Fault-tolerant quantum computation with asymmetric Bacon-Shor codes

Abstract

We develop a scheme for fault-tolerant quantum computation based on asymmetric Bacon-Shor codes, which works effectively against highly biased noise dominated by dephasing. We find the optimal Bacon-Shor block size as a function of the noise strength and the noise bias, and estimate the logical error rate and overhead cost achieved by this optimal code. Our fault-tolerant gadgets, based on gate teleportation, are well suited for hardware platforms with geometrically local gates in two dimensions.

25 pages, 16 figures. (v2) Minor revisions

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• Protected gates for superconducting qubits
• Quantum computing with rotation-symmetric bosonic codes
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• Erasure qubits: Overcoming the $T_1$ limit in superconducting circuits
• Error Rates and Resource Overheads of Repetition Cat Qubits
• 2-D Compass Codes
• Comparing the Overhead of Topological and Concatenated Quantum Error Correction
• Reducing the overhead for quantum computation when noise is biased
• Fault-tolerant interface between quantum memories and quantum processors
• High-threshold topological quantum error correction against biased noise
• Fast Route to Thermalization
• Handling Leakage with Subsystem Codes
• Low overhead Clifford gates from joint measurements in surface, color, and hyperbolic codes
• Generating Fault-Tolerant Cluster States from Crystal Structures
• Universal fault-tolerant quantum computation with Bacon-Shor codes
• Fault-tolerant Compass Codes
• Projecting 3D color codes onto 3D toric codes
• A cellular automaton decoder for a noise-bias tailored color code
• Efficient Preparation of Large Block Code Ancilla States for Fault-tolerant Quantum Computation
• Micromotion-Enhanced Fast Entangling Gates For Trapped Ion Quantum Computing
• Benchmarking quantum gates and circuits
• Asymmetric Quantum Concatenated and Tensor Product Codes with Large Z-Distances
• A lower bound on the space overhead of fault-tolerant quantum computation
• Surface Code with Imperfect Erasure Checks
• Reliable channel-adapted error correction: Bacon-Shor code recovery from amplitude damping
• Efficiently decoding the 3D toric codes and welded codes on cubic lattices
• Resource optimization for fault-tolerant quantum computing
• Optimizing the Frequency of Quantum Error Correction using the [[7,1,3]] Steane Code
• Exact Entanglement Dynamics of Two Spins in Finite Baths
• Constructions of Pure Asymmetric Quantum Alternant Codes Based on Subclasses of Alternant Codes
• Bias-preserving computation with the bit-flip code
• Fault-tolerant fidelity based on few-qubit codes: Parity-check circuits for biased error channels