Binary Gauss Stabilizers for Abelian Lattice Gauge Theories

Research Question and Approach

This paper addresses the challenge of simulating lattice gauge theories on quantum computers, specifically focusing on the connection between gauge constraints and quantum error correction. In gauge theories, the physical Hilbert space is defined by Gauss's law, which acts as a constraint. In quantum information, similar constraints are managed via the stabilizer formalism. The authors investigate whether the Gauss operators of Z_N lattice gauge theories (where N is a power of two) can be reformulated into a more convenient set of stabilizers to facilitate error correction and gauge fixing.

The authors derive a new set of operators, termed binary Gauss stabilizers, which generate the same gauge-invariant subspace as the traditional Gauss operators. By mapping the Z_N gauge theory onto a qubit system, they demonstrate that these binary stabilizers can be expressed as products of Z and multicontrolled-Z operators. This reformulation provides two primary advantages:

1. Quantum Error Correction: It enables the design of error-correcting codes that exploit the system's inherent gauge symmetries without the overhead of adding extra physical qubits.
2. Gauge Fixing: It offers a new, potentially more efficient strategy for removing gauge redundancies, which can simplify the simulation of these theories on quantum hardware compared to traditional approaches like the axial gauge.

Bridging the gap between lattice gauge theory and quantum information is essential for the future of digital quantum simulation of fundamental physics. By providing a systematic way to treat gauge constraints as stabilizers, this work offers a practical framework for protecting quantum simulations from noise. Furthermore, the ability to perform gauge fixing through these stabilizers provides a new tool for optimizing the number of qubits required in simulations, potentially making complex gauge theories more accessible to current and near-term quantum devices.