arXiv subjects

Pere Mujal

Publications and source records attributed to Pere Mujal.

14 recordsLinked to original sources

arXiv2026

Measurement-enabled online quantum processing with amplitude encoding

We introduce a quantum reservoir computing online protocol that realizes amplitude encoding on quantum hardware. Our scheme combines mid-circuit measurement and reset operations to implement the partial-trace dynamics underlying amplitude encoding, while an indirect measurement scheme provides access to reservoir observables without interrupting temporal processing. In contrast to other approaches, our method preserves online operation, avoids input buffering, and keeps the runtime linear in the number of time steps. We present the theoretical formulation of the protocol and a proof-of-principle implementation on quantum hardware, and we evaluate its performance on two standard benchmark tasks. Our results show that the reservoir dynamics can be monitored through both direct measurements of the input qubits and indirect measurements of the memory qubits, enabling observation of the full system while isolating the internal evolution of the reservoir. This work provides a practical route toward scalable hardware implementations of amplitude-encoded quantum reservoir computing and opens the door to systematic experimental studies of complex quantum reservoirs.

quant-ph↗

arXiv2025

Mapping Phase Diagrams of Quantum Spin Systems through Semidefinite-Programming Relaxations

Identifying quantum phase transitions poses a significant challenge in condensed matter physics, as this requires methods that both provide accurate results and scale well with system size. In this work, we demonstrate how relaxation methods can be used to generate the phase diagram for one- and two-dimensional quantum systems. To do so, we formulate a relaxed version of the ground-state problem as a semidefinite program, which we can solve efficiently. Then, by taking the resulting vector of moments for different model parameters, we identify all phase transitions based on their cosine similarity. Furthermore, we show how spontaneous symmetry breaking is naturally captured by bounding the corresponding observable. Using these methods, we reproduce the phase transitions for the one-dimensional transverse field Ising model and the two-dimensional frustrated bilayer Heisenberg model. We also illustrate how the phase diagram of the latter changes when a next-nearest-neighbor interaction is introduced. Overall, our work demonstrates how relaxation methods provide a novel framework for studying and understanding quantum phase transitions.

cond-mat.str-el↗

arXiv2024

Quantum reservoir computing in atomic lattices

Quantum reservoir computing (QRC) exploits the dynamical properties of quantum systems to perform machine learning tasks. We demonstrate that optimal performance in QRC can be achieved without relying on disordered systems. Systems with all-to-all topologies and random couplings are generally considered to minimize redundancies and enhance performance. In contrast, our work investigates the one-dimensional Bose-Hubbard model with homogeneous couplings, where a chaotic phase arises from the interplay between coupling and interaction terms. Interestingly, we find that performance in different tasks can be enhanced either in the chaotic regime or in the weak interaction limit. Our findings challenge conventional design principles and indicate the potential for simpler and more efficient QRC implementations tailored to specific tasks in Bose-Hubbard lattices.

quant-ph↗

arXiv2024

Harnessing quantum back-action for time-series processing

Quantum measurements affect the state of the observed systems via back-action. While projective measurements extract maximal classical information, they drastically alter the system's configuration. In contrast, indirect measurements balance information extraction with the degree of disturbance. Considering the prevalent use of projective measurements in quantum computing and communication protocols, the potential benefits of indirect measurements in these fields remain largely unexplored. In this work, we demonstrate that incorporating indirect measurements into a quantum machine-learning protocol known as quantum reservoir computing provides advantages in both execution time scaling and overall performance. We analyze different measurement settings by varying the measurement strength across two benchmarking tasks. Our results reveal that carefully optimizing both the reservoir Hamiltonian parameters and the measurement strength can significantly improve the quantum reservoir computing algorithm performance. Furthermore, our approach demonstrates improved memory performance when compared with state-of-the-art classical feedback protocols. This work provides a comprehensive and practical recipe to promote the implementation of indirect measurement-based protocols in quantum reservoir computing. Moreover, our findings motivate further exploration of experimental protocols that leverage the back-action effects of indirect measurements.

