Low-overhead fault-tolerant quantum computation by gauging logical operators

Quantum computation must be performed in a fault-tolerant manner to be useful in practice. Recent progress has established quantum error-correcting codes with sparse connectivity requirements and constant qubit overhead suitable for quantum memory. However, existing schemes that include fault-tolerant logical measurement on such quantum memories do not always achieve low qubit overhead. Here we present a low-overhead method to implement fault-tolerant logical measurement on a quantum error-correcting code by treating the logical operator as a physical symmetry and gauging it so that it is enforced by a product of local symmetries. The gauging measurement procedure introduces a high degree of flexibility that can be exploited to achieve a qubit overhead that is linear in the weight of the operator being measured up to a polylogarithmic factor. This flexibility also allows the procedure to be adapted to arbitrary quantum codes. Our results provide a more efficient approach to performing fault-tolerant quantum computation, making it more tractable for near-term implementation. Combining quantum error correction with gauge theory concepts from many-body physics enables the design of codes with improved resource requirements for fault-tolerant quantum computation.