arXiv subjects

Mikel Sanz

Publications and source records attributed to Mikel Sanz.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Barankin bounds beyond local unbiasedness: Analytic results for Gaussian states via a right-division framework

We propose a quantum version of the Barankin bound as an alternative to the quantum Cram\'er-Rao bound for quantum parameter estimation. The quantum Barankin bound provides a lower bound on the mean squared error of estimators satisfying arbitrarily chosen bias constraints at arbitrarily chosen parameter points. In particular, unbiasedness over the entire parameter space can be imposed, yielding precision limits for globally unbiased quantum parameter estimation. In contrast to the recently derived quantum Barankin bound, which is based on a symmetric division superoperator, our bound is based on a nonsymmetric right-division superoperator. This formulation enables us to find analytic expressions for the Barankin matrix for Gaussian states, which allows for an efficient calculation of the bound. We demonstrate the usefulness of our results by applying them to various examples that exhibit the threshold effect in the few-shot regime, which is invisible to the standard quantum Cram\'er-Rao bound approach.

quant-ph↗

arXiv2026

Convergence monitoring of quantum Gibbs samplers

Recent progress in fully quantum Markov chain Monte Carlo methods enables efficient Gibbs-state sampling on quantum computers [Chen et al., Nature 646, 561 (2025)]. Although rigorous worst-case bounds on mixing times remain largely inaccessible for classically intractable systems, experience from classical Monte Carlo suggests that convergence of relevant observables may nevertheless be rapid. This raises the practical question of how to diagnose convergence efficiently, i.e., with at most polynomial overhead. We propose a low-cost criterion for convergence monitoring that exploits the weak measurements inherent in quantum Gibbs samplers and their qubit-efficient variants [Ding et al., arXiv:2508.05703 (2025)]. Our approach is based on the observation that, at thermal equilibrium, the net energy flow between system and environment vanishes and energy-exchange statistics satisfy a balance condition. This condition appears in the distribution of (quasi-)frequencies extracted from the weak-measurement record and we use it to construct a Hamiltonian-agnostic stopping criterion based solely on data already generated by the sampler. We provide a statistical analysis, along with numerical and analytical studies to understand its performance, assumptions, and limitations.

quant-ph↗

arXiv2026

Qutrit-Based Neural Quantum Kernels for Classification Tasks

Neural quantum kernels (NQKs) construct quantum kernels by pretraining a quantum neural network (QNN) and subsequently reusing the trained circuit as a task-adapted embedding. Extending this framework to qudits, with local unitaries in $\mathrm{SU}(d)$, provides a natural route to richer data embeddings through the increased local degrees of freedom and a direct interface for multiclass classification via intrinsically multi-level quantum systems. In this work, focusing on qutrits ($d=3$), we extend NQKs to the qudit setting and perform a systematic study of key design choices, including the number of encoded features, the number of qutrits, the kernel construction (1-to-$n$ and $n$-to-$n$), and the parameterization of $\mathrm{SU}(3)$ unitaries. Across binary and three-class tasks on four benchmark datasets, qutrit NQKs improve over the corresponding QNN baselines in nearly all settings considered and can benefit from scaling both the feature budget and the system size, although the magnitude of these gains may saturate, is dataset-dependent, and depends on the chosen parameterization. In particular, an ablation over $\mathrm{SU}(3)$ parameterizations shows that the unitary representation can substantially impact both optimization behaviour and classifier performance. These findings highlight the potential of qudit-based quantum models not only as a straightforward generalization of qubit-based architectures, but also as a promising means to better exploit complex data structures in quantum machine learning.

quant-ph↗

arXiv2026

Phase-Programmable Free Electron Quantum States in Synthetic Momentum Space

Light-electron interactions generate synthetic momentum-space dynamics that can be used to engineer free electron quantum states. Here we develop coherent control protocols in which the optical phase acts as the controllable hopping phase of a Floquet-Bloch momentum lattice. Pontryagin optimization designs phase-only waveforms that prepare selected momentum populations and coherent few-sideband superpositions with programmable relative phases. In a complementary Bragg regime protocol, dynamical phase matching selectively couples neighboring sidebands and enables deterministic sequential state synthesis. Full wave-packet simulations based on the minimal-coupling Hamiltonian identify the tolerance window set by phase noise, detuning, and finite momentum spread. The two protocols expose a speed-selectivity tradeoff between ultrafast multilevel interference control and slower resonant engineering, establishing programmable free electron sidebands as a platform for ultrafast quantum state synthesis.

