Abstract
A general scheme is presented for simulating gauge theories, with matter fields, on a digital quantum computer. A Trotterized time-evolution operator that respects gauge symmetry is constructed, and a procedure for obtaining time-separated, gauge-invariant operators is detailed. We demonstrate the procedure on small lattices, including the simulation of a 2+1D non-Abelian gauge theory.
Highlights
Quantum simulations are motivated by inherent obstacles to the classical, nonperturbative simulation of quantum field theories [1]
While large-scale quantum computers will greatly enhance calculations in quantum field theory, for the foreseeable future quantum computers are limited to tens or hundreds of nonerror-corrected qubits with circuit depths fewer than a 1000 gates—the so-called noisy intermediate-scale quantum (NISQ) era
For the same lattice gauge theory, we demonstrate the procedure described in Sec
Summary
Quantum simulations are motivated by inherent obstacles to the classical, nonperturbative simulation of quantum field theories [1]. Theoretical issues impede full use of quantum computers Despite these limits, algorithms have been demonstrated in toy field theories [5,6,7,8,9,10,11,12]. A common suggestion is to limit the register to physical states by gauge fixing, at the cost of increased circuit depth in the time-evolution, a practical method for non-Abelian theories remains undescribed. In Euclidean lattice field theory, we can use imaginary-time evolution to separate states overlapping with the same operator. Violations of gauge invariance in the time-evolution are potentially introduced through noisy gates, digitization, and Trotterization. We construct a Trotterized time-evolution without gaugefixing, for arbitrary gauge theories with coupled matter fields.
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