Is Quantum Mechanics Useful?

Abstract

Technologies differ in their explicit utilization of quantum mechanical behaviour. A transistor, despite its roots in energy band structure, does not invoke quantum me­ chanically coherent transmission between terminals. The impressive progress in the past decade in mesoscopic physics, when combined with studies that have analysed a totally quantum mechanical computational process, suggest that we may be ready to move toward more quantum mechanical procedures for information processing. This paper is a warning signal; this possibility is beset by problems. The case will be made via two separate but complementary arguments. First, by summarizing this author's published comments on computation via totally quantum mechanical co­ herent Hamiltonians. The computation is likely to suffer from , i.e. from reflection of the computational trajectory, causing the computation to turn around. Additionally, small errors will accumulate and cause the computation to go off track. This is supplemented by analysis of specific proposals that suggest more detailed ma­ chinery than invoked in the general literature on quantum mechanical Hamiltonian computation. 1. In tr o d u c tio n My short title may be misleading; I am really concerned with utility in the handling of information. Devices and technology vary in their explicit quantum mechanical behaviour. A screw driver seems very classical. Nevertheless its shape, hardness and friction are determined by quantum mechanical interatomic forces. But we do not need to understand those to design, make or use a screw driver. The transistor is a modern device based on the motion of holes and electrons in energy bands. But it really isn't that different from a screw driver; once we know about holes and electrons and mobilities, we do not need to go back to the Schrodinger equation. The overall behaviour of the transistor does not exhibit quantum mechanical coherence; the transistor is not used for Schrodinger cat experiments. The laser with its dependence on quantized energy levels seems more quantum mechanical than the transistor. But even here we have some difficulty finding a clear demarcation when we view a set of oscillators, ranging from an apparently classical oscillator, such as a pendulum clock, to an optically pumped laser. Finally, a Josephson junction, where the relationship between the applied voltage and the emitted frequency involves Planck's constant, is undeniably quantum mechanical. Circuits involving Josephson junctions are invoked in Schrodinger cat experiment proposals. We want to suggest here that information handling techniques, despite the pressure for miniaturization, should not go too far along the kind of chain we have described. We can argue for this in two very different