Papers

We investigate collective Mpemba-type relaxation in a degenerate family of bosonic modes coupled to a common thermal reservoir. Starting from a fully symmetric M-mode description and employing a representative mean-field reduction, we derive effective master equations for weak-coupling Markovian, strong-coupling Caldeira-Leggett, and weak-coupling non-Markovian regimes. In the weak-coupling Markovian limit, relaxation separates into an incoherent thermal channel decaying at rate gamma and a collective coherent channel decaying at rate M gamma, yielding an explicit Mpemba crossing time determined by the initial-state preparation. In the strong-coupling Caldeira-Leggett regime, transient quadrature dynamics enriches the relaxation pattern, delaying crossings in the overdamped sector and generating multiple crossings in the underdamped sector. In the non-Markovian regime, reservoir memory reshapes the same channel-competition mechanism through time-dependent decay rates and a Lamb shift, producing delayed and clustered crossing windows. Numerical results based on the energy and the Kullback-Leibler divergence reveal Mpemba and anti-Mpemba behavior, criterion dependence, and multiple transient reorderings induced by collective coherence, quadrature dynamics, and reservoir memory.

Exceptional points (EPs) are non-Hermitian spectral singularities where eigenvalues and eigenvectors coalesce. We propose a geometry-controlled route to EPs in orbital-angular-momentum (OAM) photonics. In an effective torsion-free helicoidal background, the twist supplies a signed, real chiral splitting between opposite-OAM modes, while openness, gain, loss, leakage, or channel coupling, supplies the non-Hermiticity. The EP is reached when the geometric detuning compensates for a residual mode splitting and the linewidth contrast meets the non-Hermitian balance condition; the twist rate is thus the control parameter, not the source of non-Hermiticity. We obtain the OAM slope both for a confined quantum problem and, in the paraxial regime, for a helically twisted guide, and embed the OAM doublet in a multimode mode-space model to show that the EP survives spectator modes. Eigenvalue coalescence, phase-rigidity collapse, linear EP tracking with residual detuning, and branch exchange under geometric encircling provide falsifiable signatures. An OAM-resolved input-output response maps these onto spectroscopy-level observables, including spectral maps and three-dimensional Riemann-surface visualizations. A device-level paraxial simulation of two distinct photonic platforms, one reciprocal and one asymmetric-coupling Wiersig-type platform, reproduces the predicted exceptional point and its linear geometric tracking.

A central goal of quantum optimal control is to achieve high-fidelity and low-energy control pulses. When quantum optimal control methods optimize every point of a pulse discretized over small time steps independently this can yield high fidelity control but also results in broadband and energy-hungry waveforms. We extend MAGICARP, a shooting method inspired by Pontryagin's maximum principle on energy that generates an entire pulse from a small set of parameters, making it smooth and energy-efficient by construction, from driftless systems to closed systems with the constant drift Hamiltonian of two exchange-coupled spins in an external magnetic field. The optimization proceeds in stages: the dressed states of the drift Hamiltonian structure the target, an initial shooting optimization is performed in the rotating-wave frame, and an exact laboratory-frame refinement follows. Benchmarked against Krotov and GRAPE at matched gate infidelity, MAGICARP consistently achieves the lowest energy and a conserved pulse area, concentrates its spectral weight on the gate-relevant transitions, and is the most robust to fluctuations in the exchange coupling; GRAPE independently converges to essentially the same pulse while black-box Krotov meets the same error at an order-of-magnitude energy premium. This method-independence is what qualifies the bounded solver as a measurement instrument, and the central result follows: a large statistical survey of unselected optimization runs resolves a weak-driving quantum speed limit for two exchange-coupled electron spins: low-amplitude realizations of the two-qubit quantum Fourier transform cease to exist below a critical gate time, and the minimum control energy diverges on approach to this limit. The divergence obeys a simple two-parameter area–pole law, $E_2^{\mathrm{law}}(T)=A/T+B/(T-T^*)$.

