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A unitary dynamical state-locking (UNIDYSLOCK) process is a unitary processthat can transform two orthogonal states to two non-orthogonal states. Itsinverse process, i.e., the QUANSDAM process could realize an exponential QCspeedup in solving an unstructured search problem in the quantum-computing (QC)speedup theory (X. Miao, arXiv:1105.3573 [quant-ph] (2011)). In this paper theprinciple of how a UNIDYSLOCK process works is described on the basis of the QCspeedup theory. A UNIDYSLOCK process does not exist at all in pure quantummechanics. That it can change the quantum-state difference is original from thefundamental interaction between the quantum physical laws (i.e., the unitaryquantum dynamics and the Hilbert-space symmetric structure) and themathematical-logical principle of the search problem. It is characteristic forthe QC speedup theory. Even if a usual quantum computational (Qc) process thatis reversible or unitary contained a UNIDYSLOCK (or QUANSDAM) process, thecontribution of the UNIDYSLOCK (or QUANSDAM) process to the QC speedup of theusual Qc process would be secondary or negligible. Whether or not a UNIDYSLOCK(or QUANSDAM) process can make an essential contribution to a QC speedup candistinguish the QC speedup theory from any usual Qc theory. In the paper the QCspeedup mechanism of the HSSS quantum search process is also studied. Thesearch process is essentially different from a usual quantum search algorithm.It works in both the usual Hilbert space and the math Hilbert space. Due to themath Hilbert space a mathematical-parallel operation is characteristic for theQC speedup theory, while a quantum-parallel operation is characteristic for theusual Qc theory. The fundamental interaction mentioned above and thefundamental quantum-computing resource play the main role in speeding up thesearch process.

The unitary dynamical state-locking process, the HSSS quantum search process, and the quantum-computing speedup theory