arXiv subjects

Dries Sels

Publications and source records attributed to Dries Sels.

At least 55 records · Page 3Linked to original sources

arXiv2023

Enhancing the Expressivity of Variational Neural, and Hardware-Efficient Quantum States Through Orbital Rotations

Variational approaches, such as variational Monte Carlo (VMC) or the variational quantum eigensolver (VQE), are powerful techniques to tackle the ground-state many-electron problem. Often, the family of variational states is not invariant under the reparametrization of the Hamiltonian by single-particle basis transformations. As a consequence, the representability of the ground-state wave function by the variational ansatz strongly dependents on the choice of the single-particle basis. In this manuscript we study the joint optimization of the single-particle basis, together with the variational state in the VMC (with neural quantum states) and VQE (with hardware-efficient circuits) approaches. We show that the joint optimization of the single-particle basis with the variational state parameters yields significant improvements in the expressive power and optimization landscape in a variety of chemistry and condensed matter systems. We also realize the first active-space calculation using neural quantum states, where the single-particle basis transformations are applied to all of the orbitals in the basis set.

quant-ph↗

arXiv2023

Thermalization of dilute impurities in one dimensional spin chains

We analyze a crossover between ergodic and non-ergodic regimes in an interacting spin chain with a dilute density of impurities, defined as spins with a strong local field. The dilute limit allows us to unravel some finite size effects and propose a mechanism for the delocalization of these impurities in the thermodynamic limit. In particular we show that impurities will always relax by exchanging energy with the rest of the chain. The relaxation rate only weakly depends on the impurity density and decays exponentially, up to logarithmic corrections, with the field strength. We connect the relaxation to fast operator spreading and show that the same mechanism destabilizes the recursive construction of local integrals of motion at any impurity density. In the high field limit, impurities will appear to be localized, and the system will be non-ergodic, over a wide range of system sizes. However, this is a transient effect and the eventual delocalization can be understood in terms of a flowing localization length.

quant-ph↗

arXiv2023

Experimental verification of the area law of mutual information in a quantum field simulator

Theoretical understanding of the scaling of entropies and the mutual information has led to significant advances in the research of correlated states of matter, quantum field theory, and gravity. Measuring von Neumann entropy in quantum many-body systems is challenging as it requires complete knowledge of the density matrix. In this work, we measure the von Neumann entropy of spatially extended subsystems in an ultra-cold atom simulator of one-dimensional quantum field theories. We experimentally verify one of the fundamental properties of equilibrium states of gapped quantum many-body systems, the area law of quantum mutual information. We also study the dependence of mutual information on temperature and the separation between the subsystems. Our work is a crucial step toward employing ultra-cold atom simulators to probe entanglement in quantum field theories.

cond-mat.quant-gas↗

arXiv2023

Unveiling Order from Chaos by approximate 2-localization of random matrices

Quantum many-body systems are typically endowed with a tensor product structure. This structure is inherited from probability theory, where the probability of two independent events is the product of the probabilities. The tensor product structure of a Hamiltonian thus gives a natural decomposition of the system into independent smaller subsystems. Considering a particular Hamiltonian and a particular tensor product structure, one can ask: is there a basis in which this Hamiltonian has this desired tensor product structure? In particular, we ask: is there a basis in which an arbitrary Hamiltonian has a 2-local form, i.e. it contains only pairwise interactions? Here we show, using numerical and analytical arguments, that generic Hamiltonian (e.g. a large random matrix) can approximately be written as a linear combination of two-body interactions terms with high precision; that is the Hamiltonian is 2-local in a carefully chosen basis. We show that these Hamiltonians are robust to perturbations. Taken together, our results suggest a possible mechanism for the emergence of locality from chaos.

