Compare Papers
Paper 1
A Framework for Approximating Qubit Unitaries
Vadym Kliuchnikov, Alex Bocharov, Martin Roetteler, Jon Yard
- Year
- 2015
- Journal
- arXiv preprint
- DOI
- arXiv:1510.03888
- arXiv
- 1510.03888
We present an algorithm for efficiently approximating of qubit unitaries over gate sets derived from totally definite quaternion algebras. It achieves $\varepsilon$-approximations using circuits of length $O(\log(1/\varepsilon))$, which is asymptotically optimal. The algorithm achieves the same quality of approximation as previously-known algorithms for Clifford+T [arXiv:1212.6253], V-basis [arXiv:1303.1411] and Clifford+$π/12$ [arXiv:1409.3552], running on average in time polynomial in $O(\log(1/\varepsilon))$ (conditional on a number-theoretic conjecture). Ours is the first such algorithm that works for a wide range of gate sets and provides insight into what should constitute a "good" gate set for a fault-tolerant quantum computer.
Open paperPaper 2
Fault tolerance with noisy and slow measurements and preparation.
Paz-Silva GA, Brennen GK, Twamley J.
- Year
- 2010
- Journal
- Phys Rev Lett
- DOI
- 10.1103/physrevlett.105.100501
- arXiv
- -
No abstract.
Open paper