The Solovay-Kitaev algorithm
| dc.creator | Dawson, Christopher M. | |
| dc.creator | Nielsen, Michael A. | |
| dc.date | 2005-05-06 | |
| dc.date | 2005-08-23 | |
| dc.date.accessioned | 2026-07-07T06:12:44Z | |
| dc.date.available | 2026-07-07T06:12:44Z | |
| dc.description | This pedagogical review presents the proof of the Solovay-Kitaev theorem in the form of an efficient classical algorithm for compiling an arbitrary single-qubit gate into a sequence of gates from a fixed and finite set. The algorithm can be used, for example, to compile Shor's algorithm, which uses rotations of $π/ 2^k$, into an efficient fault-tolerant form using only Hadamard, controlled-{\sc not}, and $π/ 8$ gates. The algorithm runs in $O(\log^{2.71}(1/ε))$ time, and produces as output a sequence of $O(\log^{3.97}(1/ε))$ quantum gates which is guaranteed to approximate the desired quantum gate to an accuracy within $ε> 0$. We also explain how the algorithm can be generalized to apply to multi-qubit gates and to gates from $SU(d)$. | |
| dc.description | 15 pages, accepted to Quantum Information and Computation as Review Article | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0505030 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0505030 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/92874 | |
| dc.subject | Quantum Physics | |
| dc.title | The Solovay-Kitaev algorithm | |
| dc.type | text |