Necessary and Sufficient Conditions for Quantum Computation |
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| Authors: | Seth Lloyd |
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| Affiliation: | Complex Systems Group (T-13) and Center for Nonlinear Studies , Los Alamos National Laboratory , Los Alamos, New Mexico, 87545, USA |
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| Abstract: | Abstract Necessary and sufficient conditions are given for a quantummechanical system to possess a coordinate system with respect to which its behaviour at discrete times is that of a universal digital computer. The form of the diagonal representation for the unitary time evolution operator for quantum universal computers is derived; aspects of the transformation between the diagonal representation and the computational representation are shown to be uncomputable. A quantum-mechanical treatment of macroscopic, dissipative computers is given. |
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