Designing fault-tolerant circuits using detector error models
arXiv:2407.13826 · doi:10.22331/q-2025-11-06-1905
Abstract
Quantum error-correcting codes, such as subspace, subsystem, and Floquet codes, are typically constructed within the stabilizer formalism, which does not fully capture the idea of fault-tolerance needed for practical quantum computing applications. In this work, we explore the remarkably powerful formalism of detector error models, which fully captures fault-tolerance at the circuit level. We introduce the detector error model formalism in a pedagogical manner and provide several examples. Additionally, we apply the formalism to three different levels of abstraction in the engineering cycle of fault-tolerant circuit designs: finding robust syndrome extraction circuits, identifying efficient measurement schedules, and constructing fault-tolerant procedures. We enhance the surface code's resistance to measurement errors, devise short measurement schedules for color codes, and implement a more efficient fault-tolerant method for measuring logical operators.
27 pages
References in corpus (30)
- Surface codes: Towards practical large-scale quantum computation
- Topological quantum memory
- Improved Simulation of Stabilizer Circuits
- Quantum Error Correction for Quantum Memories
- Topological Quantum Distillation
- The European Quantum Technologies Roadmap
- Roads towards fault-tolerant universal quantum computation
- Surface code quantum computing by lattice surgery
- A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
- Stim: a fast stabilizer circuit simulator
- Quantum Error Correction: An Introductory Guide
- The XZZX Surface Code
- Topological and subsystem codes on low-degree graphs with flag qubits
- Fast simulation of stabilizer circuits using a graph state representation
- Sparse Blossom: correcting a million errors per core second with minimum-weight matching
- A Fault-Tolerant Honeycomb Memory
- Universal quantum computing with twist-free and temporally encoded lattice surgery
- Improved decoding of circuit noise and fragile boundaries of tailored surface codes
- Relaxing Hardware Requirements for Surface Code Circuits using Time-dynamics
- Anyon condensation and the color code
- Simulation of Qubit Quantum Circuits via Pauli Propagation
- Benchmarking the Planar Honeycomb Code
- Bias-tailored quantum LDPC codes
- Unifying flavors of fault tolerance with the ZX calculus
- Clifford-deformed Surface Codes
- Correcting non-independent and non-identically distributed errors with surface codes
- Conservation laws and quantum error correction: towards a generalised matching decoder
- XYZ ruby code: Making a case for a three-colored graphical calculus for quantum error correction in spacetime
- The domain wall color code
- Distance-four quantum codes with combined postselection and error correction
Cited by in corpus (5)
- Fault-Tolerant Stabilizer Measurements in Surface Codes with Three-Qubit Gates
- Multiqubit Rydberg Gates for Quantum Error Correction
- Decoding Correlated Errors in Quantum LDPC Codes
- Diversity Methods for Improving Convergence and Accuracy of Quantum Error Correction Decoders Through Hardware Emulation
- Streaming Belief Propagation on Mixed-Alphabet Tanner Graphs for Practical Quantum Memory