Exact Synthesis of 3-Qubit Quantum Circuits from Non-Binary Quantum Gates Using Multiple-Valued Logic and Group Theory

  • Authors:

  • Guowu Yang;William N. N. Hung;Xiaoyu Song;Marek Perkowski

  • Affiliations:

  • Portland State University, Oregon;Portland State University, Oregon;Portland State University, Oregon;Portland State University, Oregon

  • Venue:
  • Proceedings of the conference on Design, Automation and Test in Europe - Volume 1
  • Year:
  • 2005

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Abstract

We propose an approach to optimally synthesize quantum circuits from non-permutative quantum gates such as Controlled-Square-Root-of-Not (i.e. Controlled-V). Our approach reduces the synthesis problem to multiple-valued optimization and uses group theory. We devise a novel technique that transforms the quantum logic synthesis problem from a multi-valued constrained optimization problem to a group permutation problem. The transformation enables us to utilize group theory to exploit the properties of the synthesis problem. Assuming a cost of one for each two-qubit gate, we found all reversible circuits with quantum costs of 4, 5, 6, etc, and give another algorithm to realize these reversible circuits with quantum gates.