Smaller Circuits for Arbitrary n-qubit Diagonal Computations

Published

February 25, 2003

Author(s)

Stephen Bullock, I L. Markov

Abstract

A unitary operator U=Sj,ku j,k|j> ; 0 = j = 2n -1}. These relative phases are often required in applications.Constructing quantum circuits for diagonal computations using standard techniques requires either O(n22n) controlled-not gates and one-qubit Bloch sphere rotations or else O(n2n)$ such gates and a work qubit. This work provides a recursive, constructive procedure which inputs the matrix coefficients of U and outputs such a diagram containing 2n+1 - 3 alternating controlled-not gates and one-qubit z-axis Bloch sphere rotations. Up to a factor of two, these diagrams are the smallest possible. Moreover, they respect the tensor product in the following sense. Should the computation U be a tensor of diagonal one-qubit computations of the form Rz( a) = te-i a/2|1>

Citation

Quantum Information & Computation

Pub Type

Journals

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Keywords

character, diagonal quantum computation, relative phase

Citation

Bullock, S. and Markov, I. (2003), Smaller Circuits for Arbitrary n-qubit Diagonal Computations, Quantum Information & Computation, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=50679 (Accessed November 3, 2025)