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ANALYTIC ONE-BIT AND CNOT GATE CONSTRUCTIONS OF GENERAL n-QUBIT CONTROLLED GATES

YANG LIU

Department of Physics, Tsinghua University, Beijing 100084, China

Key Laboratory of Atomic and Molecular Nanosciences, Tsinghua University, Beijing 100084, China

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GUI LU LONG

Department of Physics, Tsinghua University, Beijing 100084, China

Key Laboratory of Atomic and Molecular Nanosciences, Tsinghua University, Beijing 100084, China

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YANG SUN

Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China

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https://doi.org/10.1142/S0219749908003621Cited by:62 (Source: Crossref)

Abstract

General n-qubit controlled unitary gates are frequently used in quantum information processing tasks. Barenco, Bennett, Cleve, Di Vincenzo, Margolus and Shor [Phys. Rev. A52 (1995) 3457] have given the general construction methods, and explicit results for up-to-four-qubits controlled unitary gates. We extended their calculation and gave two analytic expressions for the construction of general n-qubit controlled unitary gates in terms of one-qubit and two-qubit CNOT gates. There are two expressions – one is exponential in the qubit number which is efficient for up to ten qubits, and the other is polynomial in the qubit number, which is efficient for more than ten qubits.

Keywords:

PACS: 03.67.Lx

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