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Space, time, parallelism and noise requirements for reliable quantum computing

Andrew Steane
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Abstract

Quantum error correction methods use processing power to combat noise. The noise level which can be tolerated in a fault-tolerant method is therefore a function of the computational resources available, especially the size of computer and degree of parallelism. I present an analysis of error correction with block codes, made fault-tolerant through the use of prepared ancilla blocks. The preparation and verification of the ancillas is described in detail. It is shown that the ancillas need only be verified against a small set of errors. This, combined with previously known advantages, makes this `ancilla factory' the best method to apply error correction, whether in concatenated or block coding. I then consider the resources required to achieve $2 \times 10^{10}$ computational steps reliably in a computer of 2150 logical qubits, finding that the simplest $[[n,1,d]]$ block codes can tolerate more noise with smaller overheads than the $7^L$-bit concatenated code. The scaling is such that block codes remain the better choice for all computations one is likely to contemplate.

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Andrew Steane. 1997-08-12. Space, time, parallelism and noise requirements for reliable quantum computing. https://doi.org/10.1002/(sici)1521-3978(199806)46%3A4%2F5%3C443%3A%3Aaid-prop443%3E3.0.co%3B2-8

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