Two-dimensional $\mathbb{Z}_2$ lattice gauge theory on a near-term quantum simulator: variational quantum optimization, confinement, and topological order

TL;DR

This paper demonstrates that shallow quantum circuits can simulate a 2D $$ lattice gauge theory, detecting phase transitions and topological order, with potential for scalable quantum simulations of gauge theories.

Contribution

It introduces a feasible implementation of 2D $$ lattice gauge theory on near-term quantum devices using variational algorithms, enabling detection of confinement and topological phases.

Findings

Successful ground state preparation with high fidelity on small lattices

Detection of confined and deconfined regimes via Wilson loops and topological entropy

Transferability of solutions across topological sectors without re-optimization

Abstract

We propose an implementation of a two-dimensional $\mathbb{Z}_2$ lattice gauge theory model on a shallow quantum circuit, involving a number of single and two-qubits gates comparable to what can be achieved with present-day and near-future technologies. The ground state preparation is numerically analyzed on a small lattice with a variational quantum algorithm, which requires a small number of parameters to reach high fidelities and can be efficiently scaled up on larger systems. Despite the reduced size of the lattice we consider, a transition between confined and deconfined regimes can be detected by measuring expectation values of Wilson loop operators or the topological entropy. Moreover, if periodic boundary conditions are implemented, the same optimal solution is transferable among all four different topological sectors, without any need for further optimization on the variational parameters. 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.