Papers

The $\mathcal{H}_2$ model reduction problem for high-dimensional linear quantum systems is studied under the constraint of physical realizability (PR). This constraint requires preservation of the canonical commutation relations and the quantum input-output structure, and therefore prevents the direct use of standard projection methods. A symplectic Petrov-Galerkin framework is presented, in which reduced-order models automatically satisfy the PR identities by construction. Within this framework, a symplectic variant of the iterative rational Krylov algorithm is developed and referred to as Quantum IRKA (Q-IRKA). At each iteration, an enriched tangential rational Krylov pool is generated from shifted linear solves. A symplectic basis is then extracted by a Gram-Schmidt-type procedure, paired with symplectic conjugates, and normalized so that the reduced trial space satisfies the canonical symplectic constraint. The interpolation points are updated from selected mirror images of the poles of the current reduced-order model, while the reduced-order matrices are obtained exclusively by structure-preserving projection. Numerical experiments on low-channel oscillator-chain systems and on a bosonic Kitaev-chain-inspired benchmark show that Q-IRKA is effective for large-scale linear quantum systems. Symplecticity and PR are preserved to machine precision, and accurate reduced-order models are obtained with moderate computational cost. The results also show that reduction quality depends substantially on dissipation geometry, channel placement, heterogeneity, and reduced order. These findings indicate that scalable $\mathcal{H}_2$ model reduction of linear quantum systems can be achieved while strictly preserving the underlying physical structure.

A particle-in-a-box model of continuous space quantum annealing is proposed and studied numerically by solving the Schrödinger wave equation directly. Three types of energy landscapes with multiple local minima are considered, namely a sinusoidal wave modulated by a concave, a convex, or a flat envelope. Both static (energy spectrum) and dynamical (residual energy) behaviors are analyzed in detail, paying particular attention to the effects of landscape roughness and annealing depth. Simulation results show that the residual energy as a function of annealing speed is largely independent of these two factors. The prevalence of diabatic transitions during annealing is observed, and the discrepancy between our numerical results and the Landau-Zener formula is discussed. An interesting feature in the energy gap spectrum, which we call flat gaps, is examined. Based on it, we propose a mechanism to explain the trapping of wave function in local minima during diabatic transitions, widely observed in our data.

We investigated quantum thermal machines powered by sequential nonselective generalized measurements, taking a double quantum dot with coherent interdot tunneling as a working substance. In this platform, the competition between detuning and tunneling hybridizes the localized states and modifies the energetic response of the cycle, allowing us to analyze measurement-driven thermodynamics beyond simple diagonal qubit models. We formulate a three-stroke cycle composed of thermalization with a single reservoir and two generalized measurement channels, and derive the corresponding internal-energy and entropy variations in order to identify the operational regimes of the device. Depending on the measurement parameters, the system can operate as a heat engine, accelerator, heater, or refrigerator. We show that the introduction of tunneling not only reshapes the boundaries between these modes, but also generates refrigeration configurations that are absent in the purely detuned model. In addition, the performance maps reveal that temperature, detuning, and tunneling amplitude jointly control the most favorable regions for work extraction and cooling. Our results demonstrate that coherent interdot coupling acts as an important resource for optimizing measurement-powered quantum thermal machines and highlight double quantum dots as a promising setting for experimentally relevant implementations of measurement-assisted thermodynamic devices.

The consistent histories formalism can be used to describe histories comprised of events across many systems, times, and places, plausibly rich enough to describe our experiences of the classical world; however, many consistent history sets are nonclassical and thus not obviously relevant to our experiences. Meanwhile, the program of environmentally induced decoherence identifies dynamically privileged classical degrees of freedom, but provides no general account of when or how many such degrees of freedom consistently combine to form histories. This work shows that the strengths of these two approaches can be combined by adopting a dynamics-first perspective on decoherence. Inspired by quantum causal models and quantum Darwinism, we define the process of decoherence in terms of the causal influences through unitary dynamics required for the proliferation of information about observables. We characterise decoherence as a property of the unitary dynamics, without presupposing the existence of any quantum state. Instead, we show that the state emerges from dual decoherence, related to decoherence by time-reversal of the unitary dynamics. Indeed, for any set of systems in an arbitrary unitary circuit, decoherence and its dual single out a privileged consistent history set – and we demonstrate through examples that states emerge from dual decoherence while outcomes emerge from decoherence. Hence the idea that quantum states emerge from the process of decoherence turns out to be the key missing ingredient for unifying environmentally induced decoherence and consistent histories. Taking this idea ontologically seriously leads to a recently proposed causal interpretation of quantum theory or a dynamics-first version of the Everett interpretation. The causal approach also sheds light on the suppression of off-diagonal terms, time asymmetry, and robustness of the pointer basis.