quant-ph↗

arXiv2022

Signatures of bath-induced quantum avalanches in a many-body--localized system

Strongly correlated systems can exhibit surprising phenomena when brought in a state far from equilibrium. A spectacular example are quantum avalanches, that have been predicted to run through a many-body--localized system and delocalize it. Quantum avalanches occur when the system is locally coupled to a small thermal inclusion that acts as a bath. Here we realize an interface between a many-body--localized system and a thermal inclusion of variable size, and study its dynamics. We find evidence for accelerated transport into the localized region, signature of a quantum avalanche. By measuring the site-resolved entropy we monitor how the avalanche travels through the localized system and thermalizes it site by site. Furthermore, we isolate the bath-induced dynamics by evaluating multipoint correlations between the bath and the system. Our results have fundamental implications on the robustness of many-body--localized systems and their critical behavior.

cond-mat.quant-gas↗

arXiv2022

Semiclassical bounds on dynamics of two-dimensional interacting disordered fermions

Using the truncated Wigner approximation (TWA) we study quench dynamics of two-dimensional lattice systems consisting of interacting spinless fermions with potential disorder. First, we demonstrate that the semiclassical dynamics generally relaxes faster than the full quantum dynamics. We obtain this result by comparing the semiclassical dynamics with exact diagonalization and Lanczos propagation of one-dimensional chains. Next, exploiting the TWA capabilities of simulating large lattices, we investigate how the relaxation rates depend on the dimensionality of the studied system. We show that strongly disordered one-dimensional and two-dimensional systems exhibit a transient, logarithmic-in-time relaxation, which was recently established for one-dimensional chains. Such relaxation corresponds to the infamous $1/f$-noise at strong disorder.

cond-mat.stat-mech↗

arXiv2022

Application of Pontryagin's Maximum Principle to Quantum Metrology in Dissipative Systems

Optimal control theory, also known as Pontryagin's Maximum Principle, is applied to the quantum parameter estimation in the presence of decoherence. An efficient procedure is devised to compute the gradient of quantum Fisher information with respect to the control parameters and is used to construct the optimal control protocol. The proposed procedure keeps the control problem in the time-invariant form so that both first-order and second-order optimality conditions derived from Pontryagin's Maximum Principle apply; the second-order condition turns out to be crucial when the optimal control contains singular arcs. Concretely we look for the optimal control that maximizes quantum Fisher information for "twist and turn" problem. We find that the optimal control is singular without dissipation but can become unbounded once the quantum decoherence is introduced. An amplitude constraint is needed to guarantee a bounded solution. With quantum decoherence, the maximum quantum Fisher information happens at a finite time due to the decoherence, and the asymptotic value depends on the specific decoherence channel and the control of consideration.

quant-ph↗

arXiv2021

Universality in the onset of quantum chaos in many-body systems

We show that the onset of quantum chaos at infinite temperature in two many-body one-dimensional lattice models, the perturbed spin-1/2 XXZ and Anderson models, is characterized by universal behavior. Specifically, we show that the onset of quantum chaos is marked by maxima of the typical fidelity susceptibilities that scale with the square of the inverse average level spacing, saturating their upper bound, and that the strength of the integrability- or localization-breaking perturbation at these maxima decreases with increasing system size. We also show that the spectral function below the ``Thouless'' energy (in the quantum-chaotic regime) diverges when approaching those maxima. Our results suggest that, in the thermodynamic limit, arbitrarily small integrability- or localization-breaking perturbations result in quantum chaos in the many-body quantum systems studied here.

cond-mat.stat-mech↗

arXiv2021

Quantum Sampling Algorithms, Phase Transitions, and Computational Complexity

Drawing independent samples from a probability distribution is an important computational problem with applications in Monte Carlo algorithms, machine learning, and statistical physics. The problem can in principle be solved on a quantum computer by preparing a quantum state that encodes the entire probability distribution followed by a projective measurement. We investigate the complexity of adiabatically preparing such quantum states for the Gibbs distributions of various classical models including the Ising chain, hard-sphere models on different graphs, and a model encoding the unstructured search problem. By constructing a parent Hamiltonian, whose ground state is the desired quantum state, we relate the asymptotic scaling of the state preparation time to the nature of transitions between distinct quantum phases. These insights enable us to identify adiabatic paths that achieve a quantum speedup over classical Markov chain algorithms. In addition, we show that parent Hamiltonians for the problem of sampling from independent sets on certain graphs can be naturally realized with neutral atoms interacting via highly excited Rydberg states.

