge-vortex and Majorana-fermion tunneling processes can occur. We show that in such a multi-terminal Majorana interferometer, both the vacuum and the fermionic fusion channel for Ising anyons are possible. This is in contrast to two-arm interferometers, where only the vacuum fusion channel is accessible and the DC conductance contribution from edge vortices always vanishes. Using a low-energy effective theory derived via chiral bosonization, we find that in the X-shaped interferometer, the DC conductance tensor is completely isotropic, yielding a non-zero conductance when simultaneous edge-vortex and Majorana tunneling activates the fermionic fusion channel. Apart from conductance oscillations in a gate-tunable charge parameter, which display an offset related to the anyon topological spin, measuring a finite conductance can already provide direct evidence for non-Abelian statistics in this geometry.

We study a dimension-saturating fixed-core ansatz in which four copies of a fixed, non-tunable two-qutrit core $K\in SU(9)$ are interleaved with five adjustable local layers from $L=SU(3)\otimes SU(3)$. Since $\dim SU(9)=80$ and $5\dim L=80$, this is the shortest fixed-core architecture not excluded by parameter counting. We formulate the smooth map $\Phi_K:L^5\to SU(9)$ and use its right-trivialized differential to give verifiable certificates for local universality. We construct an explicit Clifford-word core whose Pauli-label splitting makes the identity-point differential an exact isometry, and we classify all 2304 symplectic actions satisfying the same splitting criterion. We also prove a structural obstruction for an important symmetry class: every complex-symmetric core $K=K^{T}$, including every core generated by a time-independent real-symmetric Hamiltonian in the chosen computational basis, has identity-point differential rank at most 78; hence any full-rank certificate for such a core must occur away from that point. We then assess a hardware-motivated superconducting core generated by a noncommuting, temporally asymmetric drive. Direct calculation verifies $K_{\rm sc}\neq K_{\rm sc}^{\mathsf T}$, and the core achieves $F_{\rm avg}\ge 0.999$ for all 1000 Haar-random targets tested under the stated restart protocol. We also report favorable sampled Jacobian-rank, structured-target, and robustness diagnostics. These results establish local universality at the parameter-counting-minimal, dimension-saturating depth, with an exact Clifford certificate complemented by a hardware-motivated numerical case study. Throughout, we separate exact local certificates from numerical evidence for broader synthesis performance.

We propose Tree Tensor Network Reservoir Computing (TTN-RC), a quantum-inspired reservoir computing framework for time-series prediction that uses the hierarchical structure of Tree Tensor Networks as a random reservoir. To control the exponential concentration or divergence of TTN outputs, we introduce a hierarchical ensemble method that partitions a fixed-size reservoir into multiple independent sub-reservoirs. In the tested NARMA benchmarks, TTN-RC achieves competitive or improved performance compared with conventional Echo State Networks, especially for tasks requiring higher-order nonlinear processing and longer contextual dependence. We also derive an expected contraction rate based on the reservoir Jacobian and develop a mean-field description of the reservoir-state statistics. These analyses identify an asymptotic stability boundary at $\sigma_{T}=\sqrt{2}$ in the large per-tree-size limit, where several theoretical indicators converge. Our results provide a design principle for tensor-network-based reservoir computing and clarify how hierarchical reservoir topology controls stability and nonlinear information processing.

Free-space quantum key distribution (QKD) provides crucial advantages, including mobility and deployment exibility, for securing next-generation communication networks. However, atmospheric turbulence and beam wander severely degrade single-photon coupling effciency and link stability over outdoor channels. In this work, we experimentally demonstrate a free-space decoy-state BB84 QKD system operating at 803 nm with a 100 MHz repetition rate over a 2 km outdoor link. By employing an active beam-wander correction based on fast-steering mirrors (FSMs) and position sensitive detectors (PSDs) with a 500 Hz control loop, we enhance the ?ber coupling effciency and achieve an average ?nite-key secure key rate of 110 kbps with an average quantum bit error rate (QBER) of 3.28 %, representing a 2.5 times secure key rate enhancement under an active beam stabilization. This work demonstrates the indispensability of active beam stabilization and provides an operational reference for robust, long-range free-space quantum communication.

