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A Mathematical Theory of NMR Quantum Computations

  • Tetsuro Nishino
Conference paper

Abstract

In this paper, we develop a theory of bulk quantum computations such as NMR (Nuclear Magnetic Resonance) quantum computations. For this purpose, we first define bulk quantum Turing machines (BQTMs for short) as a model of bulk quantum computation. Then, we define complexity classes EBQP, BBQP and ZBQP as counterparts of the quantum complexity classes EQP, BQP and ZQP, respectively, and show that EBQP=EQP, BBQP=BQP, and ZBQP=ZQP. This implies that BQTMs are polynomially related to ordinary QTMs as long as they are used to solve decision problems. We also show that these two types of QTMs are also polynomially related when they solve a function problem which has a unique solution. Furthermore, we show that BQTMs can solve certain instances of NP-complete problems efficiently.

Keywords

Quantum Computation Turing Machine Boolean Expression Satisfiability Problem 35th Annual IEEE Symposium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Japan 2002

Authors and Affiliations

  • Tetsuro Nishino
    • 1
  1. 1.Department of Information and Communication EngineeringThe University of Electro — CommunicationsChofu, TokyoJapan

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