Exponential speedup in quantum simulation of Kogut-Susskind Hamiltonian via orbifold lattice

• URL: http://arxiv.org/abs/2506.00755v1
• Date: Sat, 31 May 2025 23:50:27 GMT
• Title: Exponential speedup in quantum simulation of Kogut-Susskind Hamiltonian via orbifold lattice
• Authors: Georg Bergner, Masanori Hanada,
• Abstract summary: We show that the orbifold lattice Hamiltonian can reproduce the Kogut-Susskind Hamiltonian in a controlled limit.<n>This reformulation resolves longstanding technical obstacles and offers a straightforward implementation protocol for digital quantum simulation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We demonstrate that the orbifold lattice Hamiltonian -- an approach known for its efficiency in simulating SU($N$) Yang-Mills theory and QCD on digital quantum computers -- can reproduce the Kogut-Susskind Hamiltonian in a controlled limit. While the original Kogut-Susskind approach faces significant implementation challenges on quantum hardware, we show that it emerges naturally as the infinite scalar mass limit of the orbifold lattice formulation, even at finite lattice spacing. Our analysis provides both a general analytical framework applicable to SU($N$) gauge theories in arbitrary dimensions and specific numerical evidence for $(2+1)$-dimensional SU($N$) Yang-Mills theories ($N=2,3$). Using Euclidean path integral methods, we quantify the convergence rate by comparing the standard Wilson action with the orbifold lattice action, matching lattice parameters, and systematically extrapolating results as the bare scalar mass approaches infinity. This reformulation resolves longstanding technical obstacles and offers a straightforward implementation protocol for digital quantum simulation of the Kogut-Susskind Hamiltonian with exponential speedup compared to classical methods and previously known quantum methods.

Related papers

• Grassmann Variational Monte Carlo with neural wave functions [45.935798913942904]
  We formalize the framework introduced by Pfau et al.citepfau2024accurate in terms of Grassmann geometry of the Hilbert space.<n>We validate our approach on the Heisenberg quantum spin model on the square lattice, achieving highly accurate energies and physical observables for a large number of excited states.
  arXiv  Detail & Related papers  (2025-07-14T13:53:13Z)
• Universal framework with exponential speedup for the quantum simulation of quantum field theories including QCD [0.0]
  We present a quantum simulation framework universally applicable to a wide class of quantum systems.<n>Specifically, we generalize an efficient quantum simulation protocol developed for bosonic theories.<n>Our protocols do not assume oracles, but rather present explicit constructions with rigorous resource estimations.
  arXiv  Detail & Related papers  (2025-06-23T18:00:00Z)
• Variational Quantum Simulation of Anyonic Chains [0.0]
  Anyonic chains provide lattice realizations of a rich set of quantum field theories in two space-time dimensions.<n>The described quantum simulation scheme provides a systematic approach to give rise to a large family of quantum field theories.
  arXiv  Detail & Related papers  (2024-12-23T18:39:28Z)
• Quantum tomography of helicity states for general scattering processes [55.2480439325792]
  Quantum tomography has become an indispensable tool in order to compute the density matrix $rho$ of quantum systems in Physics. We present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process.
  arXiv  Detail & Related papers  (2023-10-16T21:23:42Z)
• Scalable, ab initio protocol for quantum simulating SU($N$)$\times$U(1) Lattice Gauge Theories [0.0]
  We propose a protocol for the scalable quantum simulation of SU($N$)$times$U(1) lattice gauge theories with alkaline-earth like atoms in optical lattices in both one- and two-dimensional systems. The protocol exploits the combination of naturally occurring SU($N$) pseudo-spin symmetry and strong inter-orbital interactions that is unique to such atomic species.
  arXiv  Detail & Related papers  (2023-10-12T18:09:21Z)
• Quantum and classical spin network algorithms for $q$-deformed Kogut-Susskind gauge theories [0.0]
  We introduce $q$-deformed Kogut-Susskind lattice gauge theories, obtained by deforming the defining symmetry algebra to a quantum group. Our proposal simultaneously provides a controlled regularization of the infinite-dimensional local Hilbert space while preserving essential symmetry-related properties. Our work gives a new perspective for the application of tensor network methods to high-energy physics.
  arXiv  Detail & Related papers  (2023-04-05T15:49:20Z)
• 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)
• Analyzing Prospects for Quantum Advantage in Topological Data Analysis [35.423446067065576]
  We analyze and optimize an improved quantum algorithm for topological data analysis. We show that super-quadratic quantum speedups are only possible when targeting a multiplicative error approximation. We argue that quantum circuits with tens of billions of Toffoli can solve seemingly classically intractable instances.
  arXiv  Detail & Related papers  (2022-09-27T17:56:15Z)
• 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)
• Quantum algorithms for grid-based variational time evolution [36.136619420474766]
  We propose a variational quantum algorithm for performing quantum dynamics in first quantization. Our simulations exhibit the previously observed numerical instabilities of variational time propagation approaches.
  arXiv  Detail & Related papers  (2022-03-04T19:00:45Z)
• Two-dimensional $\mathbb{Z}_2$ lattice gauge theory on a near-term quantum simulator: variational quantum optimization, confinement, and topological order [0.0]
  We propose an implementation of a two-dimensional $mathbbZ$ lattice gauge theory model on a shallow quantum circuit. The ground state preparation is numerically analyzed on a small lattice with a variational quantum algorithm. Our work shows that variational quantum algorithms provide a useful technique to be added in the growing toolbox for digital simulations of lattice gauge theories.
  arXiv  Detail & Related papers  (2021-12-22T10:45:33Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Quantum simulation of gauge theory via orbifold lattice [47.28069960496992]
  We propose a new framework for simulating $textU(k)$ Yang-Mills theory on a universal quantum computer. We discuss the application of our constructions to computing static properties and real-time dynamics of Yang-Mills theories.
  arXiv  Detail & Related papers  (2020-11-12T18:49:11Z)
• Search for Efficient Formulations for Hamiltonian Simulation of non-Abelian Lattice Gauge Theories [0.0]
  Hamiltonian formulation of lattice gauge theories (LGTs) is the most natural framework for the purpose of quantum simulation. It remains an important task to identify the most accurate, while computationally economic, Hamiltonian formulation(s) in such theories. This paper is a first step toward addressing this question in the case of non-Abelian LGTs.
  arXiv  Detail & Related papers  (2020-09-24T16:44:39Z)

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.