Gauge theories on a quantum computer

Gabriel Wong, Robert Raussendorf, Bartłomiej Czech

Measurement-Based Quantum Computation (MBQC) is a model of quantum computation, which uses local measurements instead of unitary gates. Here we explain that the MBQC procedure has a fundamental basis in an underlying gauge theory. This perspective provides a theoretical foundation for global aspects of MBQC. The gauge transformations reflect the freedom of formulating the same MBQC computation in different local reference frames. The main identifications between MBQC and gauge theory concepts are: (i) the computational output of MBQC is a holonomy of the gauge field, (ii) the adaptation of measurement basis that remedies the inherent randomness of quantum measurements is effected by gauge transformations. The gauge theory of MBQC also plays a role in characterizing the entanglement structure of symmetry-protected topologically (SPT) ordered states, which are resources for MBQC. Our framework situates MBQC in a broader context of condensed matter and high energy theory.

Guglielmo Mazzola, Simon V. Mathis, Giulia Mazzola +1 more

Anuj Apte

This thesis investigates gauge theories by combining theoretical analysis of non-invertible symmetries with computational simulations using neural network quantum states. We first investigate (3+1)d ZN gauge theories with non-invertible duality symmetries that arise from gauging one-form symmetries. These symmetries impose strict constraints on renormalization group flows, often prohibiting symmetry-preserving gapped phases. Our proof demonstrates that a self-dual theory with ZN one-form symmetry must either remain gapless or break self-duality, except when N = k²ℓ with –1 as a quadratic residue modulo ℓ. Lattice gauge theories provide concrete realizations of these constraints. We then focus on the development of neural network quantum states for studying lattice gauge theories. By implementing gauge-invariant neural networks, we compute ground-state wavefunctions for ZN lattice gauge theories in (2+1)d. For Z2 gauge theory, we characterize the continuous confinement transition and identify critical exponents consistent with the Ising universality class. In the Z3 case we observe a weakly first-order transition between the confined and deconfined phases. For both theories, we compute order and disorder parameters and verify the linear confining potential in the confining phase. These results demonstrate that neural network methods provide a powerful tool for studying quantum field theories computationally. By combining these simulations with symmetry-based analysis, this work uncovers new insights into the nonperturbative dynamics and phase structure of gauge theories.

Julius Mildenberger, W. Mruczkiewicz, Jad C. Halimeh +2 more

Zohreh Davoudi, Niklas Mueller, Connor Powers

The phase diagram of strong interactions in nature at finite temperature and chemical potential remains largely theoretically unexplored due to inadequacy of Monte-Carlo-based computational techniques in overcoming a sign problem. Quantum computing offers a sign-problem-free approach, but evaluating thermal expectation values is generally resource intensive on quantum computers. To facilitate thermodynamic studies of gauge theories, we propose a generalization of the thermal-pure-quantum-state formulation of statistical mechanics applied to constrained gauge-theory dynamics, and numerically demonstrate that the phase diagram of a simple low-dimensional gauge theory is robustly determined using this approach, including mapping a chiral phase transition in the model at finite temperature and chemical potential. Quantum algorithms, resource requirements, and algorithmic and hardware error analysis are further discussed to motivate future implementations. Thermal pure quantum states, therefore, may present a suitable candidate for efficient thermal simulations of gauge theories in the era of quantum computing.

Indrakshi Raychowdhury