Universal quantum circuit for two-qubit transformations with three controlled-NOT gates

2003/07/31 by Guifré Vidal, G. Vidal, C. M. Dawson · 5 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum-Dot Cellular Automata #quant-ph

paper · pdf · doi:10.1103/physreva.69.010301

published as Phys. Rev. A 69, 010301 (2004) · 3 pages, 7 figures. One theorem, one author and references added. Change of notational conventions. Minor correction in Theorem 1

arxiv created 2003/08/04 · openalex publication_date 2004/01/08 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

We consider quantum circuits made of controlled-NOT (CNOT) gates and single-qubit unitary gates and look for constructions that minimize the use of CNOT gates. We show, by means of an explicit quantum circuit, that three CNOT gates are necessary and sufficient in order to implement an arbitrary unitary transformation of two qubits. We also identify the subset of two-qubit gates that can be performed with only two CNOT gates and provide a simple characterization for them.

Citations

• Two-Bit Gates are Universal for Quantum Computation
• Elementary gates for quantum computation

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