As quantum computers remain susceptible to noise, QEC is essential for preserving logical information during computations. However, the performance of QEC codes breaks down beyond certain noise thresholds, revealing fundamental limits on their ability to protect quantum information. These limits can be characterized using information-theoretic measures such as the coherent information, which quantifies the maximum rate at which logical information can be reliably transmitted through a noisy quantum channel. In this work, we establish a direct connection between the CI and the binary cross-entropy loss used when training neural network decoders. Specifically, we show that the CI constitutes a sharp lower bound on the achievable loss for decoders that track logical operators across noisy channels. To this end, we develop a transformer-based neural network model based on maximum likelihood decoding. We train this network to estimate the CI and evaluate its performance on the surface code under three noise models: code capacity, phenomenological, and circuit-level noise. Our results demonstrate that the network accurately predicts CI and yields threshold estimates that closely match known theoretical limits. When used as a decoder, the network significantly outperforms the minimum weight perfect matching decoder in terms of logical error rate. We also introduce a novel soft post-selection scheme that independently treats uncertainty in both logical operators and relies on confidence-based filtering of the network's output. We prove that such post-selection strategies, based on the MLD cosets, are optimal, and demonstrate their scalability in terms of both logical error rate and abort probability. These findings establish transformer-based architectures as powerful tools for QEC and provide the first numerical evidence supporting the optimality and scalability of MLD-based post-selection.

In 1964, Yu. A. Gol'fand proposed an extension of quantum mechanics to discrete time, predicting intrinsic non-unitarity and entropy increase. While historically significant, this formalism predates the modern theory of open quantum systems. In this work, we rigorously recast Gol'fand's discrete evolution equation as a Completely Positive Trace-Preserving (CPTP) quantum channel and derive its continuous-time coarse-grained limit. We demonstrate that the dynamics converge to a specific Lindblad master equation characterized by a fundamental time scale $\tau$, which induces decoherence in both the energy basis and a fundamental operator basis $W$. We analyze the thermodynamic implications using Spohn's entropy production formalism, proving that the discrete time step induces a strictly positive entropy production rate driven by the decay of quantum coherences, thereby providing a microscopic foundation for the arrow of time independent of environmental coupling. Furthermore, we quantify the loss of quantum coherence via fidelity decay and purity loss, establishing exact constraints for fault-tolerant quantum computing. We further investigate the impact of this intrinsic decoherence on Discrete Time Crystals (DTCs), showing that Gol'fand dynamics impose a fundamental lifetime limit on time-translation symmetry breaking phases. Finally, we utilize precision data from optical lattice clocks, matter-wave interferometry, and neutrino oscillations to place stringent upper bounds on $\tau$. Our results constrain the fundamental time discretization to $\tau \lesssim 10^{-26}$ s, significantly tightening previous limits and offering a testable framework for quantum gravity phenomenology.

Quantum circuit execution estimates output distributions by repeated measurements, yet developers commonly choose a fixed shot budget before execution. This static choice is brittle: low budgets can under-sample the distribution, while high budgets waste measurements. In this paper, we present StableShots, a black-box online stopping rule for static quantum circuits. The method executes a fixed circuit in small batches, monitors the total-variation distance between cumulative empirical distributions, and stops after repeated evidence of local stability. We evaluate StableShots on 180 QSimBench traces spanning six circuit families, six sizes from 4 to 14 qubits, and five noisy IBM simulated backends. With validation-only calibration and 100 repeated backend-holdout splits, the selected configuration reaches TVD <= 0.05 on all held-out test evaluations with median 7,650 shots, whereas fixed-shot baselines either fail more often or spend substantially more shots.

We formulate an operator-algebraic mechanism by which exact Boolean records can arise from local completely positive quantum operations without being imposed as microscopic structure. The kinematic input is an algebraic process functional assigning probabilities to local normal completely positive operations in a finite operational context. From the predual response of a target algebra to source interventions, relative to a background strategy class, we define an influence algebra; exact events are then, by definition, the projections in its center. The dynamical question is whether nontrivial centers can be generated by coarse-graining rather than inserted through split-record laboratories. We address this question using state-preserving normal unital completely positive coarse-graining channels. If the Cesaro means of such a channel converge to a Choi-Effros infrared range and the range is asymptotically abelian in the GNS seminorm, then the represented infrared algebra is a commutative von Neumann algebra. Its projection lattice is therefore a complete Boolean algebra. We also give a finite-sector block-primitive criterion, motivated by locality and scrambling, which implies this asymptotic abelianness with exponential suppression of off-sector coherences and intra-sector fluctuations. The result is a conservative mathematical statement: classical facts are not identified with arbitrary projections of a Type-III local algebra, but with central projections selected by an asymptotically abelian completely positive infrared limit.

