Synthesis of Quantum Logic Circuits

Published

January 31, 2006

Author(s)

V V. Shende, Stephen Bullock, I L. Markov

Abstract

Operators acting on a collection of two-level quantum-mechanical systems can be represented by quantum circuits.  In this work we develop a decomposition of such unitary operators which reveals their top-down structure and can be implemented numerically with well-known primitives.  It leads to simultaneous improvements by a factor of two over (i) the best known  -qubit circuit synthesis algorithms for large  , and (ii) the best known three-qubit circuits.  In the worst case, our algorithm NQ produces circuits that differ from known lower bounds by approximately a factor of two.  The required number of quantum controlled-not s (i.e. two-qubit interactions)  (1/2)^.4 -3^.2^n-1+1 is only half the number of real degrees of freedom of a generic unitary operator.  This is desirable since CNOTs are typically slower and more error-prone than one-qubit rotations, and they may require physical coupling between distant two-level systems.

Citation

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

Volume

25

Issue

6

Pub Type

Journals

Download Paper

Local Download

Keywords

cosine-sine decomposition, quantum circuit, recursion

Citation

Shende, V. , Bullock, S. and Markov, I. (2006), Synthesis of Quantum Logic Circuits, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=150894 (Accessed October 27, 2025)