arXiv subjects

Xavier Waintal

Publications and source records attributed to Xavier Waintal.

At least 37 records · Page 2Linked to original sources

arXiv2024

Opening the Black Box Inside Grover's Algorithm

Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal scaling of the quadratic speedup guaranteed by the algorithm. Grover's algorithm also requires exponentially many calls to the quantum oracle to succeed (about $\sqrt{2^n}$ calls for $n$ qubits), raising the question of its implementation on both noisy and error-corrected quantum computers. In this work, we construct a quantum-inspired algorithm, executable on a classical computer, that performs Grover's task in a linear number of calls to (simulations of) the oracle - an exponentially smaller number than Grover's algorithm - and demonstrate this algorithm explicitly for Boolean satisfiability problems. The complexity of our algorithm depends on the cost to simulate the oracle once which may or may not be exponential. Indeed, Grover's algorithm does not have an a priori quantum speedup as soon as one is given access to the "source code" of the oracle. Our findings illustrate this point explicitly as our algorithm exploits the structure of the quantum circuit used to program the quantum computer to speed up the search. There remain problems where Grover's algorithm would provide an asymptotic speedup if it could be run accurately for large enough sizes. Our quantum-inspired algorithm provides lower bounds, in terms of circuit complexity, for quantum hardware to beat classical approaches for these problems. These estimates, combined with the unfavorable scaling of the success probability of Grover's algorithm - which in the presence of noise decays as a double exponential in the number of qubits - makes a practical speedup unrealistic even under extremely optimistic assumptions of the evolution of both hardware quality and availability.

quant-ph↗

arXiv2024

Matrix product states and first quantization

Common wisdom says that the entanglement of fermionic systems can be low in the second quantization formalism but is extremely large in the first quantization. Hence Matrix Product State (MPS) methods based on moderate entanglement have been overwhelmingly formulated in second quantization. Here we introduce a first-quantized MPS approach to simulate quantum many-body systems. We show that by reformulating the way the fermionic anti-symmetry is handled, we arrive at MPS with a level of entanglement comparable to the usual one found in second quantization. We demonstrate our scheme on the one-dimensional $t$-$V$ model (spinless fermions with nearest neighbour density-density interaction) for both ground state and time evolution. For time evolution, we find that the entanglement entropy in first quantization is significantly smaller than in its second quantization counterpart.

quant-ph↗

arXiv2024

Quantics Tensor Cross Interpolation for High-Resolution, Parsimonious Representations of Multivariate Functions in Physics and Beyond

Multivariate functions of continuous variables arise in countless branches of science. Numerical computations with such functions typically involve a compromise between two contrary desiderata: accurate resolution of the functional dependence, versus parsimonious memory usage. Recently, two promising strategies have emerged for satisfying both requirements: (i) The quantics representation, which expresses functions as multi-index tensors, with each index representing one bit of a binary encoding of one of the variables; and (ii) tensor cross interpolation (TCI), which, if applicable, yields parsimonious interpolations for multi-index tensors. Here, we present a strategy, quantics TCI (QTCI), which combines the advantages of both schemes. We illustrate its potential with an application from condensed matter physics: the computation of Brillouin zone integrals.

physics.comp-ph↗

arXiv2024

Cross-extrapolation reconstruction of low-rank functions and application to quantum many-body observables in the strong coupling regime

We present a general-purpose algorithm to extrapolate a low rank function of two variables from a small domain to a larger one. It is based on the cross-interpolation formula. We apply it to reconstruct physical quantities in some quantum many-body perturbative expansions in the real time Keldysh formalism, considered as a function of time $t$ and interaction $U$. These functions are of remarkably low rank. This property, combined with the convergence of the perturbative expansion in $U$ both at finite $t$ (for any $U$), and small $U$ (for any $t$), is sufficient for our algorithm to reconstruct the physical quantity at long time, strong coupling regime. Our method constitutes an alternative to standard resummation techniques in perturbative methods, such as diagrammatic Quantum Monte Carlo. We benchmark it on the single impurity Anderson model and show that it is successful even in some regime where standard conformal mapping resummation techniques fail.

