Optimization of Algorithmic Errors in Analog Quantum Simulations

• URL: http://arxiv.org/abs/2308.02642v3
• Date: Mon, 22 Apr 2024 17:15:47 GMT
• Title: Optimization of Algorithmic Errors in Analog Quantum Simulations
• Authors: Nikita A. Zemlevskiy, Henry F. Froland, Stephan Caspar,
• Abstract summary: This paper examines the interplay of errors arising from simulation of approximate time evolution with those due to practical, real-world device constraints. Errors are studied in Heisenberg-type systems on analog quantum devices described by the Ising Hamiltonian.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Analog quantum simulation is emerging as a powerful tool for uncovering classically unreachable physics such as many-body real-time dynamics. A complete quantification of uncertainties is necessary in order to make precise predictions using simulations on modern-day devices. Therefore, the inherent physical limitations of the device on the parameters of the simulation must be understood. This analysis examines the interplay of errors arising from simulation of approximate time evolution with those due to practical, real-world device constraints. These errors are studied in Heisenberg-type systems on analog quantum devices described by the Ising Hamiltonian. A general framework for quantifying these errors is introduced and applied to several proposed time evolution methods, including Trotter-like methods and Floquet-engineered constant-field approaches. The limitations placed on the accuracy of time evolution methods by current devices are discussed. Characterization of the scaling of coherent effects of different error sources provides a way to extend the presented Hamiltonian engineering methods to take advantage of forthcoming device capabilities.

Related papers

• Error Interference in Quantum Simulation [10.119306277142051]
  We introduce a novel method that directly estimates the long-time algorithmic errors with multiple segments. We identify the sufficient and necessary condition for strict error interference and introduce the concept of approximate error interference. Our work demonstrates significant improvements over prior ones and opens new avenues for error analysis in quantum simulation.
  arXiv  Detail & Related papers  (2024-11-05T16:53:22Z)
• Quantum Tunneling: From Theory to Error-Mitigated Quantum Simulation [49.1574468325115]
  This study presents the theoretical background and the hardware aware circuit implementation of a quantum tunneling simulation. We use error mitigation techniques (ZNE and REM) and multiprogramming of the quantum chip for solving the hardware under-utilization problem.
  arXiv  Detail & Related papers  (2024-04-10T14:27:07Z)
• Improved Accuracy for Trotter Simulations Using Chebyshev Interpolation [0.5729426778193399]
  We show how errors due to Trotterized time evolution can be mitigated through the use of algorithmic techniques. Our approach is to extrapolate to zero Trotter step size, akin to zero-noise extrapolation techniques for mitigating hardware errors.
  arXiv  Detail & Related papers  (2022-12-29T01:21:26Z)
• 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)
• Propagation of errors and quantitative quantum simulation with quantum advantage [0.0]
  Many-body quench dynamics is one of the most promising candidates for early practical quantum advantage. We analyse the requirements for quantitatively reliable quantum simulation beyond the capabilities of existing classical methods. We conclude for models that are directly implementable that regimes of practical quantum advantage are attained in current experiments with analogue simulators.
  arXiv  Detail & Related papers  (2022-04-28T17:05:51Z)
• Fermionic approach to variational quantum simulation of Kitaev spin models [50.92854230325576]
  Kitaev spin models are well known for being exactly solvable in a certain parameter regime via a mapping to free fermions. We use classical simulations to explore a novel variational ansatz that takes advantage of this fermionic representation. We also comment on the implications of our results for simulating non-Abelian anyons on quantum computers.
  arXiv  Detail & Related papers  (2022-04-11T18:00:01Z)
• Hybridized Methods for Quantum Simulation in the Interaction Picture [69.02115180674885]
  We provide a framework that allows different simulation methods to be hybridized and thereby improve performance for interaction picture simulations. Physical applications of these hybridized methods yield a gate complexity scaling as $log2 Lambda$ in the electric cutoff. For the general problem of Hamiltonian simulation subject to dynamical constraints, these methods yield a query complexity independent of the penalty parameter $lambda$ used to impose an energy cost.
  arXiv  Detail & Related papers  (2021-09-07T20:01:22Z)
• 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)
• Error Bounds for Variational Quantum Time Evolution [4.38301148531795]
  Variational quantum time evolution allows us to simulate the time dynamics of quantum systems with near-term compatible quantum circuits. Due to the variational nature of this method the accuracy of the simulation is a priori unknown. We derive global phase error bounds for the state simulation accuracy with variational quantum time evolution.
  arXiv  Detail & Related papers  (2021-07-30T18:00:25Z)
• Quantum-tailored machine-learning characterization of a superconducting qubit [50.591267188664666]
  We develop an approach to characterize the dynamics of a quantum device and learn device parameters. This approach outperforms physics-agnostic recurrent neural networks trained on numerically generated and experimental data. This demonstration shows how leveraging domain knowledge improves the accuracy and efficiency of this characterization task.
  arXiv  Detail & Related papers  (2021-06-24T15:58:57Z)
• Benchmarking a novel efficient numerical method for localized 1D Fermi-Hubbard systems on a quantum simulator [0.0]
  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.
  arXiv  Detail & Related papers  (2021-05-13T16:03:11Z)

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.