dorsal/arxiv
View SchemaSpace, time, parallelism and noise requirements for reliable quantum computing
| Authors | Andrew Steane |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9708021 |
| URL | https://arxiv.org/abs/quant-ph/9708021 |
| DOI | 10.1002/(SICI)1521-3978(199806)46:4/5<443::AID-PROP443>3.0.CO;2-8 |
| Journal | Fortsch.Phys. 46 (1998) 443-458 |
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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"abstract": "Quantum error correction methods use processing power to combat noise. The\nnoise level which can be tolerated in a fault-tolerant method is therefore a\nfunction of the computational resources available, especially the size of\ncomputer and degree of parallelism. I present an analysis of error correction\nwith block codes, made fault-tolerant through the use of prepared ancilla\nblocks. The preparation and verification of the ancillas is described in\ndetail. It is shown that the ancillas need only be verified against a small set\nof errors. This, combined with previously known advantages, makes this `ancilla\nfactory\u0027 the best method to apply error correction, whether in concatenated or\nblock coding. I then consider the resources required to achieve $2 \\times\n10^{10}$ computational steps reliably in a computer of 2150 logical qubits,\nfinding that the simplest $[[n,1,d]]$ block codes can tolerate more noise with\nsmaller overheads than the $7^L$-bit concatenated code. The scaling is such\nthat block codes remain the better choice for all computations one is likely to\ncontemplate.",
"arxiv_id": "quant-ph/9708021",
"authors": [
"Andrew Steane"
],
"categories": [
"quant-ph"
],
"doi": "10.1002/(SICI)1521-3978(199806)46:4/5\u003c443::AID-PROP443\u003e3.0.CO;2-8",
"journal_ref": "Fortsch.Phys. 46 (1998) 443-458",
"title": "Space, time, parallelism and noise requirements for reliable quantum computing",
"url": "https://arxiv.org/abs/quant-ph/9708021"
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