Papers

We investigate thermalization in finite quantum systems with strong long-range interactions. Nearly conserved quantities inherited from the fully connected limit organize the Hilbert space into weakly coupled sectors and split the many-body spectrum into energy bands. Despite the resulting breakdown of global ergodicity, quantum chaos develops within individual energy bands, enabling the definition of microcanonical ensembles within the bands. This supports a band-resolved formulation of thermalization, which we term fragmented eigenstate thermalization hypothesis (fETH). Unlike conventional ETH, finite-size scaling in fETH obeys a symmetry-imposed selection rule that restricts which system sizes can be compared. This band-resolved description has consequences for equilibrium statistical mechanics. While microcanonical ensembles remain confined to a single band, canonical ensembles mix different bands. This mismatch explains ensemble inequivalence without invoking equilibrium phase transitions. Our results apply broadly to Hamiltonians near a fully permutation-symmetric limit.

In Hamiltonian systems, the only basis-independent quantity is the spectrum. Given a spectrum, quantum mereology seeks preferred tensor-product decompositions into local subsystems, leading to the emergence of locality. Causal order, however, remains fixed by the Hamiltonian time evolution. In contrast, higher-order quantum theory permits more general processes that need not possess a definite global causal order. In the process-matrix framework, specifying a process requires a choice of subsystems corresponding to the input and output Hilbert spaces of each agent. A change of basis redefines both the agents and the corresponding decompositions into subsystems, while leaving the spectrum of the process matrix invariant. Here, we study how causality arises from this spectrum. First, we derive spectral constraints on processes compatible with definite causal order. Second, we show that, in the thermodynamic limit, generic quantum processes admit a preferred decomposition with a definite causal order. This suggests a mechanism for the emergence of classical causality only from algebraic ingredients.

Non-Hermitian systems offer new opportunities for quantum optimization and computation. Here, we show that non-Hermitian quantum adiabatic algorithms require not only a real, gapped spectrum, but also a stable pseudospectrum. We propose a novel framework by mapping non-unitary quantum circuits to local Hamiltonian paths, thereby preserving their optimization advantages and shallow depth. While a direct non-Hermitian extension of the Feynman-Kitaev construction suffers severe pseudospectral instability, our history-decoupled construction yields both a controlled pseudospectrum and a real, gapped spectrum. Using the CK benchmark family of maximum independent set problems, we demonstrate polynomial-evolution-time non-Hermitian adiabatic computation that remains robust against perturbations. We further discuss a feasible optical implementation using coupled waveguides with an auxiliary lossy channel. Our work establishes pseudospectral stability, alongside real, gapped spectra, as key principles and a practical route for non-Hermitian quantum adiabatic computation.

Li and Boyle showed that the Penrose tiling defines a quantum error-correcting code: superpositions of tilings over isometry orbits protect quantum information against erasure of any bounded region. We extend the construction to the aperiodic monotiles discovered by Smith, Myers, Kaplan and Goodman-Strauss. For the Hat, we prove strong local indistinguishability for all Hat tilings, and we prove local recoverability unconditionally for all nonsingular Hat tilings via the torus parametrization of the underlying cut-and-project scheme. The remaining singular case reduces to one sharply posed geometric question – can a region that is a union of hats be retiled a second way? – which we verify computationally has no counterexample up to a substantial scale: a certified $2490$-tile patch admits precisely one tiling by hats, so all $2^{2490}$ of its tile-subregions retile uniquely. Unlike the Penrose, Ammann-Beenker and Fibonacci tilings, both monotiles form two local-indistinguishability classes, so their code spaces split into two erasure-correcting sectors carrying a superselected classical label. Whether the label survives depends on which isometries are gauged: the Spectre's classes are exchanged by a $30^{\circ}$ rotation and merge once all proper isometries are gauged, whereas the Hat's are exchanged only by reflections. Under the physically natural gauge group $SE(2)$, the Hat code therefore stores one robust classical bit – the handedness of its long-range order, readable in any bounded window with separation $\Delta = |K|\sqrt{5}/3$ – alongside its protected quantum sectors. It is the reflexible monotile, not the chiral one, that carries the chirality bit. We give the exact Perron-Frobenius data of both codes, including the per-class reflected-Hat frequencies $(3\mp\sqrt{5})/6$ and the Spectre orientation-class frequencies $(5\pm\sqrt{15})/10$.