We establish a rigorous framework for quantum systems with geometric deformations by constructing a strictly self-adjoint deformed momentum operator through the generalized extended momentum operator (GEMO) formalism. Unlike previous approaches relying on boundary-condition hermiticity, our method ensures intrinsic self-adjointness for both linear ($\mu(x)=\alpha x$) and quadratic ($\mu(x)=\alpha x^{2}$) deformations within a unified non-Hermitian supersymmetric factorization scheme. This yields exact analytical spectra while revealing hidden $\mathfrak{su}(1,1)$ symmetry structures. Crucially, we provide the first complete thermodynamic characterization of such systems by analytically evaluating the partition function via the Euler–Maclaurin approximation. Geometric deformation fundamentally reshapes the density of states $\rho(E)$, producing distinct thermal signatures: a divergent heat capacity peak for linear deformation due to state accumulation near a maximal energy, and a saturation $C/k_{\mathrm{B}}\to 0.6$ (below the Dulong–Petit limit) for quadratic deformation. These results establish geometric deformation as a tunable parameter for engineering quantum thermodynamic responses in curved nanostructures.

We study transient information partition in a coherent exciton-phonon-photon system using subsystem-resolved quantum mutual information (QMI). By employing a model with excitonic, phononic, and photonic degrees of freedom, we analyze the dynamics in the $J$-$\nu$ plane, where $J$ characterizes excitonic delocalization and $\nu$ denotes the exciton-phonon coupling strength. By comparing time-averaged QMI maps with the absorbed photon number, we show that optical activity alone does not determine the character of the light-induced transient state. The exciton-centered information partition identifies a broad crossover between polariton-like and polaron-like transient responses, depending on whether excitonic information is mainly shared with the photon or phonon subsystem. In contrast, the phonon-centered partition reveals a sharper boundary-adjacent redistribution ridge near the boundary between the zero- and one-exciton ground-state sectors. This ridge is absent from both the ground-state sector map and the photon-absorption map, indicating that it is neither a static sector boundary nor an enhancement of optical absorption. A variational strength-function analysis connects the ridge to a region-II-like finite-energy polaronic excitation whose dominant spectral weight lies near the one-phonon energy, and thus the ridge represents a hidden transient correlation structure in which a limited amount of phonon-related information is preferentially shared with the photon subsystem before being predominantly allocated to exciton-phonon dressing. These results show that QMI-based information partition provides a correlation-based framework for characterizing coherent light-induced transient states in which optical and material degrees of freedom jointly participate quantum mechanically.

Low-noise parametric amplifiers are widely used as the first-stage amplifier in qubit readout chains. The performance of parametric amplifiers depends sensitively on the choice of the pump condition. We propose a strategy for determining the pump condition that is tailored for fast multiplexed readout. Choosing the amplifier pump to maximize the signal-to-noise ratio (SNR) improvement at the readout frequency of the limiting qubit–the qubit that requires the longest readout time to reach a target SNR–minimizes the total multiplexed readout time. We demonstrate our pump calibration strategy experimentally on a five-qubit multiplexed readout chain with a traveling-wave parametric amplifier. Using our strategy, we reduce the multiplexed readout time by 320 ns compared to optimizing the average SNR improvement on all qubits, without degrading the target SNR for any qubit.

Quantum phase estimation is a cornerstone algorithm for determining eigenvalues of unitary operators with Heisenberg-limited precision. Conventional implementations rely on digital controlled-unitary operations together with phase-extraction circuits, which generally results in substantial circuit depth and hardware overhead. Here, we propose a hardware-native alternative that replaces digital controlled-unitary operations by analog bosonic interactions, naturally available in circuit quantum electrodynamics. The protocol extracts the phase through a sequence of binary threshold tests. A bosonic mode serves as an efficient quantum memory where the binary digits of the phase are encoded into the direction of phase-space rotations. These digits are then read out sequentially via high-fidelity homodyne measurements. We show that the protocol preserves Heisenberg scaling in estimation precision while simultaneously providing exponentially suppressed failure probability. By exploiting bosonic degrees of freedom and analog dispersive interactions, the scheme provides a hardware-efficient realization of quantum phase estimation and establishes a natural route toward implementing high-precision phase estimation on circuit quantum electrodynamics platforms.

