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2013

Faster Phase Estimation

Svore, Krysta M., Hastings, Matthew B., Freedman, Michael

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We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing.

We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine its scaling in circuit depth and width.
We show that the use of purely random measurements requires a number of measurements that is optimal up to constant factors, albeit at the cost of exponential classical post-processing; the method can also be used to improve classical signal processing.
We then develop a quantum algorithm for phase estimation that yields an asymptotic improvement in runtime, coming within a factor of log* of the minimum number of measurements required while still requiring only minimal classical post-processing.

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Then

S. P. Jordan, K. S. M. Lee, and J. Preskill, “Quantum computation of scattering in scalar quantum field theories,” (2011), 1112.4833
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2011
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K. Temme, T. Osborne, K. Vollbrecht, D. Poulin, and F. Verstraete, Nature 471
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2011
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M. Ozols, M. Roetteler, and J. Roland, in 3rd Innovations in Theoretical Computer Science Conference (ITCS) (ACM, 2012) pp. 290–308, 1103.2774
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2012
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P. Selinger, “Efficient clifford+T approximation of single-qubit operators,” (2012), 1212.6253
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P. Pham and K. M. Svore, in Reversible Computing ’12 (2012) 1207.6655

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