arXiv subjects

Thomas Ayral

Publications and source records attributed to Thomas Ayral.

At least 37 records · Page 2Linked to original sources

arXiv2023

Quantum computing with and for many-body physics

Quantum computing technologies are making steady progress. This has opened new opportunities for tackling problems whose complexity prevents their description on classical computers. A prototypical example of these complex problems are interacting quantum many-body systems: on the one hand, these systems are known to become rapidly prohibitive to describe using classical computers when their size increases. On the other hand, these systems are precisely those which are used in the laboratory to build quantum computing platforms. This arguably makes them one of the most promising early use cases of quantum computing. In this review, we explain how quantum many-body systems are used to build quantum processors, and how, in turn, current and future quantum processors can be used to describe large many-body systems of fermions such as electrons and nucleons. The review includes an introduction to analog and digital quantum devices, the mapping of Fermi systems and their Hamiltonians onto qubit registers, as well as an overview of methods to access their static and dynamical properties. We also highlight some aspects related to entanglement, and touch on the description, influence and processing of decoherence in quantum devices.

quant-ph↗

arXiv2022

Open Source Variational Quantum Eigensolver Extension of the Quantum Learning Machine (QLM) for Quantum Chemistry

Quantum Chemistry (QC) is one of the most promising applications of Quantum Computing. However, present quantum processing units (QPUs) are still subject to large errors. Therefore, noisy intermediate-scale quantum (NISQ) hardware is limited in terms of qubits counts and circuit depths. Specific algorithms such as Variational Quantum Eigensolvers (VQEs) can potentially overcome such issues. We introduce here a novel open-source QC package, denoted Open-VQE, providing tools for using and developing chemically-inspired adaptive methods derived from Unitary Coupled Cluster (UCC). It facilitates the development and testing of VQE algorithms. It is able to use the Atos Quantum Learning Machine (QLM), a general quantum programming framework enabling to write, optimize and simulate quantum computing programs. Along with Open-VQE, we introduce myQLM-Fermion, a new open-source module (that includes the key QLM ressources that are important for QC developments (fermionic second quantization tools etc...). The Open-VQE package extends therefore QLM to QC providing: (i) the functions to generate the different types of excitations beyond the commonly used UCCSD ans{ä}tz;(ii) a new implementation of the "adaptive derivative assembled pseudo-Trotter method" (ADAPT-VQE), written in simple class structure python codes. Interoperability with other major quantum programming frameworks is ensured thanks to myQLM, which allows users to easily build their own code and execute it on existing QPUs. The combined Open-VQE/myQLM-Fermion quantum simulator facilitates the implementation, tests and developments of variational quantum algorithms towards choosing the best compromise to run QC computations on present quantum computers while offering the possibility to test large molecules. We provide extensive benchmarks for several molecules associated to qubit counts ranging from 4 up to 24.

quant-ph↗

arXiv2022

A density-matrix renormalization group algorithm for simulating quantum circuits with a finite fidelity

We develop a density-matrix renormalization group (DMRG) algorithm for the simulation of quantum circuits. This algorithm can be seen as the extension of time-dependent DMRG from the usual situation of hermitian Hamiltonian matrices to quantum circuits defined by unitary matrices. For small circuit depths, the technique is exact and equivalent to other matrix product state (MPS) based techniques. For larger depths, it becomes approximate in exchange for an exponential speed up in computational time. Like an actual quantum computer, the quality of the DMRG results is characterized by a finite fidelity. However, unlike a quantum computer, the fidelity depends strongly on the quantum circuit considered. For the most difficult possible circuit for this technique, the so-called "quantum supremacy" benchmark of Google Inc. , we find that the DMRG algorithm can generate bit strings of the same quality as the seminal Google experiment on a single computing core. For a more structured circuit used for combinatorial optimization (Quantum Approximate Optimization Algorithm or QAOA), we find a drastic improvement of the DMRG results with error rates dropping by a factor of 100 compared with random quantum circuits. Our results suggest that the current bottleneck of quantum computers is their fidelities rather than the number of qubits.

quant-ph↗

arXiv2022

Unraveling correlated material properties with noisy quantum computers: Natural orbitalized variational quantum eigensolving of extended impurity models within a slave-boson approach