Acceptor-bound hole spins in germanium (Ge) offer a promising but underexplored route to semiconductor quantum information processing. We present a theory-guided design study of a detector-grade Ge acceptor-spin platform based on intentionally incorporated indium (In) acceptors in ultra-high-purity Ge. The proposed materials strategy combines a residual impurity background near $10^{10} \mathrm{cm^{-3}}$ with a target In density of approximately $2\times10^{14} \mathrm{cm^{-3}}$, corresponding to an acceptor spacing of about 170 nanometer. A 1 $\mu$m-long active channel with a suitable transverse mode volume can contain about five acceptors on average, enabling a statistically selected post-fabrication register rather than a deterministically placed chain. We analyze the physical basis, device architecture, strain and disorder limits, coupling hierarchy, modeling workflow, fabrication pathway, and scaling prospects. Our results indicate that detector-grade Ge can suppress uncontrolled bulk electrostatic and strain disorder to levels compatible with acceptor-hole qubits, while the spin–orbit-active valence-band manifold supports all-electrical control and dipolar or phonon-mediated coupling. Direct exchange is treated as a close-pair or gate-enhanced interaction rather than the generic mean-spacing coupling. Phononic crystal engineering is identified as a second-stage enhancement for suppressing unwanted acoustic modes and enabling selected cavity-mediated interactions after baseline control, readout, and nearest-neighbor coupling are validated. Remaining challenges include statistical acceptor placement, interface disorder, charge noise, readout integration, and experimental validation. This work identifies detector-grade Ge In-acceptor qubits as a credible intermediate architecture between donor-based impurity qubits and fully gate-defined Ge hole-spin hardware.

The interplay between spin-orbit coupling (SOC) and nontrivial band topology in ferromagnets gives rise to a rich landscape of topological transport phenomena such as anomalous Hall effect (AHE) and topological Hall effect (THE). One central goal in modern spintronics lies in the realization of the active control over topological transport phenomena in a reversible fashion, while unambiguously disentangling respective contributions of THE and AHE to the net Hall effect remains a formidable challenge. Here we establish magneto ionic control as a powerful paradigm for dynamically engineering topological transports in a 4d-orbital SrRuO3 system with sizable SOC and itinerant ferromagnetism. Harnessing controllable protonation or oxygen vacancy incorporation, the Fermi-level upshift relative to avoided band crossings are realized through band filling control, giving rise to tunable reversal temperature of AHE polarity. Of particular note is the emergence of hump like Hall anomalies through extensive ionic doping that can be reversibly switched, irrespective of AHE polarity, providing evidence for a THE signal driven by broken inversion symmetry rather than a two channel AHE. Our findings provide a viable tuning knob for Berry curvature engineering, enabling on demand control of topological transports in strong SOC ferromagnets for low power, reconfigurable all oxide spintronic devices.

Large language models (LLMs) exhibit abilities beyond natural language modelling and text generation. Recent advances in their reasoning capabilities have spurred interest in applying LLMs to complex scientific tasks requiring deep domain expertise and sophisticated reasoning. Quantum computing, as a highly specialised field with significant knowledge barriers and hardware constraints, could greatly benefit from such advancements. However, a key open question that first must be answered is: How can we develop fine-tuning pipelines that instil genuine quantum reasoning in LLMs, rather than task-specific pattern matching? We study this question through quantum circuit simulation as a training objective, where the model must predict the measurement probability distribution resulting from a sequence of quantum gate operations. We propose and compare two fine-tuning pipelines: (1) Supervised Fine-Tuning (SFT) on explicit gate-by-gate state-vector simulation traces, and (2) a two-stage SFT+Group Relative Policy Optimisation (GRPO) approach that sequentially applies SFT followed by GRPO with verifiable rewards. Our findings show that SFT achieves near-perfect in-distribution and gate-count extrapolation accuracy, significantly outperforming both the base model and the GPT-OSS-120B baseline. SFT+GRPO trades some in-distribution precision for better generalisation to larger qubit systems that SFT alone cannot handle. Both pipelines significantly outperform the baselines, demonstrating that targeted fine-tuning on explicit reasoning traces is an effective strategy for advancing quantum reasoning in LLMs.