quant-ph↗

arXiv2026

Contraction and Expansion Values of Quantum Channels

The contraction coefficient of the trace distance is a central tool in quantum information, quantifying how strongly a quantum channel degrades the distinguishability of states. However, being an extremal ratio, it captures only the most optimistic behaviour of the channel and is often trivial, even for very noisy channels. Moreover, a single scalar is poorly suited to describe how contraction accumulates under channel composition. In this work we introduce the \emph{contraction and expansion values}, two monotone sequences that refine the contraction and expansion coefficients in the same way singular values refine the operator norm. They arise from a min--max variational principle over subspaces of traceless Hermitian operators, admit an operational interpretation in terms of two state-discrimination games, and are shown to coincide with the Gel'fand or Bernstein numbers of the channel restricted to traceless operators. This identification places the sequences within Pietsch's theory of $s$-numbers and yields, in particular, bounds under channel composition that the contraction coefficient alone cannot provide. We establish their main structural properties and compute or estimate them for single-qubit channels, $d$-dimensional amplitude damping channels, and direct-sum channels.

quant-ph↗

arXiv2026

Quantum Eigenvalue Transformations for Arbitrary Matrices

Quantum Signal Processing (QSP) and Quantum Singular Value Transformation (QSVT) provide an efficient framework for implementing polynomials of block-encoded matrices, and thus offer a systematic approach to quantum algorithm design. However, despite a number of recent advances, important limitations remain. In particular, QSP can only transform unitary matrices, by applying a polynomial to their eigenvalues, while QSVT is a singular-value transformation and thus one can only obtain the polynomial of Hermitian matrices. As a consequence, these techniques do not directly apply to an arbitrary non-Hermitian matrix that is not diagonalizable. In this work, we propose a simple yet powerful method to extend these ideas to arbitrary square matrices by acting on their eigenvalues. To this end, we introduce the notion of an $n$-regular block encoding, namely, a block encoding whose $k$-th power reproduces the $k$-th power of the encoded matrix for every $0 < k < n$. We show that applying QSP to any unitary with this property is equivalent to applying a polynomial of degree at most $n$ to the block-encoded matrix, independently of its internal structure. Moreover, we provide a simple construction that transforms any block encoding into an $n$-regular one using only $O(\log n)$ ancillary qubits and operations. Finally, we show that this construction induces the desired transformation on the eigenvalues associated with the Jordan normal form of the matrix; for non-diagonalizable matrices this yields the full matrix function $P(A)$, whose action on each Jordan block involves the derivatives of $P$, and not merely the map $\lambda \mapsto P(\lambda)$.

quant-ph↗

arXiv2026

Stability of nonlinear dissipative systems with applications in fluid dynamics

Nonlinear partial differential equations are central to physics, engineering, and finance. Except in a limited number of integrable cases, their solution generally requires numerical methods whose cost becomes prohibitive in high-dimensional regimes or at fine resolution. Nonlinear phenomena such as turbulence are notoriously difficult to predict because of their extreme sensitivity to small variations in initial conditions, except when certain stability conditions are fulfilled. Indeed, stability allows us to achieve reliable approximate dynamics, since it determines whether small perturbations remain bounded or are amplified, potentially leading to markedly different long-term behavior. Here, we investigate the stability of dissipative partial differential equations with second-order nonlinearities. By analyzing the time evolution of solution norms in Sobolev spaces, we establish a sufficient condition for stability that links the characteristics of the linear dissipative operator, the quadratic nonlinear term, and the external forcing. The resulting criterion is expressed as an explicit inequality that guarantees stability for a wide range of initial conditions. As an illustration, we apply the framework to fluid-dynamical models governed by nonlinear partial differential equations. In particular, for the Burgers equation, the condition admits a natural interpretation in terms of the Reynolds number, thereby directly linking the stability threshold to the competition between viscous dissipation and inertial advection. We further demonstrate the scope of the approach by extending the analysis to the KPP-Fisher and Kuramoto-Sivashinsky equations.

physics.flu-dyn↗

arXiv2026

Resource-optimal quantum mode parameter estimation with multimode Gaussian states

