Reducing the overhead for quantum computation when noise is biased

Abstract

We analyse a model for fault-tolerant quantum computation with low overhead suitable for situations where the noise is biased. The basis for this scheme is a gadget for the fault-tolerant preparation of magic states that enable universal fault-tolerant quantum computation using only Clifford gates that preserve the noise bias. We analyse the distillation of $|T⟩$-type magic states using this gadget at the physical level, followed by concatenation with the 15-qubit quantum Reed-Muller code, and comparing our results with standard constructions. In the regime where the noise bias (rate of Pauli $Z$ errors relative to other single-qubit errors) is greater than a factor of 10, our scheme has lower overhead across a broad range of relevant noise rates.

9 pages, 6 figures, comments welcome; v2 published version

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Cited by in corpus (30)

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• Bias-preserving gates with stabilized cat qubits
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• Quantum computing with rotation-symmetric bosonic codes
• Quantum information processing with bosonic qubits in circuit QED
• Tailoring surface codes for highly biased noise
• Quantum control of a cat-qubit with bit-flip times exceeding ten seconds
• Erasure qubits: Overcoming the $T_1$ limit in superconducting circuits
• Modular Bosonic Subsystem Codes
• 2-D Compass Codes
• Fault-tolerant quantum computation using large spin cat-codes
• Tailored codes for small quantum memories
• Quantum computation with cat qubits
• High-Fidelity Magic-State Preparation with a Biased-Noise Architecture
• Generating Fault-Tolerant Cluster States from Crystal Structures
• Fault-tolerant Compass Codes
• Hierarchical memories: Simulating quantum LDPC codes with local gates
• Biased Gottesman-Kitaev-Preskill repetition code
• Closest lattice point decoding for multimode Gottesman-Kitaev-Preskill codes
• Control of the $ZZ$ coupling between Kerr-cat qubits via transmon couplers
• T-count Optimized Design of Quantum Integer Multiplication
• Andreev spin relaxation time in a shadow-evaporated InAs weak link
• Surface Code with Imperfect Erasure Checks
• Dynamic compensation for pump-induced frequency shift in Kerr-cat qubit initialization
• Error correctable efficient quantum homomorphic encryption using Calderbank-Shor-Steane codes
• Fault-tolerant quantum computing with the parity code and noise-biased qubits
• Improving trapped-ion-qubit memories via code-mediated error-channel balancing
• Unfolded distillation: very low-cost magic state preparation for biased-noise qubits
• Bias-preserving computation with the bit-flip code