Current implementations of quantum batteries are constrained by limited energy density and short retention times associated with the electronic or molecular excitations. Here we propose a nuclear quantum battery based on collective excitation of the $^{57}$Fe nuclei of density $n$ embedded in a planar hard X-ray waveguide. Using a Green function waveguide-QED description, we study charging via excitation beyond linear response, where saturation and drive back-action reshape the incident pulse. We introduce a self-consistent waveform-engineering protocol that inhibits local radiative decay in the waveguide thus promoting absorption into high-lying collective nuclear excitation manifolds. We show an enhanced excitation cross section of the nuclear ensemble which yields superlinear charging, with maximum studied energy density scaling approximately like $n \sqrt{n}$. Our results provide a route to high-energy-density quantum charging at hard X-ray energies using contemporary X-ray sources and waveguide architectures by identifying nonlinear, collectively enhanced absorption as a key mechanism for nuclear quantum battery operation.

We present a variational algorithm for learning an unknown quantum unitary from time-series observable measurements, with no structural assumption about the target. The core separation: a hardware-efficient parametrised circuit learns the evolution operator U via observable matching; Hamiltonian identification follows as classical post-processing via matrix logarithm, when the target happens to be exp(-iH*tau). Three experiments establish the method's generality. First, a noiseless proof of correctness with exact gradients (L-BFGS-B) achieves MSE 1.61e-14 and recovers all Hamiltonian coefficients to six decimal places. Second, a gate-learning experiment fits CNOT, iSWAP, and a Haar-random SU(4) element – none generated by any fixed Hamiltonian – all to process fidelity 1.000000, confirming the method does not rely on Trotterisation structure. Third, quantum deployment via SPSA-Adam under Qiskit Aer depolarising noise (p1=0.001, p2=0.01, Nshots=1024) recovers all three Ising Hamiltonian terms with errors below 8%. The optimiser, SPSA-Adam, combines SPSA's hardware-efficient two-point gradient estimation with Adam's adaptive moment updates. A four-stage moment-warm curriculum progressively extends the training horizon, converting a global non-convex problem into a sequence of well-posed local ones.

Deep thermalisation characterises the emergence of universal quantum state ensembles on subsystems due to projective measurements on their complement. We study the notion of locality, or lack thereof, in this phenomenon by considering a subsystem partitioned into two disjoint subregions which remain causally disconnected at all times under unitary dynamics. We show that the onset of deep thermalisation in this geometry is fundamentally bounded by measurement-induced entanglement teleportation between the subregions. While measurements on the environment generate entanglement across the disconnected partitions – suggesting an apparent non-locality – we demonstrate that generic locally interacting systems exhibit an emergent locality. Specifically, the timescales for both deep thermalisation and entanglement teleportation scale logarithmically with the distance separating the subregions. Exceptions to this include special circuits where the randomness of the measurement outcomes is perfectly transmitted to the ensemble of states of the subsystem, conditioned on the outcomes; in such cases the timescale for deep thermalisation is finite leading to genuine non-locality.

Dynamic entanglement distribution is a key requirement for scalable, multi-user and multi-protocol quantum networks. We demonstrate a metropolitan-scale entanglement-based quantum communication network enabled by a quantum reconfigurable optical add-drop multiplexer (q-ROADM), which dynamically distributes polarisation-entangled photon pairs from a broadband source to six users over deployed campus and metropolitan fibre. The network supports programmable full-mesh, partial-mesh and sliced sub-network configurations, enabling flexible allocation of entanglement resources according to link condition and service requirement. We demonstrate stable six-user full-mesh operation over more than 150 hours, compare full-mesh and time-shared partial-mesh strategies under different source and detector conditions, and realise quantum network slicing with optional/additional interconnection links. We also show that the same infrastructure can support different quantum protocols by showcasing Secure Inaugural Authentication-Transfer (SIAT) combined with Network flooding over multiple paths to improve the security of onboarding a new user. These results demonstrate a q-ROADM-enabled entanglement distribution architecture as a novel route towards reconfigurable, service-oriented quantum networking over optical fibre infrastructure.