Recent advancements in quantum computing highlight the need for efficient encoding of classical data into quantum states to ensure robust quantum information processing. Traditional encoding schemes often impose impractical requirements about the knowledge of quantum states and lack adaptability to noisy quantum channels and broader tasks. To address these limitations, we propose a novel end-to-end learnable quantum transcoding scheme explicitly optimized for compactness and robustness in noisy quantum communication scenarios. Our approach integrates neural network-based data compression with Cholesky decomposition-based quantum encoding and bypasses full density matrix reconstruction. Through normalized quantum observables, our method enables efficient tomography and achieves high reconstruction and classification performance even under extreme noise conditions.

We obtain quantitative estimates on the decay of the multiplayer optimal value under parallel repetition. In comparison to a previous work of the author in 2025 (arXiv: 2508.09380) which sought to generalize dependency-breaking and anchoring variables from two-player Quantum games, being able to establish quantitative estimates on the decay of the optimal value of a multiplayer game under parallel repetition is of interest to establish under different assumptions. Specifically, independently of the dependency-breaking and anchoring variables that have previously been employed to remove correlations from entangled information shared between Alice and Bob (hence removing dependencies), monotonic concave functions can be used in place of such variables to obtain rates of decay on the optimal value. The game-theoretic setting with two players was first analyzed with monotonic concave functions by Lanzenberger and Maurer. For $q_i , x_i > 0$ $\forall 1 \leq i \leq N$ where $N > 0 $ is the total number of players we adddress an open question raised in their work regarding potential generalizations of two-player monotonic concave functions, through amplification functions of the form $\Psi_{\textit{Mult}} \equiv \Psi = N - \underset{1 \leq i \leq N}{\prod} \mathrm{exp} \big[ - q_i x_i \big]$, which in the multiplayer game-theoretic setting have more intricate combinatorial structures.

Zero-noise extrapolation (ZNE) reduces the bias of noisy quantum-circuit measurements, but Richardson coefficients and shot splitting increase their statistical error. This paper determines the noise strength at which Richardson ZNE starts to lower the mean-squared error relative to the unmitigated estimator at a fixed shot budget $B$. The boundary is set by the balance between the leading squared-bias improvement and the leading excess-variance penalty: depending on the variance exponent of the measurement, it shrinks with $B$, becomes a budget threshold, or disappears. For fixed Richardson extrapolation with linear leading bias, the Richardson order and the shot allocation change only constants; the boundary exponent is set by the measured observable and protocol. Deterministic stabilizer measurements and nonzero-variance Hamiltonian or variational-energy measurements have boundaries that shrink as $B^{-1}$ and $B^{-1/2}$, and for finite-outcome shot measurements these two classes are the only ones. Qiskit Aer simulations of Greenberger-Horne-Zeilinger (GHZ) and quantum approximate optimization algorithm (QAOA) circuits reproduce this separation, and on IBM Quantum hardware ZNE lowers the mean-squared error at equal budget in 75 of 101 instances.

In this work, a unified Lie-algebraic formulation of catability is constructed for relativistic quantum systems with arbitrary spin within this framework. In this case, the analysis starts with constructing catability as a quantitative measure for superposed coherent states, where coherence structure and quantum interference properties are studied using algebraic representations in this framework. Also, a generalized Foldy-Wouthuysen transformation is formulated within a Lie algebraic framework, delivering a systematic procedure for block-diagonalization of relativistic Hamiltonians and separation of positive- and negative-energy components in this framework. Within this formalism, a phase-sensitive catability operator is introduced to study phase correlations and coherence effects in the relativistic quantum dynamics framework. The approach is applied to Dirac spin-$1/2$ particles, where relativistic fermionic catability is analyzed in relation to spinorial structures and symmetry generators framework. The formalism is extended through a unified geometric and Lie-algebraic treatment, establishing a consistent description of catability in a relativistic quantum mechanics framework. In this context, the generalized framework is constructed for arbitrary spin-$s$ fields, enabling investigation of higher-spin relativistic quantum states within the same algebraic structure framework. In this context, the obtained results show a generalized theoretical platform for investigating relativistic quantum coherence, superposition effects, and algebraic symmetries in the framework of fermionic and bosonic systems.

