Tight Binding Hamiltonians and Quantum Turing Machines

Abstract

This paper extends work done to date on quantum computation by associating potentials with different types of computation steps. Quantum Turing machine Hamiltonians, generalized to include potentials, correspond to sums over tight binding Hamiltonians each with a different potential distribution. Which distribution applies is determined by the initial state. An example, which enumerates the integers in succession as binary strings, is analyzed. It is seen that for some initial states the potential distributions have quasicrystalline properties and are similar to a substitution sequence.

4 pages Latex, 2 postscript figures, submitted to Phys Rev Letters

References in corpus (4)

• Two-Bit Gates are Universal for Quantum Computation
• Universality in Quantum Computation
• Remarks on the Spectral Properties of Tight Binding and Kronig-Penney Models with Substitution Sequences
• Quantum Ballistic Evolution in Quantum Mechanics: Application to Quantum Computers

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• Exact Renormalization-Group Study of Aperiodic Ising Quantum Chains and Directed Walks
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• The Landauer Resistance and Band Spectra for the Counting Quantum Turing Machine
• Transmission and Spectral Aspects of Tight Binding Hamiltonians for the Counting Quantum Turing Machine
• Quantum network architecture of tight-binding models with substitution sequences
• Simulation of quantum interference by reactions of chemical type