Gauge Symmetry in Quantum Simulation

• URL: http://arxiv.org/abs/2512.22932v1
• Date: Sun, 28 Dec 2025 13:56:38 GMT
• Title: Gauge Symmetry in Quantum Simulation
• Authors: Masanori Hanada, Shunji Matsuura, Andreas Schafer, Jinzhao Sun,
• Abstract summary: We present universal principles for treating gauge symmetry that apply to any quantum simulation approach.<n>We show how non-singlet approaches can yield gauge-invariant observables through wave packets and string excitations.
• Score: 0.0874967598360817
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum simulation of non-Abelian gauge theories requires careful handling of gauge redundancy. We address this challenge by presenting universal principles for treating gauge symmetry that apply to any quantum simulation approach, clarifying that physical states need not be represented solely by gauge singlets. Both singlet and non-singlet representations are valid, with distinct practical trade-offs, which we elucidate using analogies to BRST quantization. We demonstrate these principles within a complete quantum simulation framework based on the orbifold lattice, which enables explicit and efficient circuit constructions relevant to real-world QCD. For singlet-based approaches, we introduce a Haar-averaging projection implemented via linear combinations of unitaries, and analyze its cost and truncation errors. Beyond the singlet-approach, we show how non-singlet approaches can yield gauge-invariant observables through wave packets and string excitations. This non-singlet approach is proven to be both universal and efficient. Working in temporal gauge, we provide explicit mappings of lattice Yang-Mills dynamics to Pauli-string Hamiltonians suitable for Trotterization. Classical simulations of small systems validate convergence criteria and quantify truncation and Trotter errors, showing concrete resource estimates and scalable circuit recipes for SU($N$) gauge theories. Our framework provides both conceptual clarity and practical tools toward quantum advantage in simulating non-Abelian gauge theories.

Related papers

• Classical shadows for sample-efficient measurements of gauge-invariant observables [0.002718525106069543]
  We develop three classical shadow protocols tailored to systems with local (or gauge) symmetries.<n>We demonstrate these trade-offs using a $mathZ$ gauge theory, where a dual formulation enables a rigorous analysis of resource requirements.
  arXiv  Detail & Related papers  (2025-11-04T19:00:01Z)
• The charge-singlet measurement toolbox [0.0]
  We show how to apply charge-singlet measurements as a flexible tool for both classical and quantum simulations discrete and continuous gauge theories.<n>Our approach extends the use of charge-singlet measurements beyond state preparation in the charge neutral (charge neutral) sector to include noise mitigation circuits.
  arXiv  Detail & Related papers  (2025-10-09T18:25:26Z)
• Predicting symmetries of quantum dynamics with optimal samples [41.42817348756889]
  Identifying symmetries in quantum dynamics is a crucial challenge with profound implications for quantum technologies.<n>We introduce a unified framework combining group representation theory and subgroup hypothesis testing to predict these symmetries with optimal efficiency.<n>We prove that parallel strategies achieve the same performance as adaptive or indefinite-causal-order protocols.
  arXiv  Detail & Related papers  (2025-02-03T15:57:50Z)
• An efficient finite-resource formulation of non-Abelian lattice gauge theories beyond one dimension [0.0]
  We propose a resource-efficient method to compute the running of the coupling in non-Abelian gauge theories beyond one spatial dimension. Our method enables computations at arbitrary values of the bare coupling and lattice spacing with current quantum computers, simulators and tensor-network calculations.
  arXiv  Detail & Related papers  (2024-09-06T17:59:24Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• 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)
• Symmetric Pruning in Quantum Neural Networks [111.438286016951]
  Quantum neural networks (QNNs) exert the power of modern quantum machines. QNNs with handcraft symmetric ansatzes generally experience better trainability than those with asymmetric ansatzes. We propose the effective quantum neural tangent kernel (EQNTK) to quantify the convergence of QNNs towards the global optima.
  arXiv  Detail & Related papers  (2022-08-30T08:17:55Z)
• 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)
• Generalization Metrics for Practical Quantum Advantage in Generative Models [68.8204255655161]
  Generative modeling is a widely accepted natural use case for quantum computers. We construct a simple and unambiguous approach to probe practical quantum advantage for generative modeling by measuring the algorithm's generalization performance. Our simulation results show that our quantum-inspired models have up to a $68 times$ enhancement in generating unseen unique and valid samples.
  arXiv  Detail & Related papers  (2022-01-21T16:35:35Z)
• 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)
• Gauge Principle and Gauge Invariance in Quantum Two-Level Systems [0.0]
  We provide an alternative derivation of the quantum Rabi model based on the implementation in two-state systems of the gauge principle. We also obtain the gauge-invariant quantum Rabi model for asymmetric two-state systems, and the multi-mode gauge-invariant quantum Rabi model beyond the approximation.
  arXiv  Detail & Related papers  (2020-06-11T16:33:23Z)

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.