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 September 9, 2024)
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS
A lock (
) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.
Smaller Circuits for Arbitrary n-qubit Diagonal Computations
Published
Author(s)
, 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
Download Paper
Keywords
character, diagonal quantum computation, relative phase
Citation
Issues
If you have any questions about this publication or are having problems accessing it, please contact reflib@nist.gov.
Created February 25, 2003, Updated February 17, 2017