Description and error analysis of quantum alghorithms in the projection evolution model -- the Deutsch algorithm case

TL;DR

This paper models the Deutsch quantum algorithm using a harmonic oscillator framework within the projection evolution model, providing a systematic way to analyze state transformations and errors.

Contribution

It introduces a novel approach to model quantum algorithms with harmonic oscillators and derives evolution operators within the projection evolution formalism.

Findings

Accurately models the Deutsch algorithm using harmonic oscillators.

Provides a systematic method for deriving evolution operators.

Analyzes projection errors in quantum state transformations.

Abstract

This work demonstrates that the Deutsch algorithm can be effectively modelled using a two-level harmonic oscillator within the second quantization formalism. By adopting this framework, evolution operators are derived. We present a projection evolution model that accurately characterizes the physical state transformation within quantum gates. This approach provides a systematic method for finding evolution operators, enabling the complete description and prediction of state evolution - including projection errors - in quantum algorithms.