The duality-character Solution-Information-Carrying (SIC) unitary propagators

Abstract

The HSSS quantum search process owns the dual character that it obeys both the unitary quantum dynamics and the mathematical-logical principle of the unstructured search problem. It is essentially different from a conventional quantum search algorithm. It is constructed with the duality-character oracle operations of unstructured search problem and the relevant quantum-mechanical unitary operators. It consists of the two consecutive steps that the first step is the search-space dynamical reduction and the second step the dynamical quantum-state-difference amplification (QUANSDAM). At the second step the QUANSDAM process is directly constructed with the SIC unitary propagators, while the latter each are prepared with the basic SIC unitary operators. All these SIC unitary operators and propagators each own the dual character. Here the preparation for the SIC unitary propagators of a typical quantum system (i.e., a single-atom system) is concretely carried out by starting from the basic SIC unitary operators. The SIC unitary propagator of a quantum system may reflect the quantum symmetry of the quantum system, while the basic SIC unitary operators may not. The quantum symmetry is considered as the fundamental quantum-computing-speedup resource in the quantum-computing speedup theory. Therefore, the purpose for the preparation of the SIC unitary propagators of a quantum system is ultimately to employ the quantum symmetry of the quantum system to simplify the construction and realization of the QUANSDAM process and hence speed up the QUANSDAM process. The preparation process is a solution-information transfer process from the original quantum subsystem (e.g., an n−qubit spin system) to the final quantum subsystem (e.g., a single-atom system). It is unitary and deterministic. It obeys the information conservation law. In methodology the preparation is based on the energy eigenfunction expansion principle and the multiple-quantum operator algebra space. Furthermore, a general theory mainly based on the Feynman The term information-carrying ( IC) used in the previous paper [1] is modified to the present term solution-information-carrying (SIC) in this paper as the latter reflects better the mathematical-logical principle of unstructured search problem.