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

• URL: http://arxiv.org/abs/2405.10416v2
• Date: Tue, 07 Jan 2025 17:13:39 GMT
• Title: Exponential improvements in the simulation of lattice gauge theories using near-optimal techniques
• Authors: Mason L. Rhodes, Michael Kreshchuk, Shivesh Pathak,
• Abstract summary: We provide explicit circuit constructions as well as T-gate counts and logical qubit counts for Hamiltonian simulation.<n>We find up to 25 orders of magnitude reduction in space-time volume over Trotter methods for simulations of non-Abelian lattice gauge theories.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We report a first-of-its-kind analysis on post-Trotter simulation of U(1), SU(2) and SU(3) lattice gauge theories including fermions in arbitrary spatial dimension. We provide explicit circuit constructions as well as T-gate counts and logical qubit counts for Hamiltonian simulation. We find up to 25 orders of magnitude reduction in space-time volume over Trotter methods for simulations of non-Abelian lattice gauge theories relevant to the standard model. This improvement results from our algorithm having polynomial scaling with the number of colors in the gauge theory, achieved by utilizing oracle constructions relying on the sparsity of physical operators, in contrast to the exponential scaling seen in state-of-the-art Trotter methods which employ explicit mappings onto Pauli operators. Our work demonstrates that the use of advanced algorithmic techniques leads to dramatic reductions in the cost of simulating fundamental interactions, bringing it in step with resources required for first principles quantum simulation of chemistry.

Related papers

• Hamiltonian Lattice Gauge Theories: emergent properties from Tensor Network methods [0.0]
  This thesis develops advanced Network (TN) methods to address Hamiltonian Lattice Theories (LGTs) A novel dressed-site formalism is introduced, enabling efficient truncation of gauge fields. These advances open current and future development pathways toward optimized, efficient, and faster simulations on scales comparable to Monte Carlo state-of-the-art.
  arXiv  Detail & Related papers  (2025-01-19T17:09:57Z)
• Parallel simulation for sampling under isoperimetry and score-based diffusion models [56.39904484784127]
  As data size grows, reducing the iteration cost becomes an important goal. Inspired by the success of the parallel simulation of the initial value problem in scientific computation, we propose parallel Picard methods for sampling tasks. Our work highlights the potential advantages of simulation methods in scientific computation for dynamics-based sampling and diffusion models.
  arXiv  Detail & Related papers  (2024-12-10T11:50:46Z)
• 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)
• Strategies for simulating time evolution of Hamiltonian lattice field theories [0.0]
  Simulating the time evolution of quantum field theories given some Hamiltonian $H$ requires developing algorithms for implementing the unitary operator e-iHt. Some techniques exist that promise better scaling in certain parameters of the theory being simulated, the most efficient of which are based on the concept of block encoding. We derive and compare the gate complexities of several commonly used simulation techniques in application to Hamiltonian Lattice Field Theories.
  arXiv  Detail & Related papers  (2023-12-18T19:00:07Z)
• 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)
• Normalizing flows for lattice gauge theory in arbitrary space-time dimension [135.04925500053622]
  Applications of normalizing flows to the sampling of field configurations in lattice gauge theory have so far been explored almost exclusively in two space-time dimensions. We discuss masked autoregressive with tractable and unbiased Jacobian determinants, a key ingredient for scalable and exact flow-based sampling algorithms. For concreteness, results from a proof-of-principle application to SU(3) gauge theory in four space-time dimensions are reported.
  arXiv  Detail & Related papers  (2023-05-03T19:54:04Z)
• 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)
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory [44.99833362998488]
  We introduce quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple quantum numbers. The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions. The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories.
  arXiv  Detail & Related papers  (2022-12-28T18:56:25Z)
• Aspects of scaling and scalability for flow-based sampling of lattice QCD [137.23107300589385]
  Recent applications of machine-learned normalizing flows to sampling in lattice field theory suggest that such methods may be able to mitigate critical slowing down and topological freezing. It remains to be determined whether they can be applied to state-of-the-art lattice quantum chromodynamics calculations.
  arXiv  Detail & Related papers  (2022-11-14T17:07:37Z)
• Measurement-based quantum simulation of Abelian lattice gauge theories [0.0]
  We show that sequential single-qubit measurements with the bases adapted according to the former measurement outcomes induce a deterministic Hamiltonian quantum simulation of the gauge theory on the boundary. We demonstrate that the generalized cluster state has a symmetry-protected topological order with respect to generalized global symmetries.
  arXiv  Detail & Related papers  (2022-10-19T22:14:45Z)
• 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)
• Gauge-equivariant flow models for sampling in lattice field theories with pseudofermions [51.52945471576731]
  This work presents gauge-equivariant architectures for flow-based sampling in fermionic lattice field theories using pseudofermions as estimators for the fermionic determinant. This is the default approach in state-of-the-art lattice field theory calculations, making this development critical to the practical application of flow models to theories such as QCD.
  arXiv  Detail & Related papers  (2022-07-18T21:13:34Z)
• Efficient simulation of Gottesman-Kitaev-Preskill states with Gaussian circuits [68.8204255655161]
  We study the classical simulatability of Gottesman-Kitaev-Preskill (GKP) states in combination with arbitrary displacements, a large set of symplectic operations and homodyne measurements. For these types of circuits, neither continuous-variable theorems based on the non-negativity of quasi-probability distributions nor discrete-variable theorems can be employed to assess the simulatability.
  arXiv  Detail & Related papers  (2022-03-21T17:57:02Z)
• 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.