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Synthesis of Quantum Logic Circuits



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


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 -3.2n-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.
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems


cosine-sine decomposition, quantum circuit, recursion


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], (Accessed April 13, 2024)
Created January 30, 2006, Updated October 12, 2021