Low-overhead fault-tolerant quantum computation by gauging logical operators
arXiv:2410.02213 · doi:10.1038/s41567-026-03220-8
Abstract
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.
6+17 pages, 3 figures; v2 published version
References in corpus (25)
- Topological quantum memory
- Fault-tolerant quantum computation with high threshold in two dimensions
- Topological Quantum Distillation
- Surface code quantum computing by lattice surgery
- Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
- High-threshold and low-overhead fault-tolerant quantum memory
- A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
- Quantum LDPC codes with positive rate and minimum distance proportional to n^{1/2}
- Fractal symmetries: Ungauging the cubic code
- Balanced Product Quantum Codes
- Low-overhead fault-tolerant quantum computing using long-range connectivity
- Long-range entanglement from measuring symmetry-protected topological phases
- Universal quantum computing with twist-free and temporally encoded lattice surgery
- Quantum Expander Codes
- Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics
- Fiber Bundle Codes: Breaking the Barrier for Quantum LDPC Codes
- Gapped boundaries, group cohomology and fault-tolerant logical gates
- Protected gates for topological quantum field theories
- Type-II fractons from coupled spin chains and layers
- Sparse Quantum Codes from Quantum Circuits
- Gauging the bulk: generalized gauging maps and holographic codes
- CSS code surgery as a universal construction
- Weight Reduced Stabilizer Codes with Lower Overhead
- Time-Efficient Logical Operations on Quantum Low-Density Parity Check Codes
- Non-Clifford and parallelizable fault-tolerant logical gates on constant and almost-constant rate homological quantum LDPC codes via higher symmetries