Topological non-trivial band structures are the core problem in the field of topological materials. In this paper, we investigate the topological band structure in a system with controllable Dirac points from the perspective of wave packet dynamics. By adding a third-nearest-neighboring coupling to the graphene model, additional pairs of Dirac points emerge. The emergence and annihilation of Dirac points result in hybrid and parabolic points, and we show that these band structures can be revealed by the dynamical behaviors of wave packets. Particularly, for the gapped hybrid point, the motion of the wave packet shows a one-dimensional Zitterbewegung motion. Furthermore, we also show that the winding number associated with the Dirac point and parabolic point can be determined via the center-of-mass and spin texture of wave packets, respectively. The results of this work could motivate new experimental methods to characterize the system's topological signatures through wave packet dynamics, which may also find application in systems of other exotic topological materials.

We present the first exact analytic study of unitary coherence dynamics in a minimal two qubit superconducting system with zz-coupling and transverse Josephson tunneling. By deriving the full time evolution operator without approximations and propagating all four Bell state initial conditions, we obtain novel closed form time dependent pure state density matrices and an explicit analytic expression for the C_(l_1 ) norm of coherence that, to our knowledge, has not been previously reported in the literature. Two of the Bell states are shown to be invariant under the model dynamics with constant coherence, whereas the other two exhibit controlled, parameter dependent coherence oscillations. The oscillatory behavior is governed by two distinct frequency scales that directly map onto the circuit coupling and tunneling parameters, allowing for predictable tuning of amplitude and periodicity. Numerical visualizations clarify operating regimes for transient enhancement or suppression of coherence. These results deliver compact, analytically tractable tools for parameter optimization and provide a clear foundation for incorporating dissipation and experimental validation.

We study the real time quantum dynamics of a matrix model consisting two bosonic fields on the fuzzy sphere using the Gaussian state approximation. Starting from the Hamiltonian formulation and using Wick's theorem, we derive a closed set of coupled nonlinear differential equations governing the time evolution of the one- and two-point correlation functions. Thermal equation of state is found by maximizing the von Neumann entropy over Gaussian states and solving algebraic self-consistency equation(s) leading to a complete determination of the symplectic spectrum of the covariance matrix. We identify near thermal initial conditions and use them to solve the equations of motion and employ our findings to probe chaos by calculating the largest Lyapunov exponent at various temperatures. Our results demonstrate that the latter tends to zero at a finite temperature indicating that the quantum dynamics respect the Maldacena,Shenker,Stanford bound across all temperatures, while approaching toward the classically chaotic regime at high temperatures. Finally, we examine the entanglement dynamics of the model in real-time by considering a sequence of bipartitions of the Hilbert space and computing the entanglement entropy and clearly exhibit the fast scrambling features that emerge in due detail.

We consider an open quantum system governed $N$-body Lindblad equation and study mean-field limits in this setting. We prove that the $N$-particle dynamics converges, in the sense of quantum relative entropy, to the tensorized solution of the limiting nonlinear equation. More precisely, we establish explicit bounds of order $1/N$ on the relative entropy between the $N$-particle density operator and the corresponding product state, thereby providing a quantitative propagation of chaos.

Quantum repeaters are essential for scalable long-distance quantum networking. As quantum information processing moves toward fault-tolerant and error-corrected operations, it becomes increasingly important to study quantum repeaters that also move beyond raw physical entanglement and towards logical entanglement. In this paper, we implement and simulate the quantum repeater with encoding and classical error correction (QRE-CEC) protocol in SeQUeNCe, a discrete-event simulator of quantum networks. The protocol distributes logical Bell pairs, performs encoded entanglement swapping, and uses classical error correction for the decoding of entanglement swapping measurement outcomes to determine Pauli-frame corrections. For this study, we extend SeQUeNCe with a stabilizer-based backend, add support for CSS code-based encoded operations, and integrate gate, measurement, idle decoherence, and state-initialization noise models. Our simulation results show that QRE-CEC suppresses all modeled errors to the second order. Also, QRE-CEC can distribute logical Bell pairs with 0.91 fidelity over a distance of 2000 km under the parameter regimes we study. Beyond protocol-level performance evaluation, our implementation exposes practical simulator and control-plane challenges that are typically abstracted away in theoretical studies.