A critical limitation of solid-state quantum devices arises from the materials from which they are fabricated: uncontrolled surfaces, interfaces, and structural imperfections introduce numerous sources of loss and decoherence. Despite extensive efforts, linking these decoherence mechanisms to their microscopic material origins – essential for developing effective mitigation strategies – remains an outstanding challenge that has slowed coherence improvements. Here, using scanning gate microscopy on live superconducting circuits we identify a previously unrecognised decoherence mechanism originating from Coulomb blockade and microwave-driven charge tunnelling in metallic grains. Such grains are ubiquitous in thin-film devices fabricated by standard lithography processes. By characterising multiple defects across different devices, we find such defects to be as common and as debilitating to device performance as two-level system (TLS) defects, while originating from a fundamentally different physical mechanism. Importantly, conventional characterisation techniques would misattribute this loss to other, microwave power-independent processes. Our observations thus reveal a widespread source of decoherence in superconducting circuits, challenging the prevailing paradigm that coherence lifetimes are primarily limited by TLS defects. Eliminating metallic grains during fabrication provides a clear and practical route to suppress this mechanism, offering a pathway towards improved coherence and reduced noise in microwave-based solid-state quantum devices.

The additivity of minimum output entropies is a central problem in quantum information theory. Nonadditivity is known for every Rényi order $p>1$, at the von Neumann point $p=1$, and for sufficiently small positive $p$, while much of the interval $0<p<1$ has remained open. In this work, we prove that for every $p>0$ there exist finite-dimensional quantum channels whose minimum output $p$-Rényi entropies violate additivity. Our proof combines two constructions: random projection-induced channels yield nonadditivity for $p>3/4$, and antisymmetric postprocessing extends the violation to all positive Rényi orders. Our estimates also improve the output-dimension bound obtained by Belinschi, Collins, and Nechita for additivity violation of minimum output von Neumann entropy.

Quantum entanglement is the fundamental hallmark of quantum mechanics and a core resource for realizing long-distance quantum communication and scalable linear quantum computing. Accordingly, the precise detection and quantitative quantification of entanglement constitute a foundational and critical problem in quantum information theory. To date, researchers have proposed numerous sufficient conditions for entanglement detection as well as a variety of entanglement measures to characterize the entanglement strength of quantum states; nevertheless, efficient and direct measurement schemes for core entanglement parameters remain underdeveloped. Based on unitary transformations and auxiliary measurements, this paper proposes a set of quantum circuit schemes capable of directly measuring the bipartite concurrence and the tripartite 3-tangle entanglement measure. By introducing auxiliary qubits and constructing specific controlled unitary operations, the proposed scheme maps the analytical expressions of the two entanglement measures onto the measurement probabilities of output states from quantum circuits. It enables efficient and direct quantitative measurement of bipartite and tripartite entanglement without performing full quantum state tomography. This work provides a feasible technical route for the experimental characterization of entanglement properties and lays a groundwork for the practical deployment of multipartite entanglement resources in quantum information processing.

We develop a backpropagation algorithm for evaluating parameter gradients in quantum circuits using Pauli propagation simulation. The method has computational complexity comparable to that of standard sparse Pauli simulation techniques, while producing gradients whose accuracy is of the same order as the corresponding observable expectation values. By exploiting the reversibility of quantum circuits, the algorithm reduces the memory cost by a factor of $\mathcal{O}(n_\text{param})$ compared with conventional reverse-mode automatic differentiation, where $n_\text{param}$ denotes the number of parameters in the circuit. Compared with finite difference methods, the algorithm is $\mathcal{O}(n_\text{param})$ more efficient in function evaluations. These features enable efficient and accurate classical optimization of quantum circuits for applications such as state preparation and time-evolution compression, while also allowing operator-complexity measures such as the operator stabilizer Rényi entropy to be monitored and regularized during optimization. We demonstrate the method by optimizing low-energy state-preparation circuits for transverse-field Ising models in one, two, and three dimensions and for the three-dimensional Heisenberg model, and by compressing two-dimensional time-evolution circuits.

