Quantum simulation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> lattice gauge theory with minimal resources
Reinis Irmejs, Mari Carmen Bañuls, J. I. Cirac
Abstract
The quantum simulation of fermionic gauge field theories is one of the anticipated uses of quantum computers in the noisy intermediate-scale quantum (NISQ) era. Recently work has been done to simulate properties of the fermionic ${\mathbb{Z}}_{2}$ gauge field theory in $(1+1)\mathrm{D}$ and the pure gauge theory in $(2+1)\mathrm{D}$. In this work, we investigate various options for simulating the fermionic ${\mathbb{Z}}_{2}$ gauge field theory in $(2+1)\mathrm{D}$. To simulate the theory on a NISQ device it is vital to minimize both the number of qubits used and the circuit depth. In this work we propose ways to optimize both criteria for simulating time dynamics. In particular, we develop a new way to simulate this theory on a quantum computer, with minimal qubit requirements. We provide a quantum circuit for simulating a single first-order Trotter step that minimizes the number of 2-qubit gates needed and gives comparable results to methods requiring more qubits. Furthermore, we investigate variational Trotterization approaches that allow us to further decrease the circuit depth.