Improved performance of the Bacon-Shor code with Steane's syndrome extraction method
arXiv:2403.01659 · doi:10.1103/PhysRevA.111.032427
Abstract
We compare Steane's and Shor's syndrome extraction methods on the Bacon-Shor code. We propose a straightforward strategy based on post-selection to prepare the logical and states of the Bacon-Shor code by using flag-like qubits to verify their constituent Greenberger-Horne-Zeilinger states. We perform stabilizer simulations with a depolarizing Pauli error model and find that Steane's method significantly outperforms Shor's. Not only does Steane's method result in pseudo-thresholds that are about 1 order of magnitude higher than Shor's, but also its advantage increases monotonically as we go from a distance-3 to a distance-9 Bacon-Shor code. The advantage of Steane's method is the greatest in the regime where gate errors dominate over measurement errors. Some of the circuit constructions we propose for Steane's method are not formally fault-tolerant, yet outperform the formally fault-tolerant Shor's protocols for experimentally relevant physical error rates. This suggest that constructing formally fault-tolerant circuits that maintain the full code distance is not strictly necessary to guarantee the usefulness of a quantum error-correcting protocol. Despite relying on post-selection, we find that our methods can be efficient. These protocols would be naturally implementable on a platform with long-range qubit interactions like trapped ions or neutral atoms.
References in corpus (59)
- Fault-tolerant quantum computation by anyons
- Surface codes: Towards practical large-scale quantum computation
- Topological quantum memory
- Universal Quantum Computation with ideal Clifford gates and noisy ancillas
- Improved Simulation of Stabilizer Circuits
- Simulated Quantum Computation of Molecular Energies
- Quantum Error Correction for Quantum Memories
- Quantum Computing with Very Noisy Devices
- Logical quantum processor based on reconfigurable atom arrays
- Reliable Quantum Computers
- High-fidelity quantum logic gates using trapped-ion hyperfine qubits
- High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions
- Stabilizer Codes and Quantum Error Correction
- Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
- Experimental Quantum Computations on a Topologically Encoded Qubit
- Stabilizer Formalism for Operator Quantum Error Correction
- Low-distance Surface Codes under Realistic Quantum Noise
- A Unified and Generalized Approach to Quantum Error Correction
- Quantum error correction with only two extra qubits
- Subsystem fault tolerance with the Bacon-Shor code
- Fault-Tolerant Quantum Computation For Local Non-Markovian Noise
- Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
- Fault-tolerant quantum error detection
- Fault-tolerant detection of a quantum error
- Fault-tolerant quantum computation with cluster states
- Single-shot fault-tolerant quantum error correction
- Effective fault-tolerant quantum computation with slow measurements
- Flag fault-tolerant error correction with arbitrary distance codes
- A theory of single-shot error correction for adversarial noise
- Triangular color codes on trivalent graphs with flag qubits
- Flag fault-tolerant error correction for any stabilizer code
- The cost of universality: A comparative study of the overhead of state distillation and code switching with color codes
- Simulating the performance of a distance-3 surface code in a linear ion trap
- Universal fault-tolerant gates on concatenated stabilizer codes
- Demonstration of fault-tolerant Steane quantum error correction
- Errors and pseudo-thresholds for incoherent and coherent noise
- Simple proof of fault tolerance in the graph-state model
- Modeling quantum noise for efficient testing of fault-tolerant circuits
- Approximation of real error channels by Clifford channels and Pauli measurements
- Simulation of rare events in quantum error correction
- Transversality and lattice surgery: exploring realistic routes towards coupled logical qubits with trapped-ion quantum processors
- 2-D Compass Codes
- Comparison of a quantum error correction threshold for exact and approximate errors
- Measurement-free fault-tolerant quantum error correction in near-term devices
- Fault Tolerance with Bare Ancillae for a [[7,1,3]] Code
- Tractable Simulation of Error Correction with Honest Approximations to Realistic Fault Models
- Handling Leakage with Subsystem Codes
- Direct measurement of Bacon-Shor code stabilizers
- Fault-tolerant measurement-free quantum error correction with multi-qubit gates
- Demonstration of Shor encoding on a trapped-ion quantum computer
- Adaptive syndrome measurements for Shor-style error correction
- A Pair Measurement Surface Code on Pentagons
- Fault-tolerant Preparation of Stabilizer States for Quantum CSS Codes by Classical Error-Correcting Codes
- Error correcting Bacon-Shor code with continuous measurement of noncommuting operators
- Efficient Preparation of Large Block Code Ancilla States for Fault-tolerant Quantum Computation
- Measurement-free fault-tolerant logical zero-state encoding of the distance-three nine-qubit surface code in a one-dimensional qubit array
- Analytical Error Analysis of Clifford Gates by the Fault-Path Tracer Method
- Dynamical subset sampling of quantum error correcting protocols
- Optimization tools for distance-preserving flag fault-tolerant error correction