Circuit-based digital adiabatic quantum simulation and pseudoquantum simulation as new approaches to lattice gauge theory

TL;DR

This paper introduces a circuit-based digital quantum simulation method for lattice gauge theories, demonstrating key physical phenomena through classical GPU simulation, and proposing a new practical approach called pseudoquantum simulation.

Contribution

It presents a novel digital quantum simulation scheme for $ ext{Z}_2$ lattice gauge theory using adiabatic algorithms and classical GPU demonstration, bridging classical and quantum computational methods.

Findings

Successfully simulated quantum phase transitions and topological properties.

Demonstrated gauge invariance and duality in classical GPU simulations.

Proposed pseudoquantum simulation as a practical computational approach.

Abstract

Gauge theory is the framework of the Standard Model of particle physics and is also important in condensed matter physics. As its major non-perturbative approach, lattice gauge theory is traditionally implemented using Monte Carlo simulation, consequently it usually suffers such problems as the Fermion sign problem and the lack of real-time dynamics. Hopefully they can be avoided by using quantum simulation, which simulates quantum systems by using controllable true quantum processes. The field of quantum simulation is under rapid development. Here we present a circuit-based digital scheme of quantum simulation of quantum $\mathbb{Z}_2$ lattice gauge theory in $2+1$ and $3+1$ dimensions, using quantum adiabatic algorithms implemented in terms of universal quantum gates. Our algorithm generalizes the Trotter and symmetric decompositions to the case that the Hamiltonian varies at each step in the decomposition. Furthermore, we carry through a complete demonstration of this scheme in classical GPU simulator, and obtain key features of quantum $\mathbb{Z}_2$ lattice gauge theory, including quantum phase transitions, topological properties, gauge invariance and duality. Hereby dubbed pseudoquantum simulation, classical demonstration of quantum simulation in state-of-art fast computers not only facilitates the development of schemes and algorithms of real quantum simulation, but also represents a new approach of practical computation.