Quantum networks for elementary arithmetic operations

1995/11/16 by Vlatko Vedral, V. Vedral, Adriano Barenco +3 · 12 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/physreva.54.147

7 pages, LaTeX, + 6 PS figures in a tar compressed file. See also http://eve.physics.ox.ac.uk/QChome.html

arxiv created 1995/11/16 · openalex publication_date 1996/07/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Quantum computers require quantum arithmetic. We provide an explicit construction of quantum networks effecting basic arithmetic operations: from addition to modular exponentiation. Quantum modular exponentiation seems to be the most difficult (time and space consuming) part of Shor's quantum factorizing algorithm. We show that the auxiliary memory required to perform this operation in a reversible way grows linearly with the size of the number to be factorized. \textcopyright 1996 The American Physical Society.

Citations

• The fabric of reality
• Elementary gates for quantum computation
• Quantum theory, the Church–Turing principle and the universal quantum computer

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• Novel Reversible Multiplier Architecture Using Reversible TSG Gate
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• Probabilistic implementation of universal quantum processors
• Demonstration of a Compiled Version of Shor’s Quantum Factoring Algorithm Using Photonic Qubits
• Quantum circuit for the fast Fourier transform
• Designing a Million-Qubit Quantum Computer Using a Resource Performance Simulator
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