Dissipative preparation of quantum order offers a route to superconductivity that does not rely on enhancing attractive interactions. Here we propose a driven-dissipative protocol to prepare superconductivity as a stationary state of a two-dimensional moiré heterostructure. The key ingredient is a bilayer moiré platform in which the layer degree of freedom acts as a pseudospin, allowing the pseudospin structure required for pairing to be implemented through optically induced spatial operations. This preparation scheme requires local dissipation, which we show to arises naturally from weakly dispersive bosonic modes in the heterostructure. In contrast, in the opposite regime of collective dissipation, the same platform exhibits an early-time superradiant burst. Our results establish driven-dissipative moiré heterostructures as a promising platform for preparing superconductivity, while also revealing a connection between steady-state pairing and transient superradiance.

Using a robust photon loss model for photonic quantum experiments, we derive $n-$th order parameter-shift rules for computing gradients of Fock boson sampling transition probabilities where $n$ photons are sent into a lossy interferometer. We also show that in general it is not possible to generalize this gradient recipe to the case of Gaussian boson sampling. Only in the specific case where the transmission matrix of the interferometer can be factorized as a diagonal loss matrix premultiplied by a pure unitary it is possible to obtain parameter-shift rules with a finite order given by twice the total number of photons detected. We demonstrate the efficacy of the proposed method by comparing its performance against finite differences on real hardware.

We construct a new family of Calderbank-Shor-Steane (CSS) codes using the generator and parity-check matrices of Low-Density Generator Matrix (LDGM) codes, with row operations applied to both matrices in order to achieve the desired quantum rate. Decoding is performed in an iterative manner, by applying message passing over the associated graph, and discrete Density Evolution (DDE) is used to optimize performance in the depolarizing channel. The proposed construction offers high flexibility and easiness in the design, producing quantum codes that possess excellent error correction capabilities. By properly designing the structure of the code, we are able to control and bound the weight of the stabilizer generators to a small value, which results in codes particularly well suited for fault-tolerant quantum computation. At the same time, these codes achieve very good performance in terms of error correction capability.

The corner transfer matrix renormalization group (CTMRG) is one of the standard contraction methods for infinite projected entangled-pair states (iPEPS), but its computational cost is dominated by repeated truncated singular value decompositions (SVDs). We introduce subspace-iteration CTMRG (SI-CTMRG), a QR-based projector construction that replaces each large-matrix SVD with an SVD of a much smaller matrix. The resulting algorithm shifts the dominant cost from decompositions to tensor contractions, making it highly suited to GPU acceleration and yielding speedups of up to two orders of magnitude over standard CTMRG. We demonstrate the efficiency and accuracy of the method for the triangular-lattice Heisenberg antiferromagnet, reaching state-of-the-art iPEPS results on a single H100 GPU in approximately 10 hours of computation.

The entanglement-assisted capacity of a quantum channel admits an additive single-letter characterization, implying that joint encodings across channel uses cannot increase the ultimate communication rate. Here, we show that this additive picture does not extend to communication reliability. Specifically, we prove that the Petz-Rényi channel information can be strictly superadditive for every $\alpha\in[1/2,1)$, yielding a genuine multi-copy enhancement of the entanglement-assisted random-coding error exponent, even though the entanglement-assisted capacity remains additive. We establish this phenomenon analytically already for measurement channels, which are entanglement-breaking and have additive unassisted capacity. Remarkably, this strict superadditivity is witnessed by a separable, classically correlated two-copy channel-input marginal, demonstrating that no entanglement between the transmitted systems is required. Our results show that, although correlations across channel uses cannot increase the ultimate rate of entanglement-assisted communication, they can enhance its reliability.