We propose a method for computing space-resolved correlation properties of the two-dimensional Hubbard model within a quantum-classical embedding strategy that uses a Noisy, Intermediate Scale Quantum (NISQ) computer to solve the embedded model. While previous approaches were limited to purely local, one-impurity embedded models, requiring at most four qubits and relatively shallow circuits, we solve a two-impurity model requiring eight qubits with an advanced hybrid scheme on top of the Variational Quantum Eigensolver algorithm. This iterative scheme, dubbed Natural Orbitalization (NOization), gradually transforms the single-particle basis to the approximate Natural-Orbital basis, in which the ground state can be minimally expressed, at the cost of measuring the one-particle reduced density-matrix of the embedded problem. We show that this transformation tends to make the variational optimization of existing (but too deep) ansatz circuits faster and more accurate, and we propose an ansatz, the Multireference Excitation Preserving (MREP) ansatz, that achieves great expressivity without requiring a prohibitive gate count. The one-impurity version of the ansatz has only one parameter, making the ground state preparation a trivial step, which supports the optimal character of our approach. Within a Rotationally Invariant Slave Boson embedding scheme that requires a minimal number of bath sites and does not require computing the full Green's function, the NOization combined with the MREP ansatz allow us to compute accurate, space-resolved quasiparticle weights and static self-energies for the Hubbard model even in the presence of noise levels representative of current NISQ processors. This paves the way to a controlled solution of the Hubbard model with larger and larger embedded problems solved by quantum computers.

quant-ph↗

arXiv2021

Benchmarking quantum co-processors in an application-centric, hardware-agnostic and scalable way

Existing protocols for benchmarking current quantum co-processors fail to meet the usual standards for assessing the performance of High-Performance-Computing platforms. After a synthetic review of these protocols -- whether at the gate, circuit or application level -- we introduce a new benchmark, dubbed Atos Q-score (TM), that is application-centric, hardware-agnostic and scalable to quantum advantage processor sizes and beyond. The Q-score measures the maximum number of qubits that can be used effectively to solve the MaxCut combinatorial optimization problem with the Quantum Approximate Optimization Algorithm. We give a robust definition of the notion of effective performance by introducing an improved approximation ratio based on the scaling of random and optimal algorithms. We illustrate the behavior of Q-score using perfect and noisy simulations of quantum processors. Finally, we provide an open-source implementation of Q-score that makes it easy to compute the Q-score of any quantum hardware.

quant-ph↗

arXiv2021

Quantum Divide and Compute: Exploring The Effect of Different Noise Sources

Our recent work (Ayral et al., 2020 IEEE Computer Society Annual Symposium on VLSI (ISVLSI)) showed the first implementation of the Quantum Divide and Compute (QDC) method, which allows to break quantum circuits into smaller fragments with fewer qubits and shallower depth. QDC can thus deal with the limited number of qubits and short coherence times of noisy, intermediate-scale quantum processors. This article investigates the impact of different noise sources -- readout error, gate error and decoherence -- on the success probability of the QDC procedure. We perform detailed noise modeling on the Atos Quantum Learning Machine, allowing us to understand tradeoffs and formulate recommendations about which hardware noise sources should be preferentially optimized. We describe in detail the noise models we used to reproduce experimental runs on IBM's Johannesburg processor. This work also includes a detailed derivation of the equations used in the QDC procedure to compute the output distribution of the original quantum circuit from the output distribution of its fragments. Finally, we analyze the computational complexity of the QDC method for the circuit under study via tensor-network considerations, and elaborate on the relation the QDC method with tensor-network simulation methods.

quant-ph↗

arXiv2020

Solving optimization problems with Rydberg analog quantum computers: Realistic requirements for quantum advantage using noisy simulation and classical benchmarks

Platforms of Rydberg atoms have been proposed as promising candidates to solve some combinatorial optimization problems. Here, we compute quantitative requirements on the system sizes and noise levels that these platforms must fulfill to reach quantum advantage in approximately solving the Unit-Disk Maximum Independent Set problem. Using noisy simulations of Rydberg platforms of up to 26 atoms interacting through realistic van der Waals interactions, we compute the average approximation ratio that can be attained with a simple quantum annealing-based heuristic within a fixed temporal computational budget. Based on estimates of the correlation lengths measured in the engineered quantum state, we extrapolate the results to large atom numbers and compare them to a simple classical approximation heuristic. We find that approximation ratios of at least $\approx 0.84$ are within reach for near-future noise levels. Not taking into account further classical and quantum algorithmic improvements, we estimate that quantum advantage could be reached by attaining a number of controlled atoms of $\sim8,000$ for a time budget of 2 seconds, and $\sim 1,000-1,200$ for a time budget of 0.2 seconds, provided the coherence levels of the system can be improved by a factor 10 while maintaining a constant repetition rate.

