Semiclassical Fourier Transform for Quantum Computation

1995/11/07 by Robert B. Griffiths, Chi-Sheng Niu · 11 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.1103/physrevlett.76.3228

published as Phys.Rev.Lett. 76 (1996) 3228-3231 · Latex 6 pages, two figures on one page in uuencoded Postscript

arxiv created 1995/11/07 · openalex publication_date 1996/04/22 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that the Fourier transform preceding the final measurement in Shor's algorithm for factorization on a quantum computer can be carried out in a semiclassical way by using the ``classical'' (macroscopic) signal resulting from measuring one bit to determine the type of measurement carried out on the next bit, and so forth. In this way all the two-bit gates in the Fourier transform can be replaced by a smaller number of one-bit gates controlled by classical signals. This suggests that it may be worthwhile looking for other uses of semiclassical methods in quantum computing.

Citations

• Two-Bit Gates are Universal for Quantum Computation
• Elementary gates for quantum computation
• Quantum theory, the Church–Turing principle and the universal quantum computer

Cited by

• Calculating the thermal rate constant with exponential speedup on a quantum computer
• Efficient classical simulation of the quantum Fourier transform
• Arbitrary accuracy iterative quantum phase estimation algorithm using a single ancillary qubit: A two-qubit benchmark
• Quantum measurement of a mesoscopic spin ensemble
• Quantum computing with trapped ions
• Microfabrication techniques for trapped ion quantum information processing
• Demonstration of a Compiled Version of Shor’s Quantum Factoring Algorithm Using Photonic Qubits
• Approximate quantum Fourier transform and decoherence
• Do we really understand quantum mechanics? Strange correlations, paradoxes, and theorems
• Teleportation as a quantum computation
• Optimal eavesdropping in quantum cryptography. II. A quantum circuit