Ternary and binary representation of coordinate and momentum in quantum mechanics
| Autor: | A. Yu. Polushkin, M. G. Ivanov |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Physics
Quantum Physics Series (mathematics) High Energy Physics - Lattice (hep-lat) Degrees of freedom (physics and chemistry) FOS: Physical sciences Observable Mathematical Physics (math-ph) 81Q35 Renormalization High Energy Physics - Lattice Quantum system Quantum Physics (quant-ph) Ternary operation Quantum Mathematical Physics Mathematical physics Quantum computer |
| Zdroj: | AIP Conference Proceedings. |
| ISSN: | 0094-243X |
| Popis: | To simulate a quantum system with continuous degrees of freedom on a quantum computer based on quantum digits, it is necessary to reduce continuous observables (primarily coordinates and momenta) to discrete observables. We consider this problem based on expanding quantum observables in series in powers of two and three analogous to the binary and ternary representations of real numbers. The coefficients of the series ("digits") are, therefore, Hermitian operators. We investigate the corresponding quantum mechanical operators and the relations between them and show that the binary and ternary expansions of quantum observables automatically leads to renormalization of some divergent integrals and series (giving them finite values). Comment: 22 pages, 8 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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