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

A new method for fault-tolerant logical measurement in quantum error-correcting codes is introduced by treating logical operators as physical symmetries and gauging them via local measurements. The gauging measurement procedure achieves a qubit overhead of O(W log³W) for measuring a logical operator of weight W, a substantial improvement over existing schemes that require Θ(Wd) auxiliary qubits. The approach is flexible, applies to arbitrary stabilizer codes including qLDPC codes, and outperforms existing methods even for small bivariate bicycle code instances. Fault tolerance is proven with spacetime fault distance d, and the framework generalizes surface code lattice surgery and other known logical measurement protocols as special cases.