We address the problem of extracting a target eigenstate from an approximate pure state. Our approach, symmetry-orbit decoupling, exploits symmetries that preserve the target state while acting differently on the residual. Averaging over the resulting orbit suppresses the target–residual coherence without reducing the target population, thereby exposing a spectral structure that is hidden in the original pure state. When the target is sufficiently separated from the residual modes, it becomes the principal mode of the orbit-averaged state and can be identified through the orbit Gram matrix. Numerical VQE simulations performed with QuESTlink for six- and eight-qubit Heisenberg and Fermi–Hubbard chains show substantial improvements in ground-state energy estimation. The remaining accuracy is limited by residual components that are indistinguishable from the target under the chosen symmetry.

We study the quantum interaction between free electrons and photons in a time-varying media, and find that periodic modulation exponentially amplifies electron-photon coupling within momentum gaps, enabling arbitrarily large momentum transfer. By preparing the light in a two-mode squeezed vacuum state, the electron momentum grows faster than its spectral spreading, establishing time-modulated photonic media as a platform for accelerating free-electrons and shaping their quantum state.

Quantifying genuine multipartite entanglement remains a significant challenge. We propose a multipartite entanglement monotone defined by the minimum entanglement drop – the reduction in global one-to-group entanglement upon tracing out a single particle. We formulate a computationally efficient variant using tangle and negativity to ensure non-vanishing values for W-class states, and rigorously prove it is a valid monotone under local operations and classical communication. In the tripartite regime, the minimum tangle drop is physically equivalent to the minimum pairwise concurrence. We establish an operational framework where the entanglement drop acts as a structural probe: by assessing sensitivity to qubit loss, it identifies inseparable clusters, extracting connectivity fingerprints that uniquely differentiate graph topologies within the same local Clifford equivalence class. Integrating this mapping with classical shadows enables efficient experimental estimation and dynamic tracking of entanglement network evolution. We derive exact analytical solutions for n-qubit W states under environmental noise, revealing robust scaling behaviors. Finally, we acknowledge limitations, noting that diagnostic sensitivity strictly vanishes for highly robust states such as the 5-qubit error-correcting code.

Scalar-induced gravitational waves (SIGWs) are usually characterized by their power spectrum, although their quadratic scalar source also carries higher-order correlation information. We investigate whether phase-sensitive correlations of a primordial Gaussian scalar state can survive decoherence and be transferred to the induced tensor sector. The scalar state is described in a fixed oscillator basis by the occupation $N_k^\zeta$ and anomalous moment $M_k^\zeta$, while the transfer is formulated through the unequal-time scalar Wightman function. The late-time tensor moments $d_k$ and $\gamma_k$ define an effective Gaussian reference state and its discord, whereas the exact SIGW state is generally non-Gaussian and contains an additional connected fourth-order cumulant. We therefore introduce the baseline-subtracted observable $\Delta\kappa_{\rm coh}=\kappa_N[G^>_{\rm coh}]-\kappa_N[G^>_{\rm ref}]$. For phase damping with $M_k^\zeta\propto e^{-D_k}$, the Gaussian-reference contribution conditionally scales as $|\gamma_k|\propto e^{-2D_k}$ and $\kappa_N^{\rm G}\propto e^{-4D_k}$. This provides a framework in which the SIGW spectrum fixes the signal band, while higher-order statistics probe residual coherence beyond the power spectrum.

Shuttle-based trapped ion quantum processors typically employ a one-dimensional (1D) linear architecture to transport ion-qubits between one ore more laser interaction zones where the quantum gates are implemented, along with several qubit register storage segments. The two-dimensional (2D) quantum CCD architecture employs also T- or X-junctions for an improved scaling and efficiency. Here, we explore the shuttling layer in the compilation of quantum algorithm typical building blocks in such architecture. To weight the effort of linear shuttle and junction shuttle, we introduce individual cost functions for each operation. This allows comparing the total cost for quantum circuit building blocks such as the QFT, Carry, Adder, Shift, and Comparator circuits. We study their scaling properties with increased qubit numbers. At equivalent transport cost for junction and linear shuttling, we show that 2D architectures outperform the 1D linear trap with the ratio improving as the number of ions increases. Finally, we discuss the use of cells, such that the entire processor is constructed from a 2D array of such interconnected cells. The work aims to optimize quantum processor architectures, implementing a co-design that fits to the specific task and scaling up in a shuttle-efficient way.

