arXiv subjects

Maxime Debertolis

Publications and source records attributed to Maxime Debertolis.

7 recordsLinked to original sources

arXiv2025

Quantum process tomography of a compressed time evolution circuit on superconducting quantum processors

As present day quantum hardware is limited by various noise mechanisms, quantum advantage can only be reached in the near-term by designing noise-resilient quantum algorithms. In this work, we employ state-of-the-art quantum process tomography (QPT) techniques to characterize the noise channels of IBM quantum processors under realistic runtime constraints. As our main application, we compare the Trotter time-evolution of three- and four-qubit wave functions to a compressed quantum circuit version of the same evolution operator. By analysing the spectral properties of the two process channels, we find that the compressed circuit systematically yields larger eigenvalue moduli, demonstrating better noise resilience.

quant-ph↗

arXiv2025

Random matrix theory of charge distribution in disordered quantum impurity models

We introduce a bare-bone random matrix quantum impurity model, by hybridizing a localized spinless electronic level with a bath of random fermions in the Gaussian Orthogonal Ensemble (GOE). While stripped out of correlations effects, this model reproduces some salient features of the impurity charge distribution obtained in previous works on interacting disordered impurity models. Computing by numerical sampling the impurity charge distribution in our model, we find a crossover from a Gaussian distribution (centered on half a charge unit) at large hybridization, to a bimodal distribution (centered both on zero and full occupations of the charge) at small hybridization. In the bimodal regime, a universal $(-3/2)$ power-law is also observed. All these findings are very well accounted for by an analytic surmise computed with a single random electron level in the bath. We also derive an exact functional integral for the general probability distribution function of eigenvalues and eigenstates, that formally captures the statistical behavior of our model for any number $N$ of fermionic orbitals in the bath. In the Gaussian regime and in the limit $N\to\infty$, we are able to solve exactly the random matrix theory (RMT) for the charge distribution, obtaining perfect agreement with the numerics. Our results could be tested experimentally in mesoscopic devices, for instance by coupling a small quantum dot to a chaotic electronic reservoir, and using a quantum point contact as local charge sensor for the quantum dot occupation.

cond-mat.mes-hall↗

arXiv2025

Super natural orbital representation of many-body operators: structured non-Gaussianity and matrix product operator compression

We introduce super natural orbitals (SNOs) for many-body operators, defined as the eigenvectors of the one-body super-density matrix associated with an operator (OBDMO). These objects provide a natural measure of the complexity of operators in terms of non-Gaussianity. We first establish analytical properties of SNOs for time-evolution operators generated by non-interacting Hamiltonians and for Haar-random unitaries. We then perform numerical tensor network simulations to compute the SNOs for both the time-evolution operator and local operators in the Heisenberg picture in two many-body systems: the fermionic $t\text{-}V$ chain and a quantum impurity model. While the $t\text{-}V$ model exhibits no preferred super-orbital basis, the operators in the impurity model display exponentially decaying SNO occupations at all times, indicating that only a few SNOs contribute significantly to quantum correlations. For local Heisenberg-picture operators in the impurity model, we find that the complexity in the SNO basis saturates at long times. Finally, we show that rotating operators into the SNO basis with an appropriate ordering leads to substantial matrix product operator compression by exposing the factorized structure of a large number of SNOs.

cond-mat.str-el↗

arXiv2025

Symmetry resolved out-of-time-order correlators of Heisenberg spin chains using projected matrix product operators

We extend the concept of operator charge in the context of an abelian U (1) symmetry and apply this framework to symmetry-preserving matrix product operators (MPOs), enabling the description of operators projected onto specific sectors of the corresponding symmetry. Leveraging this representation, we study the effect of interactions on the scrambling of information in an integrable Heisenberg spin chain, by controlling the number of particles. Our focus lies on out-of-time order correlators (OTOCs) which we project on sectors with a fixed number of particles. This allows us to link the non-interacting system to the fully-interacting one by allowing more and more particle to interact with each other, keeping the interaction parameter fixed. While at short times, the OTOCs are almost not affected by interactions, the spreading of the information front becomes gradually faster and the OTOC saturate at larger values as the number of particle increases. We also study the behavior of finite-size systems by considering the OTOCs at times beyond the point where the front hits the boundary of the system. We find that in every sector with more than one particle, the OTOCs behave as if the local operator was rotated by a random unitary matrix, indicating that the presence of boundaries contributes to the maximal scrambling of local operators.