Quantum mode parameter estimation determines parameters governing the shape of electromagnetic modes occupied by a quantum state of radiation. Canonical examples, time delays and frequency shifts, underpin radar, lidar, and optical clocks. A comprehensive framework recently established that broad families of quantum states can attain the Heisenberg limit, surpassing any classical strategy. This raises a fundamental question: among all quantum-enhanced strategies, which is truly optimal? Answering this requires identifying physically meaningful resources governing each estimation task, so quantum states can be compared on equal footing. We show these resources are connected to the eigenmode basis of the generator of the relevant mode transformation. For time-shift estimation, whose generator is diagonal in the frequency domain, the pertinent resources are the mean frequency and bandwidth; analogous quantities emerge for other transformations. Our framework unifies two historically separate perspectives: the particle-number aspect and the mode-structure of quantum light, providing a coherent picture of quantum-enhanced sensing with multimode radiation. Within this unified framework, we derive a tight upper bound on the quantum Fisher information for multimode Gaussian states, expressed in terms of these natural resources, and analytically identify the optimal Gaussian states saturating it. These optimal states take a particularly transparent form in the generator eigenbasis, a structural simplicity reflecting the deep connection between the geometry of the mode transformation and the architecture of the optimal probe. We further demonstrate that multimode homodyne detection constitutes the optimal measurement, achieving this bound and completing the end-to-end characterization of optimal quantum metrology strategies for mode parameter estimation.

quant-ph↗

arXiv2026

Squeezing-Enhanced Rotational Doppler Metrology

A rotating surface can induce a frequency shift in incident light by changing its angular momentum, a phenomenon known as the rotational Doppler effect. This effect provides a means to estimate the angular velocity of the rotating surface. In this work, we develop a continuous-variable quantum protocol for estimating the angular velocity of a rotating surface via the rotational Doppler effect. Our approach exploits squeezed and displaced Laguerre-Gaussian modes as quantum resources, which interact with a rotating metallic disc with surface roughness. The frequency shift induced by the rotational Doppler effect is then measured using a homodyne detection scheme. By analyzing the Fisher information, we demonstrate that the proposed squeezing-enhanced protocol achieves Heisenberg scaling in the ideal noiseless regime. Furthermore, we investigate the influence of noise and consider different surface models to assess their impact on the protocol's performance. While Heisenberg scaling is degraded in the presence of noise, we show that optimizing the energy allocation ratio between displacement and squeezing of the probe ensures that the quantum strategy consistently outperforms its classical counterpart.

quant-ph↗

arXiv2026

Disentangling Aleatoric and Epistemic Uncertainty in Physics-Informed Neural Networks. Application to Insulation Material Degradation Prognostics

Physics-Informed Neural Networks (PINNs) provide a framework for integrating physical laws with data. However, their application to Prognostics and Health Management (PHM) remains constrained by the limited uncertainty quantification (UQ) capabilities. Most existing PINN-based prognostics approaches are deterministic or account only for epistemic uncertainty, limiting their suitability for risk-aware decision-making. This work introduces a heteroscedastic Bayesian Physics-Informed Neural Network (B-PINN) framework that jointly models epistemic and aleatoric uncertainty, yielding full predictive posteriors for spatiotemporal insulation material ageing estimation. The approach integrates Bayesian Neural Networks (BNNs) with physics-based residual enforcement and prior distributions, enabling probabilistic inference within a physics-informed learning architecture. The framework is evaluated on transformer insulation ageing application, validated with a finite-element thermal model and field measurements from a solar power plant, and benchmarked against deterministic PINNs, dropout-based PINNs (d-PINNs), and alternative B-PINN variants. Results show that the proposed B-PINN provides improved predictive accuracy and better-calibrated uncertainty estimates than competing approaches. A systematic sensitivity study further analyzes the impact of boundary-condition, initial-condition, and residual sampling strategies on accuracy, calibration, and generalization, and the influence of measurement noise on aleatoric uncertainty. Overall, the findings highlight the capability of Bayesian physics-informed learning to support uncertainty-aware prognostics and informed decision-making in transformer asset management by tracking aleatoric and epistemic sources of uncertainty.