quant-ph↗

arXiv2024

Certifying steady-state properties of open quantum systems

Estimating the steady-state properties of open many-body quantum systems is a fundamental challenge in quantum science and technologies. In this work, we present a scalable approach based on semi-definite programming to derive certified bounds on the expectation value of an arbitrary observable in the steady state of Lindbladian dynamics. We illustrate our method on a series of many-body systems, including paradigmatic spin-1/2 chains and two-dimensional ladders, considering both equilibrium and nonequilibrium steady-states. We benchmark our method with state-of-the-art tensor-network approaches that, unlike our method, are only able to provide estimates, with no guarantee, on steady-state quantities. For the tested models, only modest computational effort is needed to obtain certified non-trivial bounds for system sizes intractable by exact methods. Our method introduces the first general numerical tool for bounding steady-state properties of open quantum dynamics, opening a new avenue in the understanding of stable configurations in many-body systems.

quant-ph↗

arXiv2022

Time Series Quantum Reservoir Computing with Weak and Projective Measurements

Quantum machine learning represents a promising avenue for data processing, also for purposes of sequential temporal data analysis, as recently proposed in quantum reservoir computing (QRC). The possibility to operate on several platforms and noise intermediate-scale quantum devices makes QRC a timely topic. A challenge that has not been addressed yet, however, is how to efficiently include quantum measurement in realistic protocols, while retaining the reservoir memory needed for sequential time series processing and preserving the quantum advantage offered by large Hilbert spaces. In this work, we propose different measurement protocols and assess their efficiency in terms of resources, through theoretical predictions and numerical analysis. We show that it is possible to exploit the quantumness of the reservoir and to obtain ideal performance both for memory and forecasting tasks with two successful measurement protocols. One consists in rewinding part of the dynamics determined by the fading memory of the reservoir and storing the corresponding data of the input sequence, while the other employs weak measurements operating online at the trade-off where information can be extracted accurately and without hindering the needed memory. Our work establishes the conditions for efficient protocols, being the fading memory time a key factor, and demonstrates the possibility of performing genuine online time-series processing with quantum systems.

quant-ph↗

arXiv2022

Quantum Reservoir Computing for Speckle-Disorder Potentials

Quantum reservoir computing is a machine-learning approach designed to exploit the dynamics of quantum systems with memory to process information. As an advantage, it presents the possibility to benefit from the quantum resources provided by the reservoir combined with a simple and fast training strategy. In this work, this technique is introduced with a quantum reservoir of spins and it is applied to find the ground-state energy of an additional quantum system. The quantum reservoir computer is trained with a linear model to predict the lowest energy of a particle in the presence of different speckle-disorder potentials. The performance of the task is analyzed with a focus on the observable quantities extracted from the reservoir and it shows to be enhanced when two-qubit correlations are employed.

quant-ph↗

arXiv2021

Opportunities in Quantum Reservoir Computing and Extreme Learning Machines

Quantum reservoir computing (QRC) and quantum extreme learning machines (QELM) are two emerging approaches that have demonstrated their potential both in classical and quantum machine learning tasks. They exploit the quantumness of physical systems combined with an easy training strategy, achieving an excellent performance. The increasing interest in these unconventional computing approaches is fueled by the availability of diverse quantum platforms suitable for implementation and the theoretical progresses in the study of complex quantum systems. In this review article, recent proposals and first experiments displaying a broad range of possibilities are reviewed when quantum inputs, quantum physical substrates and quantum tasks are considered. The main focus is the performance of these approaches, on the advantages with respect to classical counterparts and opportunities.

quant-ph↗

arXiv2021

Supervised learning of few dirty bosons with variable particle number

We investigate the supervised machine learning of few interacting bosons in optical speckle disorder via artificial neural networks. The learning curve shows an approximately universal power-law scaling for different particle numbers and for different interaction strengths. We introduce a network architecture that can be trained and tested on heterogeneous datasets including different particle numbers. This network provides accurate predictions for all system sizes included in the training set and, by design, is suitable to attempt extrapolations to (computationally challenging) larger sizes. Notably, a novel transfer-learning strategy is implemented, whereby the learning of the larger systems is substantially accelerated and made consistently accurate by including in the training set many small-size instances.