cond-mat.str-el↗

arXiv2025

Resolving space-time structures of quantum impurities with a numerically exact few-body algorithm

We introduce a numerically exact real-time evolution scheme for quantum impurities in a macroscopically large bath. The algorithm is few-body revealing, namely it identifies the electronic orbitals that can be made inactive (in a trivial product state) by a time-dependent orbital rotation. Following a quench, we show that both the number of active orbitals and their associated matrix product state bond dimensions saturate to small values, leading to an algorithm dramatically more accurate and faster than the state of the art. We are thus able to follow the dynamics for thousands of fermions, up to the long-time stationary regime, and to study subtle aspects of quantum relaxation in the spatio-temporal domain, such as the emergence of entanglement structures in the Kondo screening cloud.

cond-mat.str-el↗

arXiv2022

Simulating realistic screening clouds around quantum impurities: role of spatial anisotropy and disorder

Dynamical quantum impurities in metals induce electronic correlations in real space that are difficult to simulate due to their multi-scale nature, so that only s-wave scattering in clean metallic hosts has been investigated so far. However, screening clouds should show anisotropy due to lack of full rotational invariance in two- and three-dimensional lattices, while inherent disorder will also induce spatial inhomogeneities. To tackle these challenges, we present an efficient and robust algorithm based on the recursive generation of natural orbitals defined as eigenvectors of the truncated single-particle density matrix. This method provides well-converged many-body wave functions on lattices with up to tens of thousands of sites, bypassing some limitations of other approaches. The algorithm is put to the test by investigating the charge screening cloud around an interacting resonant level, both on clean and disordered lattices, achieving accurate spatial resolution from short to long distances. We thus demonstrate strong anisotropy of spatial correlations around an adatom in the half-filled square lattice. Taking advantage of the efficiency of the algorithm, we further compute the disorder-induced distribution of Kondo temperatures over several thousands of random realizations, at the same time gaining access to the full spatial profile of the screening cloud in each sample. While the charge screening cloud is typically shortened due to the polarization of the impurity by the disorder potential, we surprisingly find that rare disorder configurations preserve the long range nature of Kondo correlations in the electronic bath.

cond-mat.str-el↗

arXiv2020

Few-body nature of Kondo correlated ground states

The quenching of degenerate impurity states in metals generally induces a long-range correlated quantum state known as the Kondo screening cloud. While a macroscopic number of particles clearly take part in forming this extended structure, assessing the number of truly entangled degrees of freedom requires a careful analysis of the relevant many-body wavefunction. For this purpose, we examine the natural single-particle orbitals that are eigenstates of the single-particle density (correlation) matrix for the ground state of two quantum impurity problems: the interacting resonant level model (IRLM) and the single impurity Anderson model (SIAM). As a simple and general probe for few-body versus many-body character we consider the rate of exponential decay of the correlation matrix eigenvalues towards inactive (fully empty or filled) orbitals. We find that this rate remains large in the physically most relevant region of parameter space, implying a few-body character. Genuine many-body correlations emerge only when the Kondo temperature becomes exponentially small, for instance near a quantum critical point. In addition, we demonstrate that a simple numerical diagonalization of the few-body problem restricted to the Fock space of the most correlated orbitals converges exponentially fast with respect to the number of orbitals, to the true ground state of the IRLM. We also show that finite size effects drastically affect the correlation spectrum, shedding light on an apparent paradox arising from previous studies on short chains.

cond-mat.str-el↗