Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Quantum computation and quantum information
Quantum computation and quantum information
Fast parallel circuits for the quantum Fourier transform
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Classical and Quantum Computation
Classical and Quantum Computation
A logarithmic-depth quantum carry-lookahead adder
Quantum Information & Computation
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
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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. The corresponding quantum circuit requires asymptotically lower depth and width (number of qubits) than quantum phase estimation.