cs.LG↗

arXiv2025

On super additivity of Fisher information in fully Gaussian metrology

Famously, the quantum Fisher information -- the maximum Fisher information over all physical measurements -- is additive for independent copies of a system and the optimal measurement acts locally. We are left to wonder: does the same hold when the set of accessible measurements is constrained? Such constraints are necessary to account for realistic experimental restrictions. Here, we consider a fully Gaussian scenario focusing on only Gaussian measurements. We prove that the optimal Gaussian measurement protocol remains local, if the information is encoded in either the displacement or the covariance matrix. However, when the information is imprinted on both, this no longer holds true: we construct a simple global Gaussian measurement where the Fisher information becomes super additive. These results can improve parameter estimation tasks via feasible tools. Namely, in quantum optical platforms our proposed global operation requires only passive global operations and single mode Gaussian measurements. We demonstrate this in two examples where we estimate squeezing and losses. While in the former case there is a significant gap between the Fisher information of the optimal Gaussian measurement and the quantum Fisher information for a single copy, this gap can be reduced with joint Gaussian measurements and closed in the asymptotic limit of many copies.

quant-ph↗

arXiv2025

The EU Quantum Flagship's Key Performance Indicators for Quantum Computing

As quantum processors continue to scale in size and complexity, the need for well-defined, reproducible, and technology-agnostic performance metrics becomes increasingly critical. Here we present a suite of scalable quantum computing benchmarks developed as key performance indicators (KPIs) within the EU Quantum Flagship. These proposed benchmarks are designed to assess holistic system performance rather than isolated components, and to remain applicable across both noisy intermediate-scale quantum (NISQ) devices and future fault-tolerant architectures. We introduce four core benchmarks addressing complementary aspects of quantum computing capability: large multi-qubit circuit execution via a Clifford Volume benchmark, scalable multipartite entanglement generation through GHZ-state preparation, a benchmark based on the application of Shor's period-finding subroutine to simple functions, and a protocol quantifying the benefit of quantum error correction using Bell states. Each benchmark is accompanied by clearly specified protocols, reporting standards, and scalable evaluation methods. Together, these KPIs provide a coherent framework for transparent and fair performance assessment across quantum hardware platforms and for tracking progress late-NISQ toward early fault-tolerant quantum computation.

quant-ph↗

arXiv2025

QuSquare: Scalable Quality-Oriented Benchmark Suite for Pre-Fault-Tolerant Quantum Devices

As quantum technologies continue to advance, the proliferation of hardware architectures with diverse capabilities and limitations has underscored the importance of benchmarking as a tool to compare performance across platforms. Achieving fair, scalable and consistent evaluations is a key open problem in quantum computing, particularly in the pre-fault-tolerant era. To address this challenge, we introduce QuSquare, a quality-oriented benchmark suite designed to provide a scalable, fair, reproducible, and well-defined framework for assessing the performance of quantum devices across hardware architectures. QuSquare consists of four benchmark tests that evaluate quantum hardware performance at both the system and application levels: Partial Clifford Randomized, Multipartite Entanglement, Transverse Field Ising Model (TFIM) Hamiltonian Simulation, and Data Re-Uploading Quantum Neural Network (QNN). Together, these benchmarks offer an integral, hardware-agnostic, and impartial methodology to quantify the quality and capabilities of current quantum computers, supporting fair cross-platform comparisons and fostering the development of future performance standards.

quant-ph↗

arXiv2025

Digital-Analog Quantum Computing with Qudits

Digital-analog quantum computing with two-level systems is a computational paradigm that combines an analog Hamiltonian with single-qubit gates to achieve universality. We extend this framework to $d$-level systems by conjugating an analog Hamiltonian block with single-qudit gates drawn from the Weyl-Heisenberg basis, which provides a natural set of operations for qudit architectures. More specifically, we propose a protocol to simulate arbitrary two-body Hamiltonians with at most $O(d^4 n^2)$ analog blocks. The power of this approach is illustrated by the simulation of many-body qudit spin Hamiltonians including magnetic quadrupolar terms.

quant-ph↗

arXiv2025

Tight bound for the total time in digital-analog quantum computation

Digital-analog quantum computing (DAQC) is a universal computational paradigm that combines the evolution under an entangling Hamiltonian with the application of single-qubit gates. Since any unitary operation can be decomposed into a sequence of evolutions generated by two-body Hamiltonians, DAQC is inherently well-suited for realizing such operations. Suboptimal upper bounds for the total time required to perform these evolutions have been previously proposed. Here, we improve these limits by providing a tight bound for this crucial parameter, which shows a linear dependence with the number of couplings. This result enables a precise estimation of the time resources needed for quantum simulations and quantum algorithms implemented within the DAQC framework, facilitating a rigorous comparison with other approaches.

