Exponential improvements in the simulation of lattice gauge theories using near-optimal techniques

• URL: http://arxiv.org/abs/2405.10416v1
• Date: Thu, 16 May 2024 19:36:49 GMT
• Title: Exponential improvements in the simulation of lattice gauge theories using near-optimal techniques
• Authors: Mason Rhodes, Michael Kreshchuk, Shivesh Pathak,
• Abstract summary: We conduct an in-depth analysis of the cost of simulating Abelian and non-Abelian lattice gauge theories. We provide explicit circuit constructions, as well as T-gate counts and qubit counts for the entire simulation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Simulation of quantum systems of a large number of strongly interacting particles persists as one of the most challenging, and computationally demanding, tasks in classical simulation, involving both non-relativistic applications like condensed matter physics and quantum chemistry, as well as relativistic applications like lattice gauge theory simulation. One of the major motivations for building a fault-tolerant quantum computer is the efficient simulation of many-body systems on such a device. While significant developments have been made in the quantum simulation of non-relativistic systems, the simulation of lattice gauge theories has lagged behind, with state-of-the-art Trotterized simulations requiring many orders of magnitude more resources than non-relativistic simulation, in stark contrast to the similar difficulty of these tasks in classical simulation. In this work, we conduct an in-depth analysis of the cost of simulating Abelian and non-Abelian lattice gauge theories in the Kogut-Susskind formulation using simulation methods with near-optimal scaling in system size, evolution time, and error. We provide explicit circuit constructions, as well as T-gate counts and qubit counts for the entire simulation algorithm. This investigation, the first of its kind, leads to up to 25 orders of magnitude improvement over Trotterization in spacetime volume for non-Abelian simulations. Such a dramatic improvement results largely from our algorithm having polynomial scaling with the number of colors, as opposed to exponential scaling in existing approaches. Our work demonstrates that the use of advanced algorithmic techniques leads to dramatic reductions in the cost of ab initio simulations of fundamental interactions, bringing it in step with resources required for first principles quantum simulation of chemistry and condensed matter physics.

Related papers

• Entanglement accelerates quantum simulation [12.442922876322886]
  We show that product-formula approximations can perform better for entangled systems. This shows that entanglement is not only an obstacle to classical simulation, but also a feature that can accelerate quantum algorithms.
  arXiv  Detail & Related papers  (2024-06-04T14:57:21Z)
• TANQ-Sim: Tensorcore Accelerated Noisy Quantum System Simulation via QIR on Perlmutter HPC [16.27167995786167]
  TANQ-Sim is a full-scale density matrix based simulator designed to simulate practical deep circuits with both coherent and non-coherent noise. To address the significant computational cost associated with such simulations, we propose a new density-matrix simulation approach. To optimize performance, we also propose specific gate fusion techniques for density matrix simulation.
  arXiv  Detail & Related papers  (2024-04-19T21:16:29Z)
• 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)
• Lie-algebraic classical simulations for variational quantum computing [0.755972004983746]
  Methods relying on the Lie-algebraic structure of quantum dynamics have received relatively little attention. We present a framework that we call "$mathfrakg$sim", and showcase their efficient implementation in several paradigmatic variational quantum computing tasks. Specifically, we perform Lie-algebraic simulations to train and parametrized quantum circuits, design enhanced parameter strategies, solve tasks of quantum circuit synthesis, and train a quantum-phase synthesis.
  arXiv  Detail & Related papers  (2023-08-02T21:08:18Z)
• Tensor Networks or Decision Diagrams? Guidelines for Classical Quantum Circuit Simulation [65.93830818469833]
  tensor networks and decision diagrams have independently been developed with differing perspectives, terminologies, and backgrounds in mind. We consider how these techniques approach classical quantum circuit simulation, and examine their (dis)similarities with regard to their most applicable abstraction level. We provide guidelines for when to better use tensor networks and when to better use decision diagrams in classical quantum circuit simulation.
  arXiv  Detail & Related papers  (2023-02-13T19:00:00Z)
• Physical Systems Modeled Without Physical Laws [0.0]
  Tree-based machine learning methods can emulate desired outputs without "knowing" the complex backing involved in the simulations. We specifically focus on predicting specific spatial-temporal data between two simulation outputs and increasing spatial resolution to generalize the physics predictions to finer test grids without the computational costs of repeating the numerical calculation.
  arXiv  Detail & Related papers  (2022-07-26T20:51:20Z)
• 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)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• Realistic simulation of quantum computation using unitary and measurement channels [1.406995367117218]
  We introduce a new simulation approach that relies on approximating the density matrix evolution by a sum of unitary and measurement channels. This model shows an improvement of at least one order of magnitude in terms of accuracy compared to the best known approaches.
  arXiv  Detail & Related papers  (2020-05-13T14:29:18Z)
• Simulating nonnative cubic interactions on noisy quantum machines [65.38483184536494]
  We show that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. On noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates.
  arXiv  Detail & Related papers  (2020-04-15T05:16:24Z)
• Efficient classical simulation of random shallow 2D quantum circuits [104.50546079040298]
  Random quantum circuits are commonly viewed as hard to simulate classically. We show that approximate simulation of typical instances is almost as hard as exact simulation. We also conjecture that sufficiently shallow random circuits are efficiently simulable more generally.
  arXiv  Detail & Related papers  (2019-12-31T19:00:00Z)

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.