quant-ph↗

arXiv2021

Quantum Sampling Algorithms for Near-Term Devices

Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of quantum algorithms that provide unbiased samples by preparing a state encoding the entire Gibbs distribution. We show that this approach leads to a speedup over a classical Markov chain algorithm for several examples including the Ising model and sampling from weighted independent sets of two different graphs. Our approach connects computational complexity with phase transitions, providing a physical interpretation of quantum speedup. Moreover, it opens the door to exploring potentially useful sampling algorithms on near-term quantum devices as the algorithm for sampling from independent sets on certain graphs can be naturally implemented using Rydberg atom arrays.

quant-ph↗

arXiv2021

Markovian baths and quantum avalanches

In this work I will discuss some numerical results on the stability of the many-body localized phase to thermal inclusions. The work simplifies a recent proposal by Morningstar et al. [arXiv:2107.05642] and studies small disordered spin chains which are perturbatively coupled to a Markovian bath. The critical disorder for avalanche stability of the canonical disordered Heisenberg chain is shown to exceed W>20. In stark contrast to the Anderson insulator, the avalanche threshold drifts considerably with system size, with no evidence of saturation in the studied regime. I will argue that the results are most easily explained by the absence of a many-body localized phase.

cond-mat.dis-nn↗

arXiv2021

Optimal Control for Quantum Metrology via Pontryagin's principle

Quantum metrology comprises a set of techniques and protocols that utilize quantum features for parameter estimation which can in principle outperform any procedure based on classical physics. We formulate the quantum metrology in terms of an optimal control problem and apply Pontryagin's Maximum Principle to determine the optimal protocol that maximizes the quantum Fisher information for a given evolution time. As the quantum Fisher information involves a derivative with respect to the parameter which one wants to estimate, we devise an augmented dynamical system that explicitly includes gradients of the quantum Fisher information. The necessary conditions derived from Pontryagin's Maximum Principle are used to quantify the quality of the numerical solution. The proposed formalism is generalized to problems with control constraints, and can also be used to maximize the classical Fisher information for a chosen measurement.

quant-ph↗

arXiv2020

Transverse instability and universal decay of spin spiral order in the Heisenberg model

We analyze the stability of spin spiral states in the two-dimensional Heisenberg model. Our analysis reveals that the SU(2) symmetric point hosts a dynamic instability that is enabled by the existence of energetically favorable transverse deformations---both in real and spin space---of the spiral order. The instability is universal in the sense that it applies to systems with any spin number, spiral wavevector, and spiral amplitude. Unlike the Landau or modulational instabilities which require impurities or periodic potential modulation of an optical lattice, quantum fluctuations alone are sufficient to trigger the transverse instability. We analytically find the most unstable mode and its growth rate, and compare our analysis with phase space methods. By adding an easy plane exchange coupling that reduces the Hamiltonian symmetry from SU(2) to U(1), the stability boundary is shown to continuously interpolate between the modulational instability and the transverse instability. This suggests that the transverse instability is an important mechanism that hinders the formation of a spin superfluid, even in the presence of strong exchange anisotropy.

cond-mat.stat-mech↗

arXiv2020

Stochastic optimal control formalism for an open quantum system

A stochastic procedure is developed which allows one to express Pontryagin's maximum principle for dissipative quantum system solely in terms of stochastic wave functions. Time-optimal controls can be efficiently computed without computing the density matrix. Specifically, the proper dynamical update rules are presented for the stochastic costate variables introduced by Pontryagin's maximum principle and restrictions on the form of the terminal cost function are discussed. The proposed procedure is confirmed by comparing the results to those obtained from optimal control on Lindbladian dynamics. Numerically, the proposed formalism becomes time and memory efficient for large systems, and it can be generalized to describe non-Markovian dynamics.

