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arXiv:quant-ph/0611189

Optimal Control of High-Fidelity Quantum Gates in the Presence of Decoherence

Matthew Grace, Constantin Brif, HERSCHEL A. RABITZ, Ian A. Walmsley, Robert L. Kosut, Daniel A. Lidar

Published Nov 17, 2006• 1 citation
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Abstract

This paper has been withdrawn as it has been superseded by postings arXiv:quant-ph/0702147 and arXiv:0712.2935
DOI
10.48550/arxiv.quant-ph/0611189

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In seminal work (arxiv:quant-ph/9707021) Alexei Kitaev proposed topological quantum computing (arXiv:cond-mat/0010440, arxiv:quant-ph/9707021, arXiv:quant-ph/0001108, arXiv:0707.1889), whereby logic gates of a quantum computer are conducted by creating, braiding and fusing anyonic particles on a two-dimensional plane. Furthermore, he showed the proposal is inherently robust to local perturbations (arXiv:cond-mat/0010440, arxiv:quant-ph/9707021, arXiv:1001.0344, arXiv:1001.4363) when anyons are created as quasiparticle excitations of a topologically ordered lattice model prepared at zero temperature. Over the decades following this proposal there have been considerable technological developments towards the construction of a fault-tolerant quantum computer. Rather than maintaining some target ground state at zero temperature, a modern approach is to actively correct the errors a target state experiences, where we use noisy quantum circuit elements to identify and subsequently correct for deviations from the ideal state. We present an error-correction scheme that enables us to carry out robust universal quantum computation by braiding anyons. We show that our scheme can be carried out on a suitably large device with an arbitrarily small failure rate assuming circuit elements are below some threshold level of local noise. The error-corrected scheme we have developed therefore enables us to carry out fault-tolerant topological quantum computation using modern quantum hardware that is now under development.