quant-ph↗

arXiv2020

Quantum Divide and Compute: Hardware Demonstrations and Noisy Simulations

Noisy, intermediate-scale quantum computers come with intrinsic limitations in terms of the number of qubits (circuit "width") and decoherence time (circuit "depth") they can have. Here, for the first time, we demonstrate a recently introduced method that breaks a circuit into smaller subcircuits or fragments, and thus makes it possible to run circuits that are either too wide or too deep for a given quantum processor. We investigate the behavior of the method on one of IBM's 20-qubit superconducting quantum processors with various numbers of qubits and fragments. We build noise models that capture decoherence, readout error, and gate imperfections for this particular processor. We then carry out noisy simulations of the method in order to account for the observed experimental results. We find an agreement within 20% between the experimental and the simulated success probabilities, and we observe that recombining noisy fragments yields overall results that can outperform the results without fragmentation.

quant-ph↗

arXiv2018

Rotationally invariant slave-boson and density matrix embedding theory: A unified framework and a comparative study on the 1D and 2D Hubbard Model

We present detailed benchmark ground-state calculations of the one- and two-dimensional Hubbard model utilizing the cluster extensions of the rotationally invariant slave-boson (RISB) mean-field theory and the density matrix embedding theory (DMET). Our analysis shows that the overall accuracy and the performance of these two methods are very similar. Furthermore, we propose a unified computational framework that allows us to implement both of these techniques on the same footing. This provides us with a new line of interpretation and paves the ways for developing systematically new generalizations of these complementary approaches.

cond-mat.str-el↗

arXiv2017

Dynamical Mean Field Theory, Density-Matrix Embedding Theory and Rotationally Invariant Slave Bosons: a Unified Perspective

We present a unified perspective on Dynamical Mean Field Theory (DMFT), Density-Matrix Embedding Theory (DMET) and Rotationally Invariant Slave Bosons (RISB). We show that DMET can be regarded as a simplification of the RISB method where the quasiparticle weight is set to unity. This relation allows to easily transpose extensions of a given method to another: for instance, a temperature-dependent version of RISB can be used to derive a temperature-dependent free-energy formula for DMET.

cond-mat.str-el↗

arXiv2017

Chiral d-wave Superconductivity in a Triangular Surface Lattice Mediated by Long-range Interaction

Correlated ad-atom systems on the Si(111) surface have recently attracted an increased attention as strongly correlated systems with a rich phase diagram. We study these materials by a single band model on the triangular lattice including 1/r long-range interaction. Employing the recently proposed TRILEX method we find an unconventional superconducting phase of chiral d-wave symmetry in hole-doped systems. The superconductivity is driven simultaneously by both charge and spin fluctuations and is strongly enhanced by the long-range tail of the interaction. We provide an analysis of the relevant collective bosonic modes and explain how in triangular symmetry both charge and spin channels contribute to the Cooper-pairing.

cond-mat.supr-con↗

arXiv2017

Non-local Coulomb interactions on the triangular lattice in the high-doping regime: Spectra and charge dynamics from Extended Dynamical Mean Field Theory

We explore the two-dimensional extended Hubbard model on the triangular lattice in the high doping regime. On-site and nearest-neighbour repulsive interactions are treated in a non-perturbative way by means of Extended Dynamical Mean Field Theory. We compute the low-temperature phase diagram, displaying a metallic phase and a symmetry-broken phase for strong intersite repulsions. We describe the correlation effects on both single-particle and two-particle observables in the metallic phase. Whereas single-particle spectra feature a Hubbard satellite typical of strongly correlated systems, local susceptibilities remain close to their non-interacting limit, even for large on-site repulsions. We argue that this behaviour is typical of the strongly doped case. We also report a region in parameter space with negative static local screening.

cond-mat.str-el↗

arXiv2017

TRILEX and $GW$+EDMFT approach to $d$-wave superconductivity in the Hubbard model

We generalize the recently introduced TRILEX approach (TRiply Irreducible Local EXpansion) to superconducting phases. The method treats simultaneously Mott and spin-fluctuation physics using an Eliashberg theory supplemented by local vertex corrections determined by a self-consistent quantum impurity model. We show that, in the two-dimensional Hubbard model, at strong coupling, TRILEX yields a $d$-wave superconducting dome as a function of doping. Contrary to the standard cluster dynamical mean field theory (DMFT) approaches, TRILEX can capture $d$-wave pairing using only a single-site effective impurity model. We also systematically explore the dependence of the superconducting temperature on the bare dispersion at weak coupling, which shows a clear link between strong antiferromagnetic (AF) correlations and the onset of superconductivity. We identify a combination of hopping amplitudes particularly favorable to superconductivity at intermediate doping. Finally, we study within $GW$+EDMFT the low-temperature $d$-wave superconducting phase at strong coupling in a region of parameter space with reduced AF fluctuations.

cond-mat.str-el↗

arXiv2017

The Fierz convergence criterion: a controlled approach to strongly-interacting systems with small embedded clusters

