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

TL;DR

This paper introduces the UNIDYSLOCK process, a novel quantum process that can transform orthogonal states into non-orthogonal states, providing a new mechanism for exponential quantum speedup in unstructured search problems, distinct from traditional quantum algorithms.

Contribution

It proposes the UNIDYSLOCK process as a fundamental quantum mechanism for speedup, explaining its basis in quantum physical laws and mathematical principles, and analyzes its role in the HSSS quantum search process.

Findings

UNIDYSLOCK can change quantum-state differences via fundamental interactions.

The HSSS quantum search process differs from standard algorithms by utilizing both Hilbert spaces.

Mathematical-parallel operations contribute to quantum speedup in this framework.

Abstract

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