Abstract
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).
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This research was performed at the Moscow Institute of Physics and Technology (National Research University) and supported by a grant from the Russian Science Foundation (Project No. 16-11-00084).
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 196, No. 1, pp. 70–87, July, 2018.
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Ivanov, M.G. Binary Representation of Coordinate and Momentum in Quantum Mechanics. Theor Math Phys 196, 1002–1017 (2018). https://doi.org/10.1134/S0040577918070073
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DOI: https://doi.org/10.1134/S0040577918070073