arXiv subjects

Luca Arceci

Publications and source records attributed to Luca Arceci.

7 recordsLinked to original sources

arXiv2024

Gaussian process model kernels for noisy optimization in variational quantum algorithms

Variational Quantum Algorithms (VQAs) aim at solving classical or quantum optimization problems by optimizing parametrized trial states on a quantum device, based on the outcomes of noisy projective measurements. The associated optimization process benefits from an accurate modeling of the cost function landscape using Gaussian Process Models (GPMs), whose performance is critically affected by the choice of their kernel. Here we introduce trigonometric kernels, inspired by the observation that typical VQA cost functions display oscillatory behaviour with only few frequencies. Appropriate scores to benchmark the reliability of a GPM are defined, and a systematic comparison between different kernels is carried out on prototypical problems from quantum chemistry and combinatorial optimization. We further introduce RotoGP, a sequential line-search optimizer equipped with a GPM, and test how different kernels can help mitigate noise and improve optimization convergence. Overall, we observe that the trigonometric kernels show the best performance in most of the cases under study.

quant-ph↗

arXiv2021

Entanglement of formation of mixed many-body quantum states via Tree Tensor Operators

We present a numerical strategy to efficiently estimate bipartite entanglement measures, and in particular the Entanglement of Formation, for many-body quantum systems on a lattice. Our approach exploits the Tree Tensor Operator tensor network ansatz, a positive loopless representation for density matrices which, as we demonstrate, efficiently encodes information on bipartite entanglement, enabling the up-scaling of entanglement estimation. Employing this technique, we observe a finite-size scaling law for the entanglement of formation in 1D critical lattice models at finite temperature for up to 128 spins, extending to mixed states the scaling law for the entanglement entropy.

quant-ph↗

arXiv2020

Dissipation assisted Thouless pumping in the Rice-Mele model

We investigate the effect of dissipation from a thermal environment on topological pumping in the periodically-driven Rice-Mele model. We report that dissipation can improve the robustness of pumping quantisation in a regime of finite driving frequencies. Specifically, in this regime, a low-temperature dissipative dynamics can lead to a pumped charge that is much closer to the Thouless quantised value, compared to a coherent evolution. We understand this effect in the Floquet framework: dissipation increases the population of a Floquet band which shows a topological winding, where pumping is essentially quantised. This finding is a step towards understanding a potentially very useful resource to exploit in experiments, where dissipation effects are unavoidable. We consider small couplings with the environment and we use a Bloch-Redfield quantum master equation approach for our numerics: Comparing these results with an exact MPS numerical treatment we find that the quantum master equation works very well also at low temperature, a quite remarkable fact.

cond-mat.quant-gas↗

arXiv2019

Optimal working point in digitized quantum annealing

We present a study of the digitized Quantum Annealing protocol proposed by R. Barends et al., Nature 534, 222 (2016). Our analysis, performed on the benchmark case of a transverse Ising chain problem, shows that the algorithm has a well defined optimal working point for the annealing time $τ^{\mathrm{opt}}_\mathrm{P}$ --- scaling as $τ^{\mathrm{opt}}_\mathrm{P}\sim \mathrm{P}$, where $\mathrm{P}$ is the number of digital Trotter steps --- beyond which, the residual energy error shoots-up towards the value characteristic of the maximally disordered state. We present an analytical analysis for the translationally invariant transverse Ising chain case, but our numerical evidence suggests that this scenario is more general, surviving, for instance, the presence of disorder.

cond-mat.stat-mech↗

arXiv2018

On the dynamics of Simulated Quantum Annealing in random Ising chains

Simulated Quantum Annealing (SQA), that is emulating a Quantum Annealing (QA) dynamics on a classical computer by a Quantum Monte Carlo whose parameters are changed during the simulation, is a well established computational strategy to cope with the exponentially large Hilbert space. It has enjoyed some early successes but has also raised more recent criticisms. Here we investigate, on the paradigmatic case of a one-dimensional transverse field Ising chain, two issues related to SQA in its Path-Integral implementation: the question of Monte Carlo vs physical (Schrödinger) dynamics and the issue of the imaginary-time continuum limit to eliminate the Trotter error. We show that, while a proper time-continuum limit is able to restitute the correct Kibble-Zurek scaling of the residual energy $\varepsilon_\mathrm{res}(τ)\sim τ^{-1/2}$ for the ordered case --- $τ$ being the total annealing time ---, the presence of disorder leads to a characteristic sampling crisis for a large number of Trotter time-slices, in the low-temperature ordered phase. Such sampling problem, in turn, leads to SQA results which are apparently unrelated to the coherent Schrödinger QA even at intermediate $τ$.

quant-ph↗

arXiv2018

Dissipative Landau-Zener problem and thermally assisted Quantum Annealing

We revisit the issue of thermally assisted quantum annealing by a detailed study of the dissipative Landau-Zener problem in presence of a Caldeira-Leggett bath of harmonic oscillators, using both a weak-coupling quantum master equation and a quasi-adiabatic path-integral approach. Building on the known zero-temperature exact results (Wubs et al., PRL 97, 200404 (2006)), we show that a finite temperature bath can have a beneficial effect on the ground-state probability only if it couples also to a spin-direction that is transverse with respect to the driving field, while no improvement is obtained for the more commonly studied purely longitudinal coupling. In particular, we also highlight that, for a transverse coupling, raising the bath temperature further improves the ground-state probability in the fast-driving regime. We discuss the relevance of these findings for the current quantum-annealing flux qubit chips.

cond-mat.mes-hall↗

arXiv2018

On the optimal working point in dissipative quantum annealing

We study the effect of a thermal environment on the quantum annealing dynamics of a transverse-field Ising chain. The environment is modelled as a single Ohmic bath of quantum harmonic oscillators weakly interacting with the total transverse magnetization of the chain in a translationally invariant manner. We show that the density of defects generated at the end of the annealing process displays a minimum as a function of the annealing time, the so-called optimal working point, only in rather special regions of the bath temperature and coupling strength plane. We discuss the relevance of our results for current and future experimental implementations with quantum annealing hardware.

quant-ph↗