Quantum Circuit Simplification Using Templates

Authors:
D. Maslov;C. Young;D. M. Miller;G. W. Dueck
Affiliations:
University of Victoria, Canada;University of Victoria, Canada;University of Victoria, Canada;University of New Brunswick, Canada
Venue:
Proceedings of the conference on Design, Automation and Test in Europe - Volume 2
Year:
2005

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Abstract

Optimal synthesis of quantum circuits is intractable and heuristic methods must be employed. Templates are a general approach to reversible and quantum circuit simplification. In this paper, we consider the use of templates to simplify a quantum circuit initially found by other means. We present and analyze templates in the general case, and then provide particular details for circuits composed of NOT, CNOT and controlled-sqrt-of-NOT gates. We introduce templates for this set of gates and apply them to simplify both known quantum realizations of Toffoli gates and circuits found by earlier heuristic Fredkin and Toffoli gate synthesis algorithms. While the number of templates is quite small, the reduction in quantum cost is often significant.