Quantum emitters coupled to nonlinear one-dimensional waveguides provide a route for quantum-state engineering by utilizing parametric gain accumulation along with modified waveguide-mediated interactions. Since the accumulated squeezing depends on propagation distance, different emitter separations can experience different effective gain, making the spatial structure of connected quantum correlations a central feature of the dynamics. Here we investigate the transient and steady-state connected correlations of emitter arrays coupled to a parametrically driven waveguide. Using an effective master equation for nonlinear waveguide QED, we analyze second- and third-order connected correlations as functions of the squeezing parameter and interparticle distance. In the two-emitter limit, accumulated squeezing drives excitation buildup and generates a nonzero connected second-order correlation. For many-emitter arrays, tuning the interparticle distance switches the dominant local second-order correlation between the bulk and boundary regions, and enables an analogous spatial control of genuine third-order connected correlations. In the steady state, the averaged second-order correlation exhibits sign-changing and nonmonotonic behavior in the squeezing–interparticle distance parameter space, whereas the third-order connected correlation is strongly enhanced by increasing the squeezing parameter. These results identify nonlinear waveguide QED as a tunable platform for spatially controlling connected quantum correlations and provide insights into correlation engineering in open quantum optical arrays. We further show that this local contrast remains visible in both odd and even number of atomic arrays.

Astronomical interferometry is a cornerstone technique for high-resolution stellar imaging and observational astrophysics, extracting spatial information from the coherence of light collected by separated telescopes. Since the degree of coherence is complex, a genuine imaging task requires the joint recovery of the modulus and the relative phase, instead of independent singleparameter estimations. We investigate the simultaneous estimation of both parameters based on direct interferometry scheme and continuou-svariable quantum teleportation scheme. We find that in simultaneous estimation the direct interferometry scheme consistently yields a lower quantum Cramér-Rao bound, demonstrating its superiority over the continuous-variable quantum teleportation scheme. Furthermore, we establish the conditions under which the classical Cramér-Rao bound for Gaussian measurements saturates the quantum Cramér-Rao bound, identifying heterodyne detection as a near-optimal measurement scheme in the large mean photon number regime. An analysis of transmission loss reveals that the direct interferometry scheme yields superior precision in the short-baseline regime, whereas the continuous-variable quantum teleportation scheme outperforms it at longer baselines.

We investigate quark-antiquark entanglement in heavy quarkonium within a nonperturbative light-front Hamiltonian framework. By tracing over the antiquark degrees of freedom in the hadronic state vector, we construct the reduced density matrix of the quark subsystem and compute the associated von Neumann entropy. For spin-0 quarkonia, we show that this entropy reduces to the Shannon entropy of the unpolarized transverse momentum dependent parton distribution (TMD), up to constant color and spin contributions. For spin-1 quarkonia, we derive the explicit polarization dependence of the entropy and connect it to polarized and tensor-polarized TMDs. Using light-front wave functions obtained via basis light-front quantization (BLFQ), we evaluate the entanglement entropy for charmonium and bottomonium states, revealing a pronounced sensitivity to the polarization of vector mesons. Furthermore, we resolve the infrared parameter by matching the momentum-space entropy to a harmonic-oscillator representation. Ultimately, these results establish entanglement entropy as a novel probe of nonperturbative quarkonium structure, forging a direct link between quantum information measures and partonic observables.

The quantum dynamics of a double quantum dot two-level system, coupled to a leaking microwave resonator mode, is theoretically investigated. The double quantum dot is driven by applying a continuous field giving rise to time-dependent modulations of its energy separation between the ground levels of each dot, forming the qubit. Therefore, the cavity resonances occur when the difference between the resonator and the qubit frequencies equals the multiple of the modulation frequency, respectively. In the strong Coulomb interaction limit and the weak couplings of the combined system, i.e. the qubit and the single-mode cavity, to corresponding electronic, phononic or photonic reservoirs, we have demonstrated that the output cavity electromagnetic field is formed of a single-photon flux obeying the sub-Poissonian quantum photon statistics. This was proved via Fano's factor behaviour or by comparing the resonator's second- and third-order photon correlation functions, respectively. The phonon, the cavity mode dephasing or the environmental temperatures influence on the quantum properties of the photons are also discussed.

In this study, we developed and evaluated four conditional energy-based forecasting architectures: a classical Gaussian-Bernoulli CRBM, a hybrid quantum-classical QCRBM, a full-register QQRBM, and a lag-feature QFeatureQRBM with complete derivations of their conditional distributions, Contrastive-Divergence gradients, and hybrid training, bridging the energy-based formulation and the implementation-level quantum computation. Unlike prior comparisons, our evaluation enforces symmetric hyperparameter optimisation: classical and quantum-specific hyperparameters receive an equally thorough grid search across thirteen structured experiments. We test on two data classes, a Gaussian-process dataset (GP) generated with real financial data and the input-driven NARMA-10 nonlinear benchmark. Across both regimes we find no systematic evidence of a quantum advantage at the available sample size: no quantum architecture improves on the best classical baseline. The fully quantum QQRBM and QFeatureQRBM are significantly worse, whereas the hybrid QCRBM is statistically indistinguishable from the strongest classical CRBM on both datasets. A power analysis bounds this null result: at n = 12 only medium-to-large effects are detectable, so small advantages cannot be excluded. An iso-parameter (matched-budget) comparison reaches the same conclusion: the classical CRBM is lowest at three of the four budgets and no CRBM-vs-QCRBM difference is significant at any budget.

