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

Understand

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.