quant-ph↗

arXiv2025

Quantum Algorithm for Local-Volatility Option Pricing via the Kolmogorov Equation

The solution of option-pricing problems may turn out to be computationally demanding due to non-linear and path-dependent payoffs, the high dimensionality arising from multiple underlying assets, and sophisticated models of price dynamics. In this context, quantum computing has been proposed as a means to address these challenges efficiently. Prevailing approaches either simulate the stochastic differential equations governing the forward dynamics of underlying asset prices or directly solve the backward pricing partial differential equation. Here, we present an end-to-end quantum algorithmic framework that solves the Kolmogorov forward (Fokker-Planck) partial differential equation for local-volatility models by mapping it to a Hamiltonian-simulation problem via the Schrödingerisation technique. The algorithm specifies how to prepare the initial quantum state, perform Hamiltonian simulation, and how to efficiently recover the option price via a swap test. In particular, the efficiency of the final solution recovery is an important advantage of solving the forward versus the backward partial differential equation. Thus, our end-to-end framework offers a potential route toward quantum advantage for challenging option-pricing tasks. In particular, we obtain a polynomial advantage in grid size for the discretization of a single dimension. Nevertheless, the true power of our methodology lies in pricing high-dimensional systems, such as baskets of options, because the quantum framework admits an exponential speedup with respect to dimension, overcoming the classical curse of dimensionality.

quant-ph↗

arXiv2025

Bayesian Physics Informed Neural Networks for Reliable Transformer Prognostics

Scientific Machine Learning (SciML) integrates physics and data into the learning process, offering improved generalization compared with purely data-driven models. Despite its potential, applications of SciML in prognostics remain limited, partly due to the complexity of incorporating partial differential equations (PDEs) for ageing physics and the scarcity of robust uncertainty quantification methods. This work introduces a Bayesian Physics-Informed Neural Network (B-PINN) framework for probabilistic prognostics estimation. By embedding Bayesian Neural Networks into the PINN architecture, the proposed approach produces principled, uncertainty-aware predictions. The method is applied to a transformer ageing case study, where insulation degradation is primarily driven by thermal stress. The heat diffusion PDE is used as the physical residual, and different prior distributions are investigated to examine their impact on predictive posterior distributions and their ability to encode a priori physical knowledge. The framework is validated against a finite element model developed and tested with real measurements from a solar power plant. Results, benchmarked against a dropout-PINN baseline, show that the proposed B-PINN delivers more reliable prognostic predictions by accurately quantifying predictive uncertainty. This capability is crucial for supporting robust and informed maintenance decision-making in critical power assets.

cs.LG↗

arXiv2025

Ultrafast Stern-Gerlach and Anomalous Bragg Diffraction Regimes of Low-energy Free Electron Interaction with Light

Recent advances in photon-induced near-field electron microscopy (PINEM) have significantly impacted allied disciplines such as laser-driven accelerators and free electron radiations, collectively fostering the emergence of free-electron quantum optics (FEQO). A central objective of FEQO is to achieve coherent optical control of free electrons, analogous to light manipulation of atoms in atom optics. Motivated by this analogy, we propose an ultrafast Stern-Gerlach (USG) regime for low-energy quantum electron wavepacket (QEW), which crucially incorporates the effects of second-order dispersion inherent to slow electrons. We demonstrate that the USG diffraction induces spectral splitting and shifting of the QEW via a longitudinal electric field gradient, with the two dominant truncated sidebands forming a pseudospin degree of freedom for an effective "two-level" electron. Furthermore, by examining the wave-particle duality of the QEW during light interaction, we identify a dispersion-induced anomalous Bragg diffraction regime. This regime exhibits a distinct spectral pattern, differentiating it from these reported PINEM (Raman-Nath), dielectric laser accelerators (DLA), anomalous PINEM, and Bragg diffraction regimes. Our study provides a comprehensive classification for light-induced diffraction regimes for both swift and slow electrons. These findings underscore the pivotal role of slow-electron dispersion and duality nature in free-electron optics, offering promising avenues for electron wavefunction quantum engineering ultrafast interferometers.

quant-ph↗