cond-mat.str-el↗

arXiv2023

The Quantum House Of Cards

Quantum computers have been proposed to solve a number of important problems such as discovering new drugs, new catalysts for fertilizer production, breaking encryption protocols, optimizing financial portfolios, or implementing new artificial intelligence applications. Yet, to date, a simple task such as multiplying 3 by 5 is beyond existing quantum hardware. This article examines the difficulties that would need to be solved for quantum computers to live up to their promises. I discuss the whole stack of technologies that has been envisioned to build a quantum computer from the top layers (the actual algorithms and associated applications) down to the very bottom ones (the quantum hardware, its control electronics, cryogeny, etc.) while not forgetting the crucial intermediate layer of quantum error correction.

quant-ph↗

arXiv2023

Reconstructing the potential configuration in a high-mobility semiconductor heterostructure with scanning gate microscopy

The weak disorder potential seen by the electrons of a two-dimensional electron gas in high-mobility semiconductor heterostructures leads to fluctuations in the physical properties and can be an issue for nanodevices. In this paper, we show that a scanning gate microscopy (SGM) image contains information about the disorder potential, and that a machine learning approach based on SGM data can be used to determine the disorder. We reconstruct the electric potential of a sample from its experimental SGM data and validate the result through an estimate of its accuracy.

cond-mat.mes-hall↗

arXiv2022

Unveiling the charge distribution of a GaAs-based nanoelectronic device: A large experimental data-set approach

In quantum nanoelectronics, numerical simulations have become an ubiquitous tool. Yet the comparison with experiments is often done at a qualitative level or restricted to a single device with a handful of fitting parameters. In this work, we assess the predictive power of these simulations by comparing the results of a single model with a large experimental data set of 110 devices with 48 different geometries. The devices are quantum point contacts of various shapes and sizes made with electrostatic gates deposited on top of a high mobility GaAs/GaAlAs two dimensional electron gas. We study the pinch-off voltages applied on the gates to deplete the two-dimensional electron gas in various spatial positions. We argue that the pinch-off voltages are a very robust signature of the charge distribution in the device. The large experimental data set allows us to critically review the modeling and arrive at a robust one-parameter model that can be calibrated in situ, a crucial step for making predictive simulations.

cond-mat.mes-hall↗

arXiv2022

Coulomb-mediated antibunching of an electron pair surfing on sound

Electron flying qubits are envisioned as potential information link within a quantum computer, but also promise -- alike photonic approaches -- a self-standing quantum processing unit. In contrast to its photonic counterpart, electron-quantum-optics implementations are subject to Coulomb interaction, which provide a direct route to entangle the orbital or spin degree of freedom. However, the controlled interaction of flying electrons at the single particle level has not yet been established experimentally. Here we report antibunching of a pair of single electrons that is synchronously shuttled through a circuit of coupled quantum rails by means of a surface acoustic wave. The in-flight partitioning process exhibits a reciprocal gating effect which allows us to ascribe the observed repulsion predominantly to Coulomb interaction. Our single-shot experiment marks an important milestone on the route to realise a controlled-phase gate for in-flight quantum manipulations.

cond-mat.mes-hall↗

arXiv2022

Learning Feynman Diagrams with Tensor Trains

We use tensor network techniques to obtain high order perturbative diagrammatic expansions for the quantum many-body problem at very high precision. The approach is based on a tensor train parsimonious representation of the sum of all Feynman diagrams, obtained in a controlled and accurate way with the tensor cross interpolation algorithm. It yields the full time evolution of physical quantities in the presence of any arbitrary time dependent interaction. Our benchmarks on the Anderson quantum impurity problem, within the real time non-equilibrium Schwinger-Keldysh formalism, demonstrate that this technique supersedes diagrammatic Quantum Monte Carlo by orders of magnitude in precision and speed, with convergence rates $1/N^2$ or faster, where N is the number of function evaluations. The method also works in parameter regimes characterized by strongly oscillatory integrals in high dimension, which suffer from a catastrophic sign problem in Quantum Monte-Carlo. Finally, we also present two exploratory studies showing that the technique generalizes to more complex situations: a double quantum dot and a single impurity embedded in a two dimensional lattice.