Laser phase noise is one of the limiting factors that dictate gate fidelities and coherence times in trapped-ion quantum systems. Previous studies have reported that when the Rabi frequency of an ion qubit is close to the servo-bump phase-noise frequency, the driving laser limits the fidelity and coherence time. This issue has typically been mitigated by choosing a Rabi frequency outside the servo-bump region. However, this constrains the usable range of gate speeds and can limit the achievable fidelity. To address this issue, we developed an active phase-noise stabilization system for a barium-ion optical-qubit laser at 1762 nm, employing a fiber electro-optic modulator (EOM) with an electrical feedforward servo. Our results demonstrate that this setup, based on the Pound-Drever-Hall (PDH) feedforward method, can suppress servo-bump phase noise by 15 dB near the bump peak frequency in our locking system. The laser phase noise is analyzed using delayed self-heterodyne interferometry (DSHI). We further tested the stabilized laser on an optical qubit and observed a clear improvement in coherence time based on the measured amplitude decay of Rabi oscillations, even when the Rabi frequency lies within the servo-bump bandwidth. This technique can be readily adapted to other optical qubits with minimal modifications.

Designing scalable parameterized quantum circuits for machine learning faces three obstacles: barren plateaus, the absence of guarantees that the learned function class is classically hard, and prohibitive circuit evaluations per gradient step. We propose the unitary brick-wall: a $k$-particle fermionic architecture for nearest-neighbor hardware, combining Reconfigurable Beam Splitter gates with interleaved single-qubit phase gates and a non-Gaussian magic-state encoding, where $k$ is a tunable dial trading classical simulation hardness against training cost. Trainable. The brick-wall has dynamical Lie algebra $\mathfrak{u}(n)$ and is surjective onto $U(n)$ via Givens rotations, enabling Haar initialization. Two-body correlator readouts achieve gradient variance $\Theta(k^3/n^5)$, polynomial in $n$ throughout $n-2k=\Omega(n)$. Expressive. Classical hardness is controlled by $k$: best-known classical sampling algorithms run in time $2^{\Theta(k)}\mathrm{poly}(n)$, worst-case #P-hardness holds from $k=n^{\epsilon}$, and the average-case machinery of Fermion Sampling applies at $k=\Theta(n)$. At our operating point $k=60$, best-known classical simulation exceeds $10^{24}$ operations at every $n$. Efficient. A multi-layer parallel parameter-shift rule computes all $O(n^2)$ gradients from $4kn$ circuit evaluations per gradient step, a factor $n/k$ reduction over the $4n^2$ evaluations of the standard rule, growing linearly with $n$ at fixed $k$. The unitary butterfly variant targets all-to-all hardware, with depth $2\log n$ and $(3/2)n\log n$ parameters, similar hardness guarantees, and $4k\log n$ evaluations per gradient step – the same factor-$n/k$ reduction. Its trainability holds at two levels: absence of exponential barren plateaus is unconditional, while the sharp $\Theta(k^3/n^5)$ rate holds under a two-particle approximate-2-design conjecture.

Quantum computing promises transformative advances in computation, communication, sensing, and machine learning. Yet the realization of large-scale fault-tolerant quantum computers remains hindered by the enormous overhead required for quantum error correction. This challenge raises a fundamental question: Must useful quantum computing wait until fully fault-tolerant quantum hardware becomes available? In this Perspective, we propose Recoverable Quantum Computation (RQC), an information-centric paradigm for quantum computing with errors. Rather than requiring faithful preservation of the complete quantum state, RQC focuses on preserving the computational information required to accomplish a given task. A quantum computation is considered recoverable if the desired computational information can be extracted from noisy quantum outputs with an overhead that preserves quantum advantage relative to the best known classical method. We introduce recoverability as an operational principle for evaluating noisy quantum computations and propose practical metrics based on recovery overhead and recoverability efficiency. We illustrate the framework using quantum Fourier transform period estimation on IBM quantum hardware and a conceptual example from quantum machine learning, demonstrating that useful computational information may remain recoverable despite significant physical errors. Building on these examples, we propose a preliminary classification of quantum applications according to their expected recoverability and outline a research roadmap toward a predictive theory of recoverability. RQC is intended not as an alternative to fault-tolerant quantum computing, but as a complementary paradigm for understanding and evaluating useful quantum computation in the broad intermediate regime between today's noisy quantum processors and tomorrow's fault-tolerant quantum computers.

