Unconventional Quantum Computing Devices

This paper investigates a variety of unconventional quantum computation devices , including fermionic quantum computers and computers that exploit nonlinear quantum mechanics. It is shown that unconventional quantum computing devices can in principle compute some quantities more rapidly than 'conventional' quantum computers. Computers are physical: what they can and cannot do is determined by the laws of physics. When scientific progress augments or revises those laws, our picture of what computers can do changes. Currently, quantum mechanics is generally accepted as the fundamental dynamical theory of how physical systems behave. Quantum computers can in principle exploit quantum coherence to perform computational tasks that classical computers cannot [1-21]. If someday quantum mechanics should turn out to be incomplete or faulty, then our picture of what computers can do will change. In addition, the set of known quantum phenomena is constantly increasing: essentially any coherent quantum phenomenon involving nonlinear interactions between quantum degrees of freedom can in principle be exploited to perform quantum logic. This paper discusses how the revision of fundamental laws and the discovery of new quantum phenomena can lead to new technologies and algorithms for quantum computers. Since new quantum effects are discovered seemingly every day, let's first discuss two basic tests that a phenomenon must pass to be able to function as a basis for quantum computation. These are 1) The phenomenon must be nonlinear, and 2) It must be coherent. To support quantum logic, the phenomenon must involve some form of nonlinearity, e.g., a nonlinear interaction between quantum degrees of freedom. Without such a nonlinearity quantum devices, like linear classical devices, cannot perform even so simple a nonlinear operation as an AND gate. Quantum coherence is a prerequisite for performing tasks such as factoring using Shor's algorithm [10], quantum simulation a la Feynman [11] and Lloyd [12], or Grover's database search algorithm [13], all of which require extended manipulations of coherent quantum superpositions.