Binary Representation of Coordinate and Momentum in Quantum Mechanics
| Autor: | M. G. Ivanov |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Physics
Series (mathematics) 010102 general mathematics Degrees of freedom (physics and chemistry) Statistical and Nonlinear Physics Observable 01 natural sciences 010305 fluids & plasmas Renormalization Theoretical physics Qubit 0103 physical sciences Quantum system 0101 mathematics Quantum Mathematical Physics Quantum computer |
| Zdroj: | Theoretical and Mathematical Physics. 196:1002-1017 |
| ISSN: | 1573-9333 0040-5779 |
| Popis: | To simulate a quantum system with continuous degrees of freedom on a quantum computer based on qubits, it is necessary to reduce continuous observables (primarily coordinates and momenta) to binary observables. We consider this problem based on expanding quantum observables in series in powers of two, analogous to the binary representation of real numbers. The coefficients of the series (“digits”) are therefore orthogonal projectors. We investigate the corresponding quantum mechanical operators and the relations between them and show that the binary expansion of quantum observables automatically leads to renormalization of some divergent integrals and series (giving them finite values). |
| Databáze: | OpenAIRE |
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