cond-mat.str-el↗

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

Semiconductor-based electron flying qubits: Review on recent progress accelerated by numerical modelling

The progress of charge manipulation in semiconductor-based nanoscale devices opened up a novel route to realise a flying qubit with a single electron. In the present review, we introduce the concept of these electron flying qubits, discuss their most promising realisations and show how numerical simulations are applicable to accelerate experimental development cycles. Addressing the technological challenges of flying qubits that are currently faced by academia and quantum enterprises, we underline the relevance of interdisciplinary cooperation to move emerging quantum industry forward. The review consists of two main sections: Pathways towards the electron flying qubit: We address three routes of single-electron transport in GaAs-based devices focusing on surface acoustic waves, hot-electron emission from quantum dot pumps and Levitons. For each approach, we discuss latest experimental results and point out how numerical simulations facilitate engineering the electron flying qubit. Numerical modelling of quantum devices: We review the full stack of numerical simulations needed for fabrication of the flying qubits. Choosing appropriate models, examples of basic quantum mechanical simulations are explained in detail. We discuss applications of open-source (KWANT) and the commercial (nextnano) platforms for modelling the flying qubits. The discussion points out the large relevance of software tools to design quantum devices tailored for efficient operation.

cond-mat.mes-hall↗

arXiv2022

Low-symmetry topological materials for large charge-to-spin interconversion: The case of transition metal dichalcogenide monolayers

The spin polarization induced by the spin Hall effect (SHE) in thin films typically points out of the plane. This is rooted on the specific symmetries of traditionally studied systems, not in a fundamental constraint. Recently, experiments on few-layer ${\rm MoTe}_2$ and ${\rm WTe}_2$ showed that the reduced symmetry of these strong spin-orbit coupling materials enables a new form of {\it canted} spin Hall effect, characterized by concurrent in-plane and out-of-plane spin polarizations. Here, through quantum transport calculations on realistic device geometries, including disorder, we predict a very large gate-tunable SHE figure of merit $λ_sθ_{xy}\sim 1\text{--}50$ nm in ${\rm MoTe}_2$ and ${\rm WTe}_2$ monolayers that significantly exceeds values of conventional SHE materials. This stems from a concurrent long spin diffusion length ($λ_s$) and charge-to-spin interconversion efficiency as large as $θ_{xy} \approx 80$\%, originating from momentum-invariant (persistent) spin textures together with large spin Berry curvature along the Fermi contour, respectively. Generalization to other materials and specific guidelines for unambiguous experimental confirmation are proposed, paving the way towards exploiting such phenomena in spintronic devices. These findings vividly emphasize how crystal symmetry and electronic topology can govern the intrinsic SHE and spin relaxation, and how they may be exploited to broaden the range and efficiency of spintronic materials and functionalities.

cond-mat.mes-hall↗

arXiv2021

Tkwant: a software package for time-dependent quantum transport

Tkwant is a Python package for the simulation of quantum nanoelectronics devices to which external time-dependent perturbations are applied. Tkwant is an extension of the Kwant package (https://kwant-project.org/) and can handle the same types of systems: discrete tight-binding-like models that consist of an arbitrary central region connected to semi-infinite electrodes. The problem is genuinely many-body even in the absence of interactions and is treated within the non-equilibrium Keldysh formalism. Examples of Tkwant applications include the propagation of plasmons generated by voltage pulses, propagation of excitations in the quantum Hall regime, spectroscopy of Majorana fermions in semiconducting nanowires, current-induced skyrmion motion in spintronic devices, multiple Andreev reflection, Floquet topological insulators, thermoelectric effects, and more. The code has been designed to be easy to use and modular. Tkwant is free software distributed under a BSD license and can be found at https://tkwant.kwant-project.org/.

cond-mat.mes-hall↗

arXiv2020

Quantum Quasi-Monte Carlo algorithm for out-of-equilibrium Green functions at long times