Positron binding energies and Dyson orbitals for five-membered heterocycles with N, O, S and NH substituents are predicted ab initio via many-body theory. The positron-molecule correlation potential (self energy) is calculated via solution of Bethe-Salpeter equations that describe the positron-induced polarization of the target and screening of the electron-positron Coulomb interaction at the $GW$@BSE level, the infinite electron-positron ladder series that describes the crucially important process of virtual positronium formation, and the analogous positron-hole ladder series. The all-order calculations employ Gaussian-orbital bases and are implemented in the EXCITON+ code. The effect of substituting combinations of N, O and S atoms, and the NH group in the molecule's ring is studied, and the role of individual molecular orbitals, many of which are found to significantly contribute to the correlation potential, quantified. Analysis of the positron bound-state Dyson orbitals shows that the positron is typically localized next to one or two of the substituents in the ring, with the order of preference N, S, O, then NH, and is also influenced by aromaticity and the presence of double ($\pi$) bonds in the ring.

Scattering processes in high-energy physics are inherently quantum mechanical, yet are typically analyzed at the level of final states, where entanglement appears as a property of the outcome rather than a consequence of the underlying dynamics. We reformulate scattering at the level of the process itself by representing helicity transition matrices as quantum circuits. Once the kinematic configuration and scattering channel are fixed, the problem reduces to a finite-dimensional quantum map, making a circuit description natural. Within this framework, an example of the process $e^+e^-\to \mu^+\mu^-$ is shown, which decomposes into unitary and non-unitary components, corresponding to coherent mixing and postselection effects. This representation reorganizes the amplitude into distinct operational elements, providing a perspective in which collider processes can be viewed as constrained quantum circuits and their entanglement structure can be understood in terms of the underlying circuit dynamics, opening the door to analyzing their properties using the language of quantum information.

We introduce a counterdiabatic (CD) extension of the Quantum Approximate Optimization Algorithm (QAOA) for constrained portfolio optimization. By incorporating approximate adiabatic gauge potentials generated from nested commutators of the Ising-type portfolio problem Hamiltonian and the Hamming weight-preserving XY mixer Hamiltonian into our variational ansatz, the resulting Constrained Counterdiabatic QAOA (CCD-QAOA) achieves improved optimization performance under realistic budget and risk constraints. Benchmarking against standard XY-mixer QAOA, Grover-mixer QAOA, and penalty-based QAOA formulations, our numerical simulations demonstrate that, for a fixed QAOA depth, our CCD-QAOA approach consistently results in better approximation ratios.

Quantum annealing is a computational paradigm in which optimisation problems are mapped onto the energy landscape of an interacting quantum system and explored through its dynamical evolution. By continuously transforming a simple initial Hamiltonian into one whose ground state encodes the solution, the system traverses a complex landscape via a combination of quantum fluctuations, tunnelling processes, and dissipative dynamics. Unlike gate-based quantum computing, quantum annealing is a specialised and near-term approach aimed primarily at discrete optimisation and sampling tasks. While it is not expected to provide polynomial-time solutions to NP-hard problems in the worst case, it offers a physically motivated heuristic for navigating rugged energy landscapes that arise across science and engineering. Modern quantum annealers realise programmable spin systems with thousands of qubits, placing them among the largest controllable quantum devices currently available. As a result, their significance extends beyond optimisation: they also function as experimental platforms for studying non-equilibrium many-body quantum dynamics in regimes that are difficult to access using classical simulation. In this review we present an accessible introduction to the principles of quantum annealing, describe the main hardware platforms and algorithmic techniques, and analyse how tunnelling, spectral gaps, and open-system effects shape computational performance. We survey applications ranging from optimisation and machine learning to quantum simulation and many-body physics, and discuss the central challenges in benchmarking, scaling, and control. These perspectives position quantum annealing as a distinctive framework at the interface of optimisation, stochastic sampling, and programmable quantum dynamics, with a role that is complementary to both classical algorithms and gate-based quantum computing.

