The Significance to Quantum Computing of the Classical Harmonic Nature of Energy Eigenstates

Abstract

Since a pure quantum system is incapable of faithfully simulating the solutions of the Schroedinger equation that actually pertains to itself, it is proposed that quantum computing technology (as opposed to cryptographic technology) not be based on pure quantum systems such as qubits but instead on physical systems which by their nature faithfully simulate the solutions of Schroedinger equations. Every Schroedinger equation is within a unitary transformation of being a set of mutually independent classical simple harmonic oscillator equations. Thus classical simple harmonic oscillators, or "chobits", are the mathematically fundamental building blocks for all Schroedinger equations. In addition, classical harmonic oscillators are, as a practical matter, far easier to deal with than any pure quantum system -- e.g., their phases and absolute amplitudes are readily physically accessible, they have little predilection for environmental decoherence, and they abound as cavity electromagnetic standing-wave modes. We study in mathematical detail the use of chobits to compute discrete quantum Fourier transforms, including gates, chobit counts, and chobit operation counts. The results suggest that thirty chobits and under a thousand chobit phase operations could generate discrete quantum Fourier transforms of a billion terms. Chobits can be technologically realized as semiconductor dynatron-type electronic oscillator circuits, which ought to be amenable to very considerable miniaturization.