We propose an implementation of a two-dimensional Z2 lattice gauge theory model on a shallow quan-tum circuit, involving a number of single-and two-qubit 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.

Two-Dimensional Lattice Gauge Theory on a Near-Term Quantum Simulator: Variational Quantum Optimization, Confinement, and Topological Order

Elisa Ercolessi;
2022

Abstract

We propose an implementation of a two-dimensional Z2 lattice gauge theory model on a shallow quan-tum circuit, involving a number of single-and two-qubit 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.
Luca Lumia; Pietro Torta; Glen B. Mbeng; Giuseppe E. Santoro; Elisa Ercolessi; Michele Burrello; Matteo M. Wauters
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/904520
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? 1
social impact