Motivated by the advance of dynamical quantum phase transitions (DQPTs), we analyze the zeros of the complex-time survival (Loschmidt) amplitude in finite quantum systems and develop a general framework for their approximation based on the stability of zeros of holomorphic functions. We show that the large-scale properties of the distribution of zeros are governed by the envelope of the energy distribution of the initial state and can be constructed from chains of periodic zeros associated with its dominant contributions. In this picture, zeros reach the real-time axis when two or more eigenstates become equally populated at the maximum of the envelope, providing a finite-size precursor of DQPTs. We apply the method to quenched ground states in the Ising model with tunable interaction range and demonstrate close agreement between the approximate and exact distributions of zeros. We prove that the approximate construction becomes exact for BCS ground-state quenches in two-band models. To describe short-time dynamics, we introduce a minimal Gaussian model with a nearly equidistant spectrum. Slow dephasing continuously deforms the initial zero pattern into the asymptotic two-level structure, explaining anomalous DQPTs as a delayed approach of zeros to the real-time axis. Our results identify the energy envelope as the key ingredient shaping dynamical critical behavior and provide a universal interpretation of the whole zero distribution of the complex-time survival amplitude.

According to Quantum Darwinism, system-environment interactions both einselect particular system properties and encode them redundantly in many independent subsets of the environment, called fragments. This redundancy implies that an observer can recover the einselected information by accessing just one such fragment. However, the protocol by which such reconstruction should occur is often left unspecified. Considering a system $\Gamma$ interacting with a multipartite environment $\Xi$, we investigate whether, and under what conditions, the einselected state of $\Gamma$ can be recovered from environmental fragments using the Petz recovery map. We show that the fidelity between the system's initial state and the state reconstructed via Petz recovery develops a plateau as a function of the fragment size. Our results are supported by both analytical arguments and numerical simulations of large but tractable models.

Quantum simulation of fermionic Hamiltonians is a leading application of quantum computing, but accurate execution on present-day hardware is limited by error accumulation in deep Trotter circuits. We present a device-matched noise-reduction framework for encoded Hamiltonian simulation that combines symplectic-transvection-based Trotter synthesis in the Generalized Superfast Encoding (GSE) with Clifford Noise Reduction (CliNR) and Shor-style stabilizer verification enabled by mid-circuit measurement. We implement this approach for a six-qubit encoded Clifford Trotter step on a Barium development system similar to the forthcoming IonQ Tempo line and benchmark it against direct execution using both hardware experiments and a calibrated device-level noise model. The encoded CliNR execution achieves up to 54% lower logical error rate. Crucially, this advantage disappears when stabilizer readout is deferred to the end of the circuit, showing that timely mid-circuit fault detection, rather than verification overhead alone, drives the improvement. As a proof of concept, we further show that machine-learning-guided stabilizer selection can identify verification operators that outperform random choices. These results demonstrate that encoding-native verification combined with dynamic-circuit primitives can materially improve application-motivated quantum simulation without the full overhead of quantum error correction.

We introduce a modular quantum circuit primitive to model entanglement dynamics in QCD parton splitting and use it as a composable building block for data-driven, physics-consistent modelling of parton-shower kinematics. For the pure-gluon channel, we derive an analytic expression for the helicity entanglement generated at the splitting vertex, quantified via the concurrence, and construct a two-qubit circuit whose $\sigma_3$ expectation values encode the momentum shared between outgoing gluons. The circuit reproduces the QCD-predicted concurrence by construction, which fixes a two-qubit correlator that the momentum fractions alone do not determine. Iterating the primitive, the concurrence obeys a product rule across successive splittings. Calibrating the circuit parameters to LHC jet substructure data relates the reconstructed momentum-sharing fractions directly to circuit rotation angles. Composing multiple splitting primitives yields multi-prong momentum-fraction distributions; we compare the three- and four-prong cases against experimental data, reproducing the core of the distributions. For the three-prong configuration, we execute the circuit on superconducting quantum hardware, recover the momentum-fraction distributions after a device-bias correction calibrated on a held-out subset, and study how noise alters the entanglement-dependent observable. This work provides a concrete framework for quantum-native parton-shower modules that encode quantum correlations at the level of splitting dynamics, and offers physics-informed ansätze for future quantum algorithms for QCD.

