Quantum recognition of eigenvalues, structure of devices, and thermodynamic properties
Yu. I. Ozhigov · Journal of Experimental and Theoretical Physics · 2003
Quantum algorithms that speed up their classical counterparts are proposed for the following problems: recognition of eigenvalues with a fixed precision, recognition of molecular and electronic device structures, and the finding of thermodynamic functions. We mainly consider structures that generate sparse spectra. These algorithms require a time from about the square root to the logarithm of the time of the classical analogues, and they provide exponential savings in memory for the first three problems. For example, the time required for distinguishing two devices with the same given spectrum is about the seventh root of the time of the direct classical method, and about the sixth root for the recognition of an eigenvalue. Microscopic quantum devices can therefore recognize molecular structures and physical properties of environment faster than large classical computers.