We present a tunable, single-mode-optical-fiber-based source of polarization entangled photon pairs for the near-infrared telecommunication band that is deployable in standard infrastructure. The photon pairs are generated via spontaneous parametric down-conversion (SPDC) in a submicron-scale thin film of the inversion-broken rhombohedral polytype of the transition metal dichalcogenide molybdenum disulfide (3R-MoS$_2$), located between two fiber connectors. By exploiting the intrinsic symmetries of the second-order nonlinear susceptibility tensor of 3R-MoS$_2$, this hybrid approach offers control over the generated two-photon polarization state through the incident pump polarization. Most notably, two of the four maximally entangled Bell states, as well as fully co-polarized pairs can be produced. This represents a substantial improvement in terms of tunability and simplicity over established fiber-integrated sources, which require additional optical elements, precise alignment, or careful engineering of design parameters. Additionally, a nonlinear drop in the background photoluminescence signal of 3R-MoS$_2$ is observed at low pump powers, allowing us to reach a coincidences-to-accidentals ratio (CAR) of $(8.3\pm1.8)\times10^{3}$, the highest value recorded for SPDC in van der Waals materials to date.

Nonequilibrium systems maintain spatiotemporal order through energy dissipation and entropy production. Here, we demonstrate this principle by engineering a quantum limit cycle that emerges from the interplay between a first-order absorbing-state phase transition and feedback mechanism coupling order and control parameters. The quantum limit cycle manifests dynamical correlations driven by multiplicative quantum noise and periodic traverses through tipping points, which act as a robust early-warning signal for state transitions. This periodic crossing results in the enhanced dynamical susceptibility and transient rise of long-range correlations near each tipping event and their subsequent disappearance away from it. These critical transitions are accompanied by a sharp increase in the energy dissipation rate, leading to a stepwise accumulation of dynamical entropy production over time. Our results provide a way for realizing dynamical fluctuations and long-range correlations in strongly interacting driven-dissipative open quantum systems.

Scalar-induced gravitational waves are usually treated as a classical stochastic background sourced by phase-random curvature perturbations. We show that this description can miss residual quantum information. Starting from a decohered two-mode Gaussian scalar state, we derive explicit transfer relations between the scalar anomalous coherence and the covariance matrix of induced tensor modes. For a localized scalar power spectrum, the ordinary tensor power is sourced by scalar power contractions, whereas the opposite-mode tensor coherence is sourced by scalar anomalous-coherence contractions. This coherence can generate nonzero tensor discord and a connected tensor-power covariance even after scalar entanglement has vanished. We identify the connected covariance and phase-sensitive strain correlations as probes of primordial quantum coherence in secondary gravitational-wave backgrounds, and discuss their possible relevance for future space-based interferometers and pulsar timing arrays.

Many-body quantum quenches are typically associated with heating. In this work, we show that quantum quenches that perform positive work on the system can still lead to effective cooling of low-energy degrees of freedom if the quench energy is deposited in long-lived high-energy excitations. We discuss this explicitly for a quench of the hopping term t in the strong-coupling (U >> t) fermionic Hubbard model at half filling, where the quench induces a very long-lived non-equilibrium doublon density. The associated prethermal state persists for a time exponentially large in (U/t)^2. During this time window, we find an effective prethermal temperature that is reduced by the square of the ratio of final to initial hopping amplitude with respect to the initial temperature. This manifests as an effective fluctuation-dissipation relation that holds for doublon-number conserving operators. In a practical implementation the Hubbard system acts as a refrigerant to cool a target system provided the coupling conserves doublon number. Our protocol can be thought of as a quantum quench many-body generalization of adiabatic demagnetization.

We introduce and study quantum phase operators associated with the Quantum Harmonic Oscillator (QHO). We show that these operators are trace-class perturbations of the Susskind-Glogower operators and examine their mathematical and physical properties. The construction is motivated by the physically relevant two-phase case.

We establish a direct quantum–classical duality based on the degree-$2$ Sum-of-Squares (SoS) semidefinite programming cone: the matrix of two-qubit Pauli-$Z$ correlation functions obtained from any quantum state $\rho$ is automatically a feasible point of the classical Goemans–Williamson (GW) relaxation. This observation provides a universal safety net for variational quantum optimization algorithms: applying GW random hyperplane rounding to the quantum-driven moment matrix yields a certified expected cut value bounded below by $\alpha_{\text{GW}} \langle \mathcal{H} \rangle_\rho$, which holds for every state generated by variational algorithms such as the Quantum Alternating Operator Ansatz (QAOA) or the Variational Quantum Power Method (VQPM), regardless of convergence quality. We further show that the same moment matrix reveals the tensor-product structure of the underlying unitary circuit, enabling a polynomial-time, correlation-based circuit cutting procedure with rigorous error bounds. The framework is validated numerically on Max-Cut instances for variational algorithms and on random states for circuit cutting, demonstrating that two-point correlation data are sufficient to locate near-optimal bipartitions while theoretical error bounds hold in practice.

