arXiv subjects

Gabriel Escrig

Publications and source records attributed to Gabriel Escrig.

5 recordsLinked to original sources

arXiv2026

From Hilbert's Tenth Problem to Quantum Speedup: Explicit Oracles for Bounded Diophantine Systems

Solving non-linear Diophantine systems lies at the mathematical core of integer optimization and cryptography. While the general unbounded problem is undecidable, even over bounded integer domains it remains classically intractable in the worst case. In this work, we introduce a fully reversible quantum algorithmic framework tailored to solve arbitrary polynomial Diophantine equations over bounded integer domains. The core of our approach is the explicit, gate-level synthesis of an evaluation oracle for amplitude amplification. By coherently evaluating polynomial constraints via in-place two's complement arithmetic and routing operations into a single recycled accumulator, this garbage-free strategy achieves a compact and scalable synthesis of the underlying non-linear arithmetic. Through analytical derivations and empirical circuit simulations, we prove that the overall spatial complexity is bounded by $q = \mathcal{O}((n + d^2)\log_2 N)$ logical qubits for $n$ variables, maximum degree $d$, and interval length $N$. The non-Clifford Toffoli depth is upper-bounded by $\mathcal{O}(q^2)$. This structural scaling exponent remains invariant to the variable count, modulated linearly only by the coefficients' Hamming weights. By moving beyond abstract black-box assumptions, this explicit architectural synthesis guarantees that the necessary quantum arithmetic acts as a bounded polynomial overhead. This ensures a quadratic speedup over classical exhaustive search, whether retrieving a unique assignment or dynamically enumerating an unknown number of solutions.

quant-ph↗

arXiv2026

Resource-Scalable Fully Quantum Metropolis-Hastings for Integer Linear Programming

Integer linear programming (ILP) remains computationally challenging due to its NP-complete nature despite its central role in scheduling, logistics, and design optimization. We introduce a fully quantum Metropolis-Hastings algorithm for ILP that implements a coherent random walk over the discrete feasible region using only reversible quantum circuits, without quantum-RAM assumptions or classical pre/post-processing. Each walk step is a unitary update that prepares coherent candidate moves, evaluates the objective and constraints reversibly -- including a constraint-satisfaction counter to enforce feasibility -- and encodes Metropolis acceptance amplitudes via a low-overhead linearized rule. At the logical level, the construction uses $\mathcal{O}(n\log_2 N)$ qubits to represent $n$ integer variables over the interval $[-N,\,N-1]$, and the Toffoli-equivalent cost per Metropolis step grows linearly with the total logical qubit count. Using explicit ripple-carry adder constructions, we support linear objectives and mixed equality/inequality constraints. Numerical circuit-level simulations on a broad ensemble of randomly generated instances validate the predicted linear resource scaling and exhibit progressive thermalization toward low-cost feasible solutions under the annealing schedule. Overall, the method provides a coherent, resource-characterized baseline for fully quantum constraint programming and a foundation for incorporating additional quantum speedups in combinatorial optimization.

quant-ph↗

arXiv2024

Deep-Learning Classification and Parameter Inference of Rotational Core-Collapse Supernovae

We test deep-learning (DL) techniques for the analysis of rotational core-collapse supernovae (CCSN) gravitational-wave (GW) signals by performing classification and parameter inference of the maximum (peak) frequency and the GW strain amplitude ($\Delta h$) multiplied by the luminosity distance ($D$) attained at core bounce, respectively, $(f_{peak})$ and $(D \cdot \Delta h)$. Our datasets are built from a catalog of numerically generated CCSN waveforms assembled by Richers et al. 2017. Those waveforms are injected into noise from the Advanced Laser Interferometer Gravitational Wave Observatory and Advanced Virgo detectors corresponding to the O2 and O3a observing runs. For a network signal-to-noise ratio (SNR) above 5, our classification network using time series detects Galactic CCSN GW signals buried in detector noise with a false positive rate of 0.10% and a 98% accuracy, being able to detect all signals with SNR>10. The inference of $f_{peak}$ is more accurate than for $D \cdot \Delta h $, particularly for our datasets with the shortest time window (0.25 s) and for a minimum SNR=15. From the calibration plots of predicted versus true values of the two parameters, the standard deviation ($\sigma$) and the slope deviation with respect to the ideal value are computed. We find $\sigma_{D \cdot \Delta h} = 52.6$ cm and $\sigma_{f_{peak}} = 18.3$ Hz, with respective slope deviations of 11.6% and 8.3%. Our best model is also tested on waveforms from a recent CCSN catalog built by Mitra et al. 2023, different from the one used for the training. For these new waveforms, the true values of the two parameters are mostly within the $1\sigma$ band around the network's predicted values. Our results show that DL techniques hold promise to infer physical parameters of Galactic rotational CCSN events.

astro-ph.HE↗

arXiv2024

Quantum Bayesian Inference with Renormalization for Gravitational Waves

Advancements in gravitational-wave interferometers, particularly the next generation, are poised to profoundly impact gravitational wave astronomy and multimessenger astrophysics. A hybrid quantum algorithm is proposed to carry out quantum inference of parameters from compact binary coalescences detected in gravitational-wave interferometers. It performs quantum Bayesian Inference with Renormalization and Downsampling (qBIRD). We choose binary black hole (BBH) mergers from LIGO observatories as the first case to test the algorithm, but its application can be extended to more general instances. The quantum algorithm is able to generate corner plots of relevant parameters such as chirp mass, mass ratio, spins, etc. by inference of simulated gravitational waves with known injected parameter values with zero noise, Gaussian noise and real data, thus recovering an accuracy equivalent to that of classical Markov Chain Monte Carlo inferences. The simulations are performed with sets of 2 and 4 parameters. These results enhance the possibilities to extend our capacity to track signals from coalescences over longer durations and at lower frequencies extending the accuracy and promptness of gravitational wave parameter estimation.

quant-ph↗

arXiv2022

Parameter Estimation of Gravitational Waves with a Quantum Metropolis Algorithm

After the first detection of a gravitational wave in 2015, the number of successes achieved by this innovative way of looking through the universe has not stopped growing. However, the current techniques for analyzing this type of events present a serious bottleneck due to the high computational power they require. In this article we explore how recent techniques based on quantum algorithms could surpass this obstacle. For this purpose, we propose a quantization of the classical algorithms used in the literature for the inference of gravitational wave parameters based on the well-known Quantum Walks technique applied to a Metropolis-Hastings algorithm. Finally, we develop a quantum environment on classical hardware, implementing a metric to compare quantum versus classical algorithms in a fair way. We further test all these developments in the real inference of several sets of parameters of all the events of the first detection period GWTC-1 and we find a polynomial advantage in the quantum algorithms, thus setting a first starting point for future algorithms.

gr-qc↗