Quantum compilers optimize execution-only proxies such as gate count, depth, and fidelity, treating the compiled circuit as the unit of cost. This conflates two distinct resources, how much the substrate has to do at run time, and how much has to be said to describe what to do. Unrolling a looped program leaves run-time cost unchanged while erasing the hierarchical structure on which downstream optimization and reuse rely. We propose lifting the compiler objective from execution to life cycle complexity by pairing the circuit complexity $\mathcal{C}_{\mathrm{circ}}$ with a Kolmogorov-style description complexity $\mathcal{C}_{\mathrm{Kol}}$ of the emitted circuit, and minimizing the additive total $\mathcal{C}_{\mathrm{tot}} = \alpha\,\mathcal{C}_{\mathrm{circ}} + \beta\,\mathcal{C}_{\mathrm{Kol}}$. The mirrors the additive positional and kinetic entropy of the second law of quantum complexity, and reads as a minimum-description-length regularizer over the otherwise degenerate set of $\mathcal{C}_{\mathrm{circ}}$-minimizers. We instantiate the objective on $SU(2)$ through exhaustive HT-enumeration with compression-based surrogates upper-bounding $\mathcal{C}_{\mathrm{Kol}}$. Across a Haar-representative target grid the two surrogates correlate positively with $\mathcal{C}_{\mathrm{circ}}$ yet break its rank order on a non-trivial fraction of points, ruling out a tight functional dependence. With calibrated weights the joint cost selects, for a small but operationally meaningful fraction of targets, a candidate that is neither the shortest nor the most compressible HT-string in the $\varepsilon$-ball, exhibiting the compilation choices a $\mathcal{C}_{\mathrm{circ}}$-only optimizer discards and motivating $\mathcal{C}_{\mathrm{Kol}}$ as an active optimization signal for hierarchical intermediate representation for compiler.

We scale a CUDA-Q-native pipeline coupling a generative quantum eigensolver (GQE) to quantum-selected configuration interaction (QSCI) across active spaces of 14 to 44 qubits, applied to the extreme-ultraviolet (EUV) photoresist chemistry of monoalkyltin oxo-hydroxides. A GPT-2 policy emits UCCSD operator sequences; sampled bitstrings become determinants, diagonalised classically, and a cross-circuit generalised-eigenvalue refinement makes every reported GQE+QSCI energy a variational upper bound. Every rung from 14 to 40 qubits carries an exact CASCI or FCI reference, up to 166 million determinants for SnO at 32 qubits. The pipeline is chemically accurate, below 1.6 mHa, through 30 qubits on methyltin trihydroxide and through 32 on SnO, on the best seed at the top rungs. Circuit depth rather than training length is the scaling lever; the refined subspace grows near-linearly with the operator count while staying a vanishing fraction of the determinant space, 0.017% at the 32-qubit SnO rung. It also runs on the 54-qubit IQM Emerald processor, at the shallow depths its routed two-qubit gates allow, reaching +0.330 mHa for SnO at 14 qubits from a CCSD-amplitude-ordered pool prefix and +3.92 mHa for the industrial n-butyltin ligand at 22 qubits from depth-truncated trained circuits under per-circuit readout self-calibration, 81% of the active-space correlation; classical configuration recovery on those counts tightens the 22-qubit result to +0.18 to 0.21 mHa. For the methyl resist, ionisation collapses the classical UCCSD(T) Sn-C bond dissociation energy from 72.6 to 21.2 kcal/mol, the switch that flips solubility on exposure. Against that, the 40-qubit result is support-limited at 22.8 mHa, the full trained ansatz on hardware awaits better fidelities, and classical subspace expansion reaches the 32 to 40-qubit spaces with no quantum sampler, so that boundary is mapped, not beaten.

The precision of quantum parameter estimation is traditionally constrained by the quantum Cramér-Rao bound, which is based on the Hermitian measurement framework. Recent studies of non-Hermitian systems have suggested new possibilities for enhancing parameter-estimation sensitivity. Here, we experimentally realize quantum parameter estimation using a non-Hermitian observable on a linear optical platform. The parameter is encoded in single-photon probe states and read out with a Sagnac interferometer, which allows us to reconstruct the complex expectation value of the implemented non-Hermitian observable from interference fringes. We observe a reduced error-propagation variance compared with the optimal Hermitian observable for the same probe-state model. This advantage remains visible under amplitude-damping noise. We further analyze the complete optical measurement as a physical positive-operator-valued measure (POVM) and show, through the corresponding classical Fisher information (CFI), that the observed non-Hermitian advantage is consistent with the standard quantum metrological limit when all output ports are included. Our results provide an experimental route to non-Hermitian observable readout and clarify its operational meaning in quantum sensing.