Valleytronics and valley photonics exploit the valley degree of freedom to encode and manipulate information. Here we show that photonic valleys can be selectively addressed in quantum optics using a simple two-level emitter, provided it is coupled nonlocally to the field, thereby realizing a so-called giant atom. Specifically, we consider a qubit coupled at multiple points to an engineered honeycomb lattice of resonators with detuned sublattice frequencies. By tailoring the geometry of the coupling points, the giant atom can be made to emit selectively into a single valley. The emitted photons thereby acquire a well-defined valley character and inherit the associated Berry curvature. By placing the qubit near a domain wall between regions of opposite sublattice detuning, whose interface supports valley-polarized edge modes, emission becomes chiral along the domain wall. This provides a promising route toward implementation of single-photon disorder-robust chiral emission without breaking time-reversal symmetry of the electromagnetic medium in platforms such as circuit QED.

Fast Weight Programmers (FWPs) encode temporal dependencies through dynamically updated parameters rather than recurrent hidden states. Quantum FWPs (QFWPs) extend this idea with variational quantum circuits (VQCs), but existing implementations rely on multi-qubit architectures that are difficult to scale on noisy intermediate-scale quantum (NISQ) devices and expensive to simulate classically. We propose gated QKAN-FWP, a fast-weight framework that integrates FWP with Quantum-inspired Kolmogorov-Arnold Network (QKAN) using single-qubit data re-uploading circuits as learnable nonlinear activation, known as DatA Re-Uploading ActivatioN (DARUAN). We further introduce a scalar-gated fast-weight update rule that stabilizes parameter evolution, supported by a theoretical analysis of its adaptive memory kernel, geometric boundedness, and parallelizable gradient paths. We evaluate the framework across time-series benchmarks, MiniGrid reinforcement learning, and highlight real-world solar cycle forecasting as our main practical result. In the long-horizon setting with 528-month input window and 132-month forecast horizon, our 12.5k-parameter model achieves lower scaled Mean Square Error (MSE), peak amplitude error, and peak timing error than a suite of classical recurrent baselines with up to 13x more parameters, including Long Short-Term Memory (LSTM) networks (25.9k-89.1k parameters), WaveNet-LSTM (167k), Vanilla recurrent neural network (11.5k), and a Modified Echo State Network (132k). To validate NISQ compatibility, we further deploy the trained fast programmer on IonQ and IBM Quantum processors, recovering forecasting accuracy within 0.1% relative MSE of the noiseless simulator at 1024 shots. These results position gated QKAN-FWP as a scalable, parameter-efficient, and NISQ-compatible approach to quantum-inspired sequence modeling.

Quantum thermalization describes how interacting quantum systems relax toward thermal equilibrium, a central problem in modern physics. Yet most experimental information on many-body systems comes from short-time transition spectroscopy, typically interpreted within Kubo's linear-response framework. These perspectives-long-time equilibration versus short-time response-seem fundamentally disconnected. Here we establish an exact link between them: the Kubo-Thermalization correspondence, which connects long-time thermalized magnetization under weak driving to short-time linear-response spectra for a spin coupled to a thermal bath. The correspondence holds even when the steady state differs substantially from the initial state and when each regime is individually difficult to describe theoretically. We experimentally confirm the correspondence using effective spin-$1/2$ impurities realized with ultracold fermions in two internal states coupled to a Fermi sea. Our results provide a rare exact statement about quantum thermalization and offer a novel route to infer thermalization dynamics from equilibrium response measurements in strongly interacting quantum systems, independent of microscopic details of the system–bath coupling.

Machine learning nowadays becomes a useful instrument in many subjects. In this paper we use interpretable machine learning to build quantum algorithm. By studying the parameters of the machine learning algorithm we were able to construct universal shortest analytic quantum algorithm for arbitrary diagonal matrix of any size.

