The basic principles to construct a generalized state-locking pulse field and simulate efficiently the reversible and unitary halting protocol of a universal quantum computer

Abstract

It has been shown (Arxiv: quant-ph/0507236) that a universal quantum computer could be powerful enough to solve efficiently the quantum search problem, and the reversible and unitary halting protocol based on the state-locking pulse field is the key component to construct the efficient quantum search processes, while the state-locking pulse field is the key component to generate the reversible and unitary halting protocol. In this paper the reversible and unitary halting protocol and the generalized state-locking pulse field have been extensively investigated theoretically. The basic principles to construct the state-locking pulse field and design the reversible and unitary halting protocol are studied in detail. A generalized state-locking pulse field is generally dependent upon the time and space variables. It could be a sequence of time- and space-dependent electromagnetic pulse fields and could also contain the time- and space-dependent potential fields. Thus, the reversible and unitary halting protocol built up out of the state-locking pulse field generally consists of a sequence of time- and space-dependent unitary evolution processes. It is shown how the quantum control process is constructed to simulate efficiently the reversible and unitary halting protocol. An improved subspace-reduction quantum program and circuit based on the reversible and unitary halting protocol is proposed as the key component to construct further an efficient quantum search process. A simple atomic physical system that is an atomic ion or a neutral atom in the double-well potential field is proposed to show how the state-locking pulse field is generated and how to implement the reversible and unitary halting protocol.