Quantum many-body scars provide an exception to generic thermalising dynamics, but their relation to integrability remains unclear. Here we apply the periodic-orbit framework to the integrable XYZ/XXZ spin-1/2 chain, developing an energy-resolved approach that enables us to locate and track periodic orbits across the spectrum. We identify families of scarred orbits and resolve their supporting eigenstates in terms of Bethe-ansatz quantum numbers, revealing a common string core dressed by zero-momentum magnon pairs. This allows us to reconstruct both the scarred eigenstates and the associated towers directly within the Bethe ansatz, and explain the equidistant tower spacing analytically from the decoupling of zero-momentum magnon pairs in the Bethe equations, providing a microscopic realisation of scar phenomenology in an integrable setting. We further show that this structure persists upon breaking integrability with a transverse field, with the periodic orbits continuing to govern the dynamics. Our results establish a direct connection between the periodic-orbit picture of quantum scarring and the algebraic structure of integrable models, showing that key features of scar dynamics can be understood analytically within the Bethe ansatz framework.

The concept of finite entanglement scaling forms one of the pillars on which the tensor network ecosystem is built. In this paper, we resolve the open problem of determining the actual perturbations induced by matrix product state approximations of critical systems, and we demonstrate that these can be quite different than the ones predicted by conformal field theory. To that aim, we develop a sparse linear solver to calculate the forward and backward derivatives of 2-dimensional tensor networks with respect to their defining parameters in an implicit way. This algorithm is of independent interest as it provides a primitive for the variational optimization of projected entangled pair states that circumvents the instabilities plaguing traditional automatic differentiation methods.

In recent years, quantum lock-in detection has emerged as a promising technique to accurately detect weak signals submerged in background noise. However, the signal-to-noise ratio of existing protocols is severely limited by spectral leakage resulting from control operations implemented in pulse form. Here, we propose a general protocol for realizing quantum lock-in detection by employing successive quantum adiabatic evolution. In our protocol, the signal modulation is achieved by adiabatically controlling the time evolution of the quantum probe, which enables the implementation of sinusoidal modulation functions. The realization of sinusoidal-wave modulation substantially mitigates the problem of spectral leakage and facilitates the extraction of the complete characteristics of the target signals. We present a practical implementation scheme of adiabatic quantum lock-in detection based on nitrogen-vacancy centers in diamond, and demonstrate that the proposed protocol possesses strong resilience against experimental imperfections. Our results establish adiabatic quantum lock-in detection as a robust and experimentally accessible approach to detection of weak alternating signals in noisy environments, thus promoting the advance of real-world quantum sensing technologies.

Magnetic monopoles lie at the crossroads of gauge fields, topology, geometric phases, and charge quantization, yet they remain elusive as fundamental particles. Here we show that an emergent Dirac-monopole framework arises naturally from the dynamics of massive quantum vortices in a spherical superfluid shell. Their dynamics is formally equivalent to that of interacting charged particles constrained to a sphere in the field of a magnetic monopole. The monopole charge is fixed by the superfluid density and automatically satisfies Dirac's quantization condition. The emergent monopole description predicts cyclotron-like vortex motion, in quantitative agreement with Gross–Pitaevskii simulations. We further show that topological frustration induced by two like-charged polar vortices gives rise to the formation of an equatorial vortex necklace, a configuration reminiscent of the polygonal cyclone clusters observed around Jupiter's poles, before its subsequent breakup through a Kelvin–Helmholtz-like instability. Within this framework, the equatorial vortex necklace emerges as the quantized realization of the effective electrostatic line charge that restores global charge neutrality on the sphere. Our results establish spherical superfluids as a versatile platform for realizing and exploring fundamental aspects of Dirac-monopole physics.

We employ a mathematically equivalent form of the GKLS master equation to arrive at an exact theoretical description of a two-level system strongly coupled to the environment. The framework, while intuitive, shedding light on the physics of the problem, and agreeing with existing results, such as thermalisation to a non-canonical state, is based around three parameters that are unknown outside of the weak coupling regime – the analogue to the detailed balance relation, and two coupling strength constants. As a way forward, we propose a feasible experimental protocol based on a solid-state electronic quantum dot device, through which the fundamental parameters of the problem can be revealed, which would further the fundamental understanding of strong coupling.