Matrix product states provide efficient classical descriptions of quantum systems that may be useful as reference states for quantum algorithms such as quantum phase estimation and quantum-selected configuration interaction. Shallow circuit constructions for loading matrix product states onto quantum computers is necessary for this to be practical on near-term hardware. We present a decomposition of matrix product states to log-depth quantum circuits via a simple tree tensor network renormalisation procedure. Our method exposes an explicit parameter which can be used to trade a small amount of fidelity for large savings in circuit depth. We extend this decomposition to the case of matrix product operators allowing us to construct log-depth and ancilla-free circuits to calculate overlaps of the form $\left |\langle\phi|U|\psi\rangle\right |^2$. In particular, we demonstrate an interpretation of these circuits as verifier circuits with application to circuit-level device calibration.

The Schrödinger–Newton (SN) equation provides a semiclassical framework for the evolution of self-gravitating of massive quantum systems. We propose a two-body Schrödinger–Newton model that separates local nonlinear self-localization from the nonseparable Newtonian pair potential. Analytically, we show that the nonlinear self-field preserves the Schmidt spectrum, whereas direct entanglement generation arises from the nonseparable pair potential. Using numerical simulations in a regularized one-dimensional geometry, we find that entanglement generation depends sensitively on the initial spatial configuration and on the mass ratio. Highly localized, self-bound wavepackets experience minimal entanglement growth during scattering. Spatial delocalization and kinetic dispersion broaden the interaction region, amplifying the entangling power of the pair potential and exciting higher-order spatial modes. For dispersive Gaussian initial states, mass asymmetry shatters the lighter particle, producing Wigner negativity and rapid entanglement growth, whereas stationary SN profiles strongly suppress this effect. Stationary SN profiles isolate the bare pair-potential contribution; dispersive Gaussian initial states inflate it.

We present a constructive framework for designing transformations between structured light fields using birefringent optical elements, formulated in terms of SU(2) operations on polarization. Within this framework, transformations between vector beams are treated as spatially varying SU(2) operations, leading to a direct procedure for designing doubly inhomogeneous waveplates (d-plates) that implement the desired mapping. We identify a condition under which a single element implements a prescribed transformation exactly, including the global phase, and provide an explicit prescription for constructing the corresponding doubly inhomogeneous waveplate (d-plate) when this condition is satisfied, along with its realization using a finite sequence of singly inhomogeneous plates, including a QHQ configuration. Within this formulation, a broad class of problems in structured light can be treated within a single framework, including vector beam transformations, spin-orbital dynamics, and complex beam shaping. Crucially, the same SU(2) operations directly realize quantum channels on the orbital angular momentum degree of freedom, with polarization serving as a physical ancilla. These results establish a unified and explicitly constructive route to complex beam shaping and vector beam transformations based on SU(2) parameter synthesis, and provide a systematic foundation for designing next-generation photonic elements for structured light and spin-orbit information processing.

Quantum low-density parity-check codes are promising candidates for low-overhead fault-tolerant quantum computing, but degeneracy is known to impair the convergence of belief-propagation (BP) decoding of these codes. In this work, we show that appending linearly independent rows to a check matrix of a stabilizer code can reduce the search space for a valid degenerate solution. Motivated by this, we extend the recently proposed affine subcode ensemble decoding technique from the classical to the quantum setting. Moreover, we employ overcomplete matrices for each decoding path. Monte-Carlo simulations on toric and generalized bicycle codes demonstrate improved convergence and reduced logical error rate.

Using Schwinger-Keldysh field theory (SKFT), we engineer a dissipative and driven (i.e., out of equilibrium) bosonic bath acting on classical localized spins within a ferromagnetic insulator (FI) layer whose dynamics is governed by the Landau-Lifshitz-Gilbert equation, as is usually assumed in spintronics and magnonics. The bosonic bath is comprised of quantum magnons within a layer of altermagnetic insulator (AMI) that is attached to a conventional FI layer, often one of the key ingredients within spintronic and magnonic multilayers, so that interaction between slow classical (in the FI layer) and fast quantum (in the AMI layer) localized spins ensues. Such a bath, including its driving to produce a nonequilibrium distribution of altermagnetic magnons, generates a rich structure of the SKFT-derived extended LLG equation for classical spins within the FI layer. Our LLG equation contains two damping terms, both of which are spatially nonlocal and anisotropic, while one of them is also intrinsically non-Markovian, i.e., nonlocal in time. We demonstrate how to exploit these terms for tuning spintronic and magnonic effects within the FI layer of AMI/FI bilayers that involve spin wave or domain wall propagation, as well as skyrmion annihilation.