arXiv subjects

Gabriel Gouraud

Publications and source records attributed to Gabriel Gouraud.

6 recordsLinked to original sources

arXiv2026

A fidelity metric for quantum annealing benchmarked by extreme scaling quantum Monte-Carlo simulations

Quantum annealers are supposed to follow adiabatically the ground state of a system as its Hamiltonian slowly interpolates between a trivial phase and a non-trivial one; the non-trivial ground state being the solution to an optimization problem. Overwhelmingly, their performances are measured in terms of how well or fast the optimization problem is solved. While pragmatic, this approach is inherently brittle as it strongly depends on the problem considered and the classical algorithm used as the reference benchmark. Here, we propose a quantity that not only measures the end result but also the quality of the actual quantum annealing process itself. Our metric is the quantum annealing counterpart of the fidelity-per gate of gate-based quantum computers. It takes the form of an accuracy $\epsilon$ for the equation of state of the annealer. We calculate benchmark values of $\epsilon$ using two variants of the simulated quantum annealing technique for Rydberg atoms systems. Our first approach uses variational quantum Monte-Carlo with an ansatz inspired by thermal annealing. It suggests that within $\epsilon \sim 10^{-2}-10^{-3}$, a quantum annealer is indistinguishable from its thermal classical counterpart. Critically, we could reach this precision up to $100,000,000$ atoms on a single CPU. Our second approach (based on Green function quantum Monte-Carlo) reaches accuracies around $\epsilon \sim 10^{-4}$ and we have run it up to $100,000$ atoms. These results outperform current Rydberg atom quantum annealing experimental platforms in both precision and size by orders of magnitude and put severe constraints for future hardware.

quant-ph↗

arXiv2026

Replica Tensor Train

We describe a numerical many-body technique that is based on both tensor networks and quantum Monte Carlo. The variational ansatz is a tensor network that can harvest volume-law entanglement. It is constructed from a tensor train to which one applies a set of non-local operators that force several indices of the tensor train to represent the same physical index, hence its name -- replica tensor train (RTT). From the tensor network toolbox, it inherits the possibility to make linear combinations of these states and apply a certain class of operators. We can therefore find the ground-state of a local Hamiltonian in a purely algebraic way as in standard tensor network algorithms -- i.e. without using gradient descent methods. On the other hand, the volume-law structure forbids calculating physical observables directly. In much the same way as on a quantum computer where one can prepare a state but can only sample it at the end, here we have to use Markov Chain Monte Carlo to compute the observables. We further show that the approach can be extended to build Krylov-subspace ground-state methods within the variational manifold. We illustrate the different algorithms on a two-dimensional spin model with a transverse magnetic field, which can be solved by this approach at low computational cost.

cond-mat.str-el↗

arXiv2024

Quantum propagating front and the edge of the Wigner function

In the first part of the article, we study one-dimensional noninteracting fermions in the continuum and in the presence of the repulsive inverse power law potential, with an emphasis on the Wigner function in the semiclassical limit. In this limit, the Wigner function exhibits an edge called the Fermi surf that depends only on the classical one-particle Hamiltonian. Around the Fermi surf, under a well-defined semiclassical limit, the Wigner function can be expressed in terms of Airy functions which yield a smooth matching between the two regions delimited by the Fermi surf. In the second part of the article, the system is prepared in the ground state of the inverse power law potential where only the left half line is filled with fermions. Then the potential is switched off, resulting in the emergence of a propagating quantum front. We show that the power law decay of the pre-quench potential that separates the left and right half systems leads to the emergence of the Airy kernel (well known in Random Matrix Theory) at the quantum front in the long-time limit. This also comes with anomalous diffusive spreading around the front.

cond-mat.stat-mech↗

arXiv2022

Stationary time correlations for fermions after a quench in the presence of an impurity

We consider the quench dynamics of non-interacting fermions in one dimension in the presence of a finite-size impurity at the origin. This impurity is characterized by general momentum-dependent reflection and transmission coefficients which are changed from ${\sf r}_0(k), {\sf t}_0(k)$ to ${\sf r}(k), {\sf t}(k)$ at time $t=0$. The initial state is at equilibrium with ${\sf t}_0(k)=0$ such that the system is cut in two independent halves with ${\sf r}_0^R(k)$, ${\sf r}_0^L(k)$ respectively to the right and to the left of the impurity. We obtain the exact large time limit of the multi-time correlations. These correlations become time translationally invariant, and are non-zero in two different regimes: (i) for $x=O(1)$ where the system reaches a non-equilibrium steady state (NESS) (ii) for $x \sim t$, i.e., the ray-regime. For a repulsive impurity these correlations are independent of ${\sf r}_0^R(k)$, ${\sf r}_0^L(k)$, while in the presence of bound states they oscillate and memory effects persist. We show that these nontrivial relaxational properties can be retrieved in a simple manner from the large time behaviour of the single particle wave functions.

cond-mat.stat-mech↗

arXiv2022

Quench dynamics of noninteracting fermions with a delta impurity

We study the out-of-equilibrium dynamics of noninteracting fermions in one dimension and in continuum space, in the presence of a delta impurity potential at the origin whose strength $g$ is varied at time $t=0$. The system is prepared in its ground state with $g=g_0=+\infty$, with two different densities and Fermi wave-vectors $k_L$ and $k_R$ on the two half-spaces $x>0$ and $x<0$ respectively. It then evolves for $t>0$ as an isolated system, with a finite impurity strength $g$. We compute exactly the time dependent density and current. For a fixed position $x$ and in the large time limit $t \to \infty$, the system reaches a non-equilibrium stationary state (NESS). We obtain analytically the correlation kernel, density, particle current, and energy current in the NESS, and characterize their relaxation, which is algebraic in time. In particular, in the NESS, we show that, away from the impurity, the particle density displays oscillations which are the non-equilibrium analog of the Friedel oscillations. In the regime of "rays", $x/t=ξ$ fixed with $x, t \to \infty$, we compute the same quantities and observe the emergence of two light cones, associated to the Fermi velocities $k_L$ and $k_R$ in the initial state. Interestingly, we find non trivial quantum correlations between two opposite rays with velocities $ξ$ and $-ξ$ which we compute explicitly. We extend to a continuum setting and to a correlated initial state the analytical methods developed in a recent work of Ljubotina, Sotiriadis and Prosen, in the context of a discrete fermionic chain with an impurity. We also generalize our results to an initial state at finite temperature, recovering, via explicit calculations, some predictions of conformal field theory in the low energy limit.

cond-mat.stat-mech↗

arXiv2021

Hole probability for noninteracting fermions in a $d$-dimensional trap

The hole probability, i.e., the probability that a region is void of particles, is a benchmark of correlations in many body systems. We compute analytically this probability $P(R)$ for a spherical region of radius $R$ in the case of $N$ noninteracting fermions in their ground state in a $d$-dimensional trapping potential. Using a connection to the Laguerre-Wishart ensembles of random matrices, we show that, for large $N$ and in the bulk of the Fermi gas, $P(R)$ is described by a universal scaling function of $k_F R$, for which we obtain an exact formula ($k_F$ being the local Fermi wave-vector). It exhibits a super exponential tail $P(R)\propto e^{- κ_d (k_F R)^{d+1}}$ where $κ_d$ is a universal amplitude, in good agreement with existing numerical simulations. When $R$ is of the order of the radius of the Fermi gas, the hole probability is described by a large deviation form which is not universal and which we compute exactly for the harmonic potential. Similar results also hold in momentum space.

cond-mat.stat-mech↗