Benchmarking a novel efficient numerical method for localized 1D Fermi-Hubbard systems on a quantum simulator

• URL: http://arxiv.org/abs/2105.06372v2
• Date: Mon, 8 Nov 2021 19:07:36 GMT
• Title: Benchmarking a novel efficient numerical method for localized 1D Fermi-Hubbard systems on a quantum simulator
• Authors: Bharath Hebbe Madhusudhana, Sebastian Scherg, Thomas Kohlert, Immanuel Bloch, Monika Aidelsburger
• Abstract summary: We show that a quantum simulator can be used to in-effect solve for the dynamics of a many-body system. We use a neutral-atom Fermi-Hubbard quantum simulator with $L_textexpsimeq290$ lattice sites to benchmark its performance. We derive a simple prediction of the behaviour of interacting Bloch oscillations for spin-imbalanced Fermi-Hubbard systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum simulators have made a remarkable progress towards exploring the dynamics of many-body systems, many of which offer a formidable challenge to both theoretical and numerical methods. While state-of-the-art quantum simulators are in principle able to simulate quantum dynamics well outside the domain of classical computers, they are noisy and limited in the variability of the initial state of the dynamics and the observables that can be measured. Despite these limitations, here we show that such a quantum simulator can be used to in-effect solve for the dynamics of a many-body system. We develop an efficient numerical technique that facilitates classical simulations in regimes not accessible to exact calculations or other established numerical techniques. The method is based on approximations that are well suited to describe localized one-dimensional Fermi-Hubbard systems. Since this new method does not have an error estimate and the approximations do not hold in general, we use a neutral-atom Fermi-Hubbard quantum simulator with $L_{\text{exp}}\simeq290$ lattice sites to benchmark its performance in terms of accuracy and convergence for evolution times up to $700$ tunnelling times. We then use these approximations in order to derive a simple prediction of the behaviour of interacting Bloch oscillations for spin-imbalanced Fermi-Hubbard systems, which we show to be in quantitative agreement with experimental results. Finally, we demonstrate that the convergence of our method is the slowest when the entanglement depth developed in the many-body system we consider is neither too small nor too large. This represents a promising regime for near-term applications of quantum simulators.

Related papers

• Coherent-State Ladder Time-Dependent Variational Principle for Open Quantum Systems [0.0]
  We present a new paradigm for the dynamical simulation of interacting bosonic systems. The method relies on a variational ansatz for the $n$-boson density matrix, in terms of a superposition of photon-added coherent states. We test our method on several examples, demonstrating its potential application to the predictive simulation of interacting bosonic systems and cat qubits.
  arXiv  Detail & Related papers  (2023-06-23T18:00:00Z)
• Towards Neural Variational Monte Carlo That Scales Linearly with System Size [67.09349921751341]
  Quantum many-body problems are central to demystifying some exotic quantum phenomena, e.g., high-temperature superconductors. The combination of neural networks (NN) for representing quantum states, and the Variational Monte Carlo (VMC) algorithm, has been shown to be a promising method for solving such problems. We propose a NN architecture called Vector-Quantized Neural Quantum States (VQ-NQS) that utilizes vector-quantization techniques to leverage redundancies in the local-energy calculations of the VMC algorithm.
  arXiv  Detail & Related papers  (2022-12-21T19:00:04Z)
• Quantum emulation of the transient dynamics in the multistate Landau-Zener model [50.591267188664666]
  We study the transient dynamics in the multistate Landau-Zener model as a function of the Landau-Zener velocity. Our experiments pave the way for more complex simulations with qubits coupled to an engineered bosonic mode spectrum.
  arXiv  Detail & Related papers  (2022-11-26T15:04:11Z)
• Efficiently Extracting Multi-Point Correlations of a Floquet Thermalized System [9.824488596665613]
  Nonequilibrium dynamics of many-body systems is challenging for classical computing. Our work paves the way towards practical quantum advantage in simulating Floquet dynamics of many-body systems.
  arXiv  Detail & Related papers  (2022-10-16T14:55:49Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• Benchmarking Quantum Simulators using Ergodic Quantum Dynamics [4.2392660892009255]
  We analyze a sample-efficient protocol to estimate the fidelity between an experimentally prepared state and an ideal state. We numerically demonstrate our protocol for a variety of quantum simulator platforms.
  arXiv  Detail & Related papers  (2022-05-24T17:18:18Z)
• Digital quantum simulation of non-perturbative dynamics of open systems with orthogonal polynomials [0.0]
  We propose the use of the Time Evolving Density operator with Orthogonal Polynomials Algorithm (TEDOPA) on a quantum computer. We show that exponential scalings of computational resources can potentially be avoided for time-evolution simulations of the systems considered in this work.
  arXiv  Detail & Related papers  (2022-03-28T11:16:33Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Digital-analog quantum simulation of fermionic models [0.0]
  We introduce a digital-analog quantum algorithm to simulate a wide class of fermionic Hamiltonians. These methods allow quantum algorithms to run beyond digital versions via an efficient use of coherence time.
  arXiv  Detail & Related papers  (2021-03-29T15:25:23Z)
• Preparing random states and benchmarking with many-body quantum chaos [48.044162981804526]
  We show how to predict and experimentally observe the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a wider context.
  arXiv  Detail & Related papers  (2021-03-05T08:32:43Z)
• Fast and differentiable simulation of driven quantum systems [58.720142291102135]
  We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods. We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
  arXiv  Detail & Related papers  (2020-12-16T21:43:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.