We study time-discrete parametric approximations of evolution equations in Hilbert spaces based on residual minimization. The solution is represented by a parametrized ansatz belonging to a low-dimensional nonlinear manifold, and time stepping is performed by minimizing suitably defined residuals at each step. Two natural residual formulations are considered: discretization followed by parametrization of the evolution equation, and discretization of the Dirac–Frenkel variational principle governing the parameter dynamics. A unified error analysis is developed for both approaches within the family of $\zeta$-methods. The resulting bounds separate the effects of time discretization from those of residual minimization and yield first- and second-order convergence under Lipschitz, one-sided Lipschitz, and dissipativity assumptions. For the variational formulation, additional stability conditions involving the conditioning of the parametrization map arise naturally. The framework is applied to Gaussian approximation manifolds, for which residual norms and gradients admit explicit closed-form expressions when polynomial operators are involved. This enables efficient implementation without spatial discretization. Numerical experiments for time-dependent Schrödinger equations illustrate the theoretical convergence rates and the influence of residual accuracy on conservation properties.

Sample-based Quantum Diagonalization (SQD) recovers ground-state energies by classically diagonalizing a Hamiltonian in the subspace spanned by quantum samples, requiring only bitstrings with sufficient ground-state overlap rather than an accurate variational energy. We reveal and exploit this underexplored robustness property: how much non-Clifford and variational expressivity can be removed from the sampling circuit before SQD accuracy degrades? We answer through two complementary compression techniques: gradient-based operator pruning, which discards low-impact excitation operators, and Clifford rounding, which snaps remaining parameters to the nearest Clifford angle. Both of these techniques can be applied to a VQE ansatz on a qubit-reduced Hamiltonian. A systematic ablation study across 21 molecules shows that median SQD error stays within chemical accuracy even at 50% compression on both axes, while simulation speedup reaches $33\times$. Hardware validation on 6 molecules on IBM quantum hardware confirms up to $2.8\times$ transpiled-depth reduction with zero loss in SQD accuracy. Our implementation can be found at: https://github.com/zkysfls/cs-vqe-sqd

We investigate the Casimir effect for a massive real scalar field confined between two perfectly reflecting parallel plates in the presence of a position-dependent effective mass, a mechanism for coupling a scalar background to a scalar field. Exact normal modes are obtained by solving the corresponding Klein-Gordon equation, leading to a transverse energy spectrum that exhibits a characteristic Landau-like structure despite the absence of an external magnetic field. Upon quantization of the field, the vacuum energy is evaluated by means of generalized zeta-function regularization together with an appropriate renormalization procedure. The renormalized vacuum energy naturally separates into a Landau-like contribution and an additional term induced by the spatial dependence of the effective mass. We show analytically and numerically that both contributions are exponentially suppressed in the strong-coupling regime. In the opposite limit, the Landau-like contribution smoothly reproduces the standard vacuum energy for a massive scalar field confined between parallel plates, whereas the additional contribution becomes singular owing to the restricted domain of validity of the exact spectrum. Except in the vicinity of this singular limit, the vacuum energy is shown to be dominated by the Landau-like sector. Our results establish a direct connection between position-dependent effective masses and boundary-induced quantum vacuum phenomena, providing a new exactly solvable framework for the investigation of Casimir effects in spatially inhomogeneous relativistic systems.

Low-overhead quantum error-correction schemes are essential for enabling quantum computation on registers containing multiple logical qubits. For planar architectures with limited nearest-neighbor qubit connectivity, the surface code has emerged as the leading paradigm. Recent theoretical and experimental work has shown that a physical-qubit connectivity of degree three is sufficient to implement fault-tolerant quantum error correction. In this work, we study lattice surgery in the context of such trivalent architectures and introduce scalable circuit constructions to implement it. Compared with the four-valent measurement scheme, the trivalent lattice-surgery protocol reduces the required resources by $\mathcal{O}(d)$ qubits out of a total qubit count of $\mathcal{O}(d^2)$ and by $\mathcal{O}(d)$ two-qubit gates out of a total two-qubit gate count of $\mathcal{O}(d^3)$. We benchmark the logical fidelity of both lattice-surgery schemes in terms of experimentally realistic simulations targeting an implementation with a fluxonium qubit based architecture and find a potential improvement of up to $\approx25\%$ for distance-three. These results open a way for scalable planar trivalent qubit architectures to host a surface-code-based logical quantum processor.