We present an embedded-cluster method, based on the TRILEX formalism. It turns the Fierz ambiguity, inherent to approaches based on a bosonic decoupling of local fermionic interactions, into a convergence criterion. It is based on the approximation of the three-leg vertex by a coarse-grained vertex computed by solving a self-consistently determined multi-site effective impurity model. The computed self-energies are, by construction, continuous functions of momentum. We show that, in three interaction and doping regimes of parameters of the two-dimensional Hubbard model, self-energies obtained with clusters of size four only are very close to numerically exact benchmark results. We show that the Fierz parameter, which parametrizes the freedom in the Hubbard-Stratonovich decoupling, can be used as a quality control parameter. By contrast, the $GW$+extended dynamical mean field theory approximation with four cluster sites is shown to yield good results only in the weak-coupling regime and for a particular decoupling. Finally, we show that the vertex has spatially nonlocal components only at low Matsubara frequencies.

cond-mat.str-el↗

arXiv2017

Influence of Fock exchange in combined many-body perturbation and dynamical mean field theory

In electronic systems with long-range Coulomb interaction, the nonlocal Fock exchange term has a band-widening effect. While this effect is included in combined many-body perturbation theory and dynamical mean field theory schemes, it is not taken into account in standard extended DMFT (EDMFT) calculations. Here, we include this instantaneous term in both approaches and investigate its effect on the phase diagram and dynamically screened interaction. We show that the largest deviations between previously presented EDMFT and $GW$+EDMFT results originate from the nonlocal Fock term, and that the quantitative differences are especially large in the strong-coupling limit. Furthermore, we show that the charge-ordering phase diagram obtained in $GW$+EDMFT methods for moderate interaction values is very similar to the one predicted by dual boson methods that include the fermion-boson or four-point vertex.

cond-mat.str-el↗

arXiv2016

Mott physics and collective modes: an atomic approximation of the four-particle irreducible functional

We discuss a generalization of the dynamical mean field theory (DMFT) for strongly correlated systems close to a Mott transition based on a systematic approximation of the fully irreducible four-point vertex. It is an atomic-limit approximation of a functional of the one- and two-particle Green functions, built with the second Legendre transform of the free energy with respect to the two-particle Green function. This functional is represented diagrammatically by four-particle irreducible (4PI) diagrams. Like the dynamical vertex approximation (D$Γ$A), the fully irreducible vertex is computed from a quantum impurity model whose bath is self-consistently determined by solving the parquet equations. However, in contrast with D$Γ$A and DMFT, the interaction term of the impurity model is also self-consistently determined. The method interpolates between the parquet approximation at weak coupling and the atomic limit, where it is exact. It is applicable to systems with short-range and long-range interactions.

cond-mat.str-el↗

arXiv2016

Large effects of subtle electronic correlations on the energetics of vacancies in alpha-Fe

We study the effect of electronic Coulomb correlations on the vacancy formation energy in paramagnetic alpha-Fe within ab initio dynamical mean-field theory. The calculated value for the formation energy is substantially lower than in standard density-functional calculations and in excellent agreement with experiment. The reduction is caused by an enhancement of electronic correlations at the nearest neighbors of the vacancy. This effect is explained by subtle changes in the corresponding spectral function of the d-electrons. The local lattice relaxations around the vacancy are substantially increased by many-body effects.

cond-mat.str-el↗

arXiv2016

Mott physics and spin fluctuations: a functional viewpoint

We present a formalism for strongly correlated systems with fermions coupled to bosonic modes. We construct the three-particle irreducible functional $\mathcal{K}$ by successive Legendre transformations of the free energy of the system. We derive a closed set of equations for the fermionic and bosonic self-energies for a given $\mathcal{K}$. We then introduce a local approximation for $\mathcal{K}$, which extends the idea of dynamical mean field theory (DMFT) approaches from two- to three-particle irreducibility. This approximation entails the locality of the three-leg electron-boson vertex $Λ(iω,iΩ)$, which is self-consistently computed using a quantum impurity model with dynamical charge and spin interactions. This local vertex is used to construct frequency- and momentum-dependent electronic self-energies and polarizations. By construction, the method interpolates between the spin-fluctuation or GW approximations at weak coupling and the atomic limit at strong coupling. We apply it to the Hubbard model on two-dimensional square and triangular lattices. We complement the results of Phys.Rev. B 92, 115109 by (i) showing that, at half-filling, as DMFT, the method describes the Fermi-liquid metallic state and the Mott insulator, separated by a first-order interacting-driven Mott transition at low temperatures, (ii) investigating the influence of frustration and (iii) discussing the influence of the bosonic decoupling channel.

cond-mat.str-el↗