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.

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