We extend the recently developed Quantum Quasi-Monte Carlo (QQMC) approach to obtain the full frequency dependence of Green functions in a single calculation. QQMC is a general approach for calculating high-order perturbative expansions in power of the electron-electron interaction strength. In contrast to conventional Markov chain Monte Carlo sampling, QQMC uses low-discrepancy sequences for a more uniform sampling of the multi-dimensional integrals involved and can potentially outperform Monte Carlo by several orders of magnitudes. A core concept of QQMC is the a priori construction of a "model function" that approximates the integrand and is used to optimize the sampling distribution. In this paper, we show that the model function concept extends to a kernel approach for the computation of Green functions. We illustrate the approach on the Anderson impurity model and show that the scaling of the error with the number of integrand evaluations $N$ is $\sim 1/N^{0.86}$ in the best cases, and comparable to Monte Carlo scaling $\sim 1/N^{0.5}$ in the worst cases. We find a systematic improvement over Monte Carlo sampling by at least two orders of magnitude while using a basic form of model function. Finally, we compare QQMC results with calculations performed with the Fork Tensor Product State (FTPS) method, a recently developed tensor network approach for solving impurity problems. Applying a simple Padé approximant for the series resummation, we find that QQMC matches the FTPS results beyond the perturbative regime.

cond-mat.str-el↗

arXiv2020

Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions

High order perturbation theory has seen an unexpected recent revival for controlled calculations of quantum many-body systems, even at strong coupling. We adapt integration methods using low-discrepancy sequences to this problem. They greatly outperform state-of-the-art diagrammatic Monte Carlo. In practical applications, we show speed-ups of several orders of magnitude with scaling as fast as $1/N$ in sample number $N$; parametrically faster than $1/\sqrt{N}$ in Monte Carlo. We illustrate our technique with a solution of the Kondo ridge in quantum dots, where it allows large parameter sweeps.

cond-mat.str-el↗

arXiv2020

Measurement of the Spin Absorption Anisotropy in Lateral Spin Valves

The spin absorption process in a ferromagnetic material depends on the spin orientation relativelyto the magnetization. Using a ferromagnet to absorb the pure spin current created within a lateralspin-valve, we evidence and quantify a sizeable orientation dependence of the spin absorption inCo, CoFe and NiFe. These experiments allow determining the spin-mixing conductance, an elusivebut fundamental parameter of the spin-dependent transport. We show that the obtained valuescannot be understood within a model considering only the Larmor, transverse decoherence and spindiffusion lengths, and rather suggest that the spin-mixing conductance is actually limited by theSharvin conductance.

cond-mat.mtrl-sci↗

arXiv2020

Canted Spin Texture and Quantum Spin Hall Effect in WTe2

We report an unconventional quantum spin Hall phase in the monolayer T$_\text{d}$-WTe$_2$, which exhibits hitherto unknown features in other topological materials. The low-symmetry of the structure induces a canted spin texture in the $yz$ plane, which dictates the spin polarization of topologically protected boundary states. Additionally, the spin Hall conductivity gets quantized ($2e^2/h$) with a spin quantization axis parallel to the canting direction. These findings are based on large-scale quantum simulations of the spin Hall conductivity tensor and nonlocal resistances in multi-probe geometries using a realistic tight-binding model elaborated from first-principle methods. The observation of this canted quantum spin Hall effect, related to the formation of topological edge states with nontrivial spin polarization, demands for specific experimental design and suggests interesting alternatives for manipulating spin information in topological materials.

cond-mat.mes-hall↗

arXiv2020

Nonlocal Spin Dynamics in the Crossover from Diffusive to Ballistic Transport

Improved fabrication techniques have enabled the possibility of ballistic transport and unprecedented spin manipulation in ultraclean graphene devices. Spin transport in graphene is typically probed in a nonlocal spin valve and is analyzed using spin diffusion theory, but this theory is not necessarily applicable when charge transport becomes ballistic or when the spin diffusion length is exceptionally long. Here, we study these regimes by performing quantum simulations of graphene nonlocal spin valves. We find that conventional spin diffusion theory fails to capture the crossover to the ballistic regime as well as the limit of long spin diffusion length. We show that the latter can be described by an extension of the current theoretical framework. Finally, by covering the whole range of spin dynamics, our study opens a new perspective to predict and scrutinize spin transport in graphene and other two-dimensional material-based ultraclean devices.

cond-mat.mes-hall↗