quant-ph↗

arXiv2020

Dynamical obstruction to localization in a disordered spin chain

We analyze a one-dimensional XXZ spin chain in a disordered magnetic field. As the main probes of the system's behavior we use the sensitivity of eigenstates to adiabatic transformations, as expressed through the fidelity susceptibility, in conjunction with the low frequency asymptotes of the spectral function. We identify a region of maximal chaos -- with exponentially enhanced susceptibility -- which separates the many-body localized phase from the diffusive ergodic phase. This regime is characterized by slow transport and we argue that the presence of such slow dynamics is incompatible with the localization transition in the thermodynamic limit. Instead of localizing, the system appears to enter a universal subdiffusive relaxation regime at moderate values of disorder, where the spectral function of the local longitudinal magnetization is inversely proportional to the frequency, corresponding to logarithmic in time relaxation of its auto-correlation function.

quant-ph↗

arXiv2020

Non-Gaussian correlations imprinted by local dephasing in fermionic wires

We study the behavior of an extended fermionic wire coupled to a local stochastic field. Since the quantum jump operator is Hermitian and quadratic in fermionic operators, it renders the model soluble, allowing investigation of the properties of the non-equilibrium steady-state and the role of dissipation-induced fluctuations. We derive a closed set of equations of motion solely for the two-point correlator; on the other hand, we find, surprisingly, that the many-body state exhibits non-Gaussian correlations. Density-density correlation function demonstrates a crossover from a regime of weak dissipation characterized by moderate heating and stimulated fluctuations to a quantum Zeno regime ruled by strong dissipation, which tames quantum fluctuations. Instances of soluble dissipative impurities represent an experimentally viable platform to understand the interplay between dissipation and Hamiltonian dynamics in many-body quantum systems.

cond-mat.quant-gas↗

arXiv2020

Quantum approximate Bayesian computation for NMR model inference

Recent technological advances may lead to the development of small scale quantum computers capable of solving problems that cannot be tackled with classical computers. A limited number of algorithms has been proposed and their relevance to real world problems is a subject of active investigation. Analysis of many-body quantum system is particularly challenging for classical computers due to the exponential scaling of Hilbert space dimension with the number of particles. Hence, solving problems relevant to chemistry and condensed matter physics are expected to be the first successful applications of quantum computers. In this paper, we propose another class of problems from the quantum realm that can be solved efficiently on quantum computers: model inference for nuclear magnetic resonance (NMR) spectroscopy, which is important for biological and medical research. Our results are based on the cumulation of three interconnected studies. Firstly, we use methods from classical machine learning to analyze a dataset of NMR spectra of small molecules. We perform a stochastic neighborhood embedding and identify clusters of spectra, and demonstrate that these clusters are correlated with the covalent structure of the molecules. Secondly, we propose a simple and efficient method, aided by a quantum simulator, to extract the NMR spectrum of any hypothetical molecule described by a parametric Heisenberg model. Thirdly, we propose an efficient variational Bayesian inference procedure for extracting Hamiltonian parameters of experimentally relevant NMR spectra.

quant-ph↗

arXiv2020

Adiabatic eigenstate deformations as a sensitive probe for quantum chaos

In the past decades, it was recognized that quantum chaos, which is essential for the emergence of statistical mechanics and thermodynamics, manifests itself in the effective description of the eigenstates of chaotic Hamiltonians through random matrix ensembles and the eigenstate thermalization hypothesis. Standard measures of chaos in quantum many-body systems are level statistics and the spectral form factor. In this work, we show that the norm of the adiabatic gauge potential, the generator of adiabatic deformations between eigenstates, serves as a much more sensitive measure of quantum chaos. We are able to detect transitions from non-ergodic to ergodic behavior at perturbation strengths orders of magnitude smaller than those required for standard measures. Using this alternative probe in two generic classes of spin chains, we show that the chaotic threshold decreases exponentially with system size and that one can immediately detect integrability-breaking (chaotic) perturbations by analyzing infinitesimal perturbations even at the integrable point. In some cases, small integrability-breaking is shown to lead to anomalously slow relaxation of the system, exponentially long in system size.

quant-ph↗