Abstract
Efficient digitization is required for quantum simulations of gauge theories. Schemes based on discrete subgroups use fewer qubits at the cost of systematic errors. We systematize this approach by deriving a single plaquette action for approximating general continuous gauge groups through integrating out field fluctuations. This provides insight into the effectiveness of these approximations, and how they could be improved. We accompany the scheme by simulations of pure gauge over the largest discrete subgroup of $SU(3)$ up to the third order.
Highlights
Large-scale quantum computers can simulate nonperturbative quantum field theories which are intractable classically [1]
Noisy intermediate-scale quantum (NISQ) era systems will be limited both in qubits and circuit depths
Whether any gauge theory simulations in this period are possible depends upon efficient formulations
Summary
Large-scale quantum computers can simulate nonperturbative quantum field theories which are intractable classically [1]. Digitizing reduces symmetries—either explicitly or through finite-truncations [10] These breakings mean a priori the original model may not be recovered in the continuum limit [29,30,31,32,33,34]. We systematize the proposal of replacing continuous gauge groups G by their discrete subgroups H [11,28] by deriving lattice actions using the group space decimation procedure of [36,37]. After deriving the general third order action, we will investigate the behavior of discretizing three distinct gauge groups Uð1Þ, SUð2Þ, and SUð3Þ.
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