We compare repetition-based ultra-low-rate information reconciliation with dedicated ultra-low-rate codes for CV-QKD. Repetition coding offers a favorable performance-complexity trade-off, incurring only a moderate error-rate penalty while reducing decoding complexity by $2\times$, making it attractive for implementation-constrained systems.

Using the path-integral formalism, we develop an accurate and easy-to-compute semi-analytical approximation for a general class of {default intensity} models. We illustrate the accuracy of the method by presenting results for the Black-Karasinski model for which the proposed approximation provides remarkably accurate results, even in regimes of high volatility and multi-year time horizons. The accuracy and the computational efficiency of the proposed approximation makes it a viable alternative to fully numerical schemes for a variety of applications in econometrics and derivatives pricing, including the computation of XVA for credit products. As a practical example, we consider the pricing of a quanto Credit Default Swap (CDS) under stochastic intensity of default and an FX devaluation model.

In this work, we present a methodology for first-quantized relativistic quantum simulation on one-dimensional finite domains under the two boundary conditions most commonly used in lattice models: periodic boundary conditions (PBC) and Dirichlet boundary conditions (DBC). Starting from the positive-energy relativistic kinetic operator, we construct weakly relativistic lattice Hamiltonians whose leading correction requires the boundary-consistent discretized momentum moments $\langle \hat{P}^{2}\rangle$ and $\langle \hat{P}^{4}\rangle$. These moments are reconstructed in the PBC Hamiltonian from moments of a unitary cyclic translation while the DBC Hamiltonian uses the open-chain finite-difference. In a qubit-register implementation, it can be evaluated as the corresponding cyclic translation estimator plus boundary-local terms that remove the unphysical wrap-around link. The resulting energy-estimation workflow uses translation measurements for the kinetic terms, a small number of endpoints and near-endpoints overlap probabilities for DBC, and position-basis sampling for diagonal potentials. We valdate the framework of the relativistic quantum simulation in various benchmark potentials such as no potential and a cosine potential for PBC as well as an infinite square well and a harmonic potential for DBC, with finite-shot sampling tests. These benchmarks show good agreement between the estimator reconstruction and direct matrix evaluation while separating the finite-grid discretization, weak-relativistic truncation, and measurement errors.

Violations of Bell's inequalities imply that joint probabilities generated by non-commutative measurements on two (non-identical) quantum particles do not have a single common cause. But joint probabilities generated for such non-identical particles via commutative measurements do have non-trivial common cause variables. We focus on commutative measurements and consider two identical quantum particles, whose density matrices and observables (hermitian operators) are necessarily permutation-symmetric. It is natural to demand that the common cause describing joint probabilities is also permutation symmetric, i.e., it acts symmetrically on both particles. Looking at various ways of defining joint probabilities from the same measurement data, we conclude that either symmetric common causes need not exist (i.e., that the particles can be hiddenly distinguishable), or that symmetric screening variables exist, but they are trivial, i.e., no single common cause can explain all single-measurement correlations.

Dynamical decoupling (DD) is a widely used and resource-efficient technique for error suppression, but conventional DD relies on periodically repeating a short pulse block to refocus the qubit state during idle periods. Imperfections in this block cause residual errors to accumulate, ultimately degrading state recovery over long idle times. Here, we introduce a universal optimal tracking approach that extends the original tracking concept to a fully state-independent setting for designing DD sequences. By monitoring the qubit's evolution at predefined waypoints during optimization, the method dynamically compensates residual errors while preserving regular refocusing. Experimental demonstrations on a superconducting-qubit platform confirm the suppression of error accumulation under static control imperfections, in agreement with numerical predictions. Complementary simulations further show that optimal-tracking-based sequences maintain strong performance under time-dependent noise. These results establish optimal tracking as a practical and hardware-agnostic approach to designing short, robust DD sequences suitable for noisy quantum devices.