We propose a machine-learning-empowered approach to the quantum sensing of the plaquette phase, a gauge-invariant quantity arising in three-level $\Delta$ systems. This phase profoundly affects the system dynamics, breaking coherent population trapping and inducing a non-trivial phase dependence of the dynamics. We demonstrate that a multi-layer perceptron (MLP), trained in a supervised-learning framework, can accurately estimate the plaquette phase from STImulated Raman Adiabatic Passage (STIRAP) population transfer efficiencies measured under different driving conditions, which provide experimentally accessible observables. Our results highlight how the combination of coherent control and machine learning (ML) enables effective phase identification in closed-loop quantum systems, opening new perspectives for quantum technologies, specifically quantum sensing applications including synthetic gauge fields.

The current leading approach to the variational optimization of projected entangled-pair states (PEPS) is based on automatic differentiation, which allows for a convenient evaluation of the energy gradient with respect to the local variational degrees of freedom. However, evaluating the energy gradient not only remains a major computational bottleneck of the optimization procedure, but also suffers from frequent numerical instabilities. In this work, we adopt recent advances in implicit differentiation techniques to address these challenges in PEPS optimization. By reformulating the core step of the gradient computation in terms of a single characteristic equation for the contraction environment, we reduce the cost of the gradient computation and improve its scaling with the problem size. By choosing a suitable parametrization of this characteristic equation based on the intrinsic symmetries of the contraction environment, we can directly remove instabilities from the global gradient computation that would otherwise arise from the derivatives of subroutines of the contraction algorithm. Finally, we demonstrate how this approach drastically simplifies the practical implementation of stable gradient-based PEPS optimization.

Stabilizer codes are often constructed within the Calderbank–Shor–Steane (CSS) framework, where two mutually orthogonal binary classical codes define $X$ and $Z$-type stabilizer generators. While this structure is algebraically convenient, additional non-CSS constraints may help suppress low-weight logical operators and improve decoding performance in the finite-length regime. We thus introduce quantum XYZ stabilizer codes, whose parity-check matrix (PCM) is built from three pairwise orthogonal binary PCMs associated with $X$-, $Y$-, and $Z$-type stabilizer generators. A nontrivial point is that an XYZ code instance is not automatically genuinely non-CSS: the same stabilizer group may admit a CSS generating set. We characterize this collapse, obtaining algebraic and rank conditions for deciding when the $Y$-type checks are redundant and when they define genuinely non-CSS stabilizer constraints. We also derive upper and lower bounds on the quantum minimum distance, including bounds for mixed Pauli logical operators. The novel framework includes a known non-CSS topological code, namely the XYZ$^2$ hexagonal code, and yields also sparse finite-length quantum low-density parity-check (qLDPC) constructions from intersecting-subset and quasi-dyadic code families. Simulations under depolarizing code-capacity noise and quaternary belief propagation decoding show that the proposed XYZ qLDPC instances can outperform representative CSS qLDPC instances with similar finite-length parameters.

We study a finite-time quantum information engine in which a two-level system is measured by a quantum harmonic oscillator acting as a meter and where useful work is extracted conditionally on the measurement outcome. Using multi-objective optimisation, we find a Pareto-optimal trade-off between extractable work and its fluctuations and show that reducing fluctuations entails higher thermodynamic costs: greater information consumption, more engine cycles, longer operation time, and reduced average work output. In the limit of a highly accurate meter, we obtain the work distribution, its moments, and the Pareto front analytically. In this regime, the work statistics of the engine reduce to those of a qubit in contact with a single thermal bath. We further analyse the associated information flows by examining the mutual information and Fisher information, and show that the Pareto-optimal engine designs lie very close to local maxima of the latter with respect to the operation time of the device. Our results provide a compact description of the trade-offs between work, its fluctuations, and thermodynamic costs in quantum information engines.