Quantum circuit complexity

  • Authors:
  • A. Chi-Chih Yao

  • Affiliations:
  • Dept. of Comput. Sci., Princeton Univ., NJ, USA

  • Venue:
  • SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
  • Year:
  • 1993

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Abstract

We propose a complexity model of quantum circuits analogous to the standard (acyclic) Boolean circuit model. It is shown that any function computable in polynomial time by a quantum Turing machine has a polynomial-size quantum circuit. This result also enables us to construct a universal quantum computer which can simulate, with a polynomial factor slowdown, a broader class of quantum machines than that considered by E. Bernstein and U. Vazirani (1993), thus answering an open question raised by them. We also develop a theory of quantum communication complexity, and use it as a tool to prove that the majority function does not have a linear-size quantum formula.