cond-mat.quant-gas↗

arXiv2020

Spin-orbit coupled bosons interacting in a two-dimensional harmonic trap

A system of bosons in a two-dimensional harmonic trap in the presence of Rashba-type spin-orbit coupling is investigated. An analytic treatment of the ground state of a single atom in the weak-coupling regime is presented and used as a basis for a perturbation theory in the interacting two-boson system. The numerical diagonalization of both the single-particle and the two-boson Hamiltonian matrices allows us to go beyond those approximations and obtain not only the ground state, but also the low-energy spectra and the different energy contributions separately. We show that the expectation value of the spin-orbit term is related to the expectation value of $\hatσ_z \hat{L}_z$ for the eigenstates of the system, regardless of the trapping potential. The low-energy states of the repulsively interacting two-boson system are characterized. With the presence of a sufficiently strong interaction and spin-orbit coupling strength, there is a direct energy-level crossing in the ground state of the system between states of different $J_z$, the third component of the total angular momentum, that changes its structure. This is reflected in a discontinuity in the different energy terms and it is signaled in the spatial density of the system.

cond-mat.quant-gas↗

arXiv2019

Few-boson localization in a continuum with speckle disorder

The disorder-induced localization of few bosons interacting via a contact potential is investigated through the analysis of the level-spacing statistics familiar from random matrix theory. The model we consider is defined in a continuum and describes one-dimensional bosonic atoms exposed to the spatially correlated disorder due to an optical speckle field. % First, we identify the speckle-field intensity required to observe, in the single-particle case, the Poisson level-spacing statistics, which is characteristic of localized quantum systems, in a computationally and experimentally feasible system size. Then, we analyze the two-body and the three-body systems, exploring a broad interaction range, from the noninteracting limit up to moderately strong interactions. Our main result is that the contact potential does not induce a shift towards the Wigner-Dyson level-spacing statistics, which would indicate the emergence of an ergodic chaotic state, indicating that localization can occur also in interacting few-body systems in a continuum. We also analyze how the ground-state energy evolves as a function of the interaction strength

cond-mat.quant-gas↗

arXiv2018

Fermionic properties of two interacting bosons in a two-dimensional harmonic trap

The system of two interacting bosons in a two-dimensional harmonic trap is compared with the system consisting of two noninteracting fermions in the same potential. In particular, we discuss how the properties of the ground state of the system, e.g., the different contributions to the total energy, change as we vary both the strength and range of the atom-atom interaction. In particular, we focus on the short-range and strong interacting limit of the two-boson system and compare it to the noninteracting two-fermion system by properly symmetrizing the corresponding degenerate ground state wave functions. In that limit, we show that the density profile of the two-boson system has a tendency similar to the system of two noninteracting fermions. Similarly, the correlations induced when the interaction strength is increased result in a similar pair correlation function for both systems.

cond-mat.quant-gas↗

arXiv2017

Quantum correlations and degeneracy of identical bosons in a 2D harmonic trap

We consider a few number of identical bosons trapped in a 2D isotropic harmonic potential and also the $N$-boson system when it is feasible. The atom-atom interaction is modelled by means of a finite-range Gaussian interaction. The spectral properties of the system are scrutinized, in particular, we derive analytic expressions for the degeneracies and their breaking for the lower-energy states at small but finite interactions. We demonstrate that the degeneracy of the low-energy states is independent of the number of particles in the noninteracting limit and also for sufficiently weak interactions. In the strongly interacting regime, we show how the many-body wave function develops holes whenever two particles are at the same position in space to avoid the interaction, a mechanism reminiscent of the Tonks-Girardeau gas in 1D. The evolution of the system as the interaction is increased is studied by means of the density profiles, pair correlations and fragmentation of the ground state for $N=2$, $3$, and $4$ bosons.

cond-mat.quant-gas↗

arXiv2016

Quantum properties of a binary bosonic mixture in a double well

This work contains a detailed analysis of the properties of the ground state of a two-component two-sites Bose-Hubbard model, which captures the physics of a binary mixture of Bose-Einstein condensates trapped in a double-well potential. The atom-atom interactions within each species and among the two species are taken as variable parameters while the hopping terms are kept fixed. To characterize the ground state we use observables such as the imbalance of population and its quantum uncertainty. The quantum many-body correlations present in the system are further quantified by studying the degree of condensation of each species, the entanglement between the two sites and the entanglement between the two species. The latter is measured by means of the Schmidt gap, the von Neumann entropy or the purity obtained after tracing out a part of the system. A number of relevant states are identified, e.g. Schrödinger catlike many-body states, in which the outcome of the population imbalance of both components is completely correlated, and other states with even larger von Neumann entropy which have a large spread in Fock space.

cond-mat.quant-gas↗