Efficient Truncations of SU($N_c$) Lattice Gauge Theory for Quantum Simulation

• URL: http://arxiv.org/abs/2503.11888v2
• Date: Fri, 25 Apr 2025 16:51:25 GMT
• Title: Efficient Truncations of SU($N_c$) Lattice Gauge Theory for Quantum Simulation
• Authors: Anthony N. Ciavarella, I. M. Burbano, Christian W. Bauer,
• Abstract summary: lattice gauge theories offer potential to study non-perturbative dynamics of quantum chromodynamics.<n> naive analyses suggest that they require large computational resources.<n>It is shown that the computational resources required for quantum simulation of time evolution generated by these Hamiltonians is 17-19 orders of magnitude smaller than previous approaches.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum simulations of lattice gauge theories offer the potential to directly study the non-perturbative dynamics of quantum chromodynamics, but naive analyses suggest that they require large computational resources. Large $N_c$ expansions are performed to order 1/$N_c$ to simplify the Hamiltonian of pure SU($N_c$) lattice gauge theories. A reformulation of the electric basis is introduced with a truncation strategy based on the construction of local Krylov subspaces with plaquette operators. Numerical simulations show that these truncated Hamiltonians are consistent with traditional lattice calculations at relatively small couplings. It is shown that the computational resources required for quantum simulation of time evolution generated by these Hamiltonians is 17-19 orders of magnitude smaller than previous approaches.

Related papers

• Digital quantum simulation of lattice fermion theories with local encoding [0.0]
  We numerically analyze the feasibility of a platform-neutral, general strategy to perform quantum simulations of fermionic lattice field theories. We observe a timescale separation for spin- and charge-excitations in a spin-$frac12$ Hubbard ladder in the $t-J$ model limit.
  arXiv  Detail & Related papers  (2023-10-23T16:54:49Z)
• A new basis for Hamiltonian SU(2) simulations [0.0]
  We develop a new basis suitable for the simulation of an SU(2) lattice gauge theory in the maximal tree gauge. We show how to perform a Hamiltonian truncation so that the eigenvalues of both the magnetic and electric gauge-fixed Hamiltonian are mostly preserved.
  arXiv  Detail & Related papers  (2023-07-21T18:03:26Z)
• 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)
• Studying chirality imbalance with quantum algorithms [62.997667081978825]
  We employ the (1+1) dimensional Nambu-Jona-Lasinio (NJL) model to study the chiral phase structure and chirality charge density of strongly interacting matter. By performing the Quantum imaginary time evolution (QITE) algorithm, we simulate the (1+1) dimensional NJL model on the lattice at various temperature $T$ and chemical potentials $mu$, $mu_5$.
  arXiv  Detail & Related papers  (2022-10-06T17:12:33Z)
• Preparations for Quantum Simulations of Quantum Chromodynamics in 1+1 Dimensions: (II) Single-Baryon $\beta$-Decay in Real Time [0.0]
  A framework for quantum simulations of real-time weak decays of hadrons and nuclei is presented. A single generation of the Standard Model is found to require 16 qubits per spatial lattice site. Quantum circuits which implement time evolution in this lattice theory are developed and run on Quantinuum's H1-1 20-qubit trapped ion system.
  arXiv  Detail & Related papers  (2022-09-22T04:58:54Z)
• Improved Hamiltonians for Quantum Simulations [8.771066413050963]
  Hamiltonians with improved discretization errors will reduce quantum resources. $mathcalO(a2)$-improved Hamiltonians for pure gauge theories. $bbZ$ gauge theory is presented including exploratory tests using the ibm_perth device.
  arXiv  Detail & Related papers  (2022-03-05T21:59:41Z)
• Variational Adiabatic Gauge Transformation on real quantum hardware for effective low-energy Hamiltonians and accurate diagonalization [68.8204255655161]
  We introduce the Variational Adiabatic Gauge Transformation (VAGT) VAGT is a non-perturbative hybrid quantum algorithm that can use nowadays quantum computers to learn the variational parameters of the unitary circuit. The accuracy of VAGT is tested trough numerical simulations, as well as simulations on Rigetti and IonQ quantum computers.
  arXiv  Detail & Related papers  (2021-11-16T20:50:08Z)
• 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)
• Efficient construction of tensor-network representations of many-body Gaussian states [59.94347858883343]
  We present a procedure to construct tensor-network representations of many-body Gaussian states efficiently and with a controllable error. These states include the ground and thermal states of bosonic and fermionic quadratic Hamiltonians, which are essential in the study of quantum many-body systems.
  arXiv  Detail & Related papers  (2020-08-12T11:30:23Z)
• State preparation and measurement in a quantum simulation of the O(3) sigma model [65.01359242860215]
  We show that fixed points of the non-linear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. We apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes. We present and analyze a quantum algorithm based on non-unitary randomized simulation methods.
  arXiv  Detail & Related papers  (2020-06-28T23:44:12Z)
• Toward scalable simulations of Lattice Gauge Theories on quantum computers [0.0]
  We provide a resource for simulations of real-time dynamics in lattice gauge theories on arbitrary dimensions. We study the phenomena of flux-string breaking up to a genuine bi-dimensional model using classical quantum circuits.
  arXiv  Detail & Related papers  (2020-05-20T18:00:30Z)
• Quantum Algorithms for Simulating the Lattice Schwinger Model [63.18141027763459]
  We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$. We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
  arXiv  Detail & Related papers  (2020-02-25T19:18:36Z)

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.