Krzysztof Lider | Searcharxiv

arXiv2026

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

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.

quant-ph↗

arXiv2026

Delayed Choice Phenomena in the Projection Evolution Model

In the Schrödinger evolution of a quantum state time enters as a real parameter representing the coordinate. In a more consistent approach time should be defined as a quantum observable, with the evolution taking place in a four-dimensional spacetime. This is possible in the projection evolution model in which the wave function is defined in both space and time. This allows to construct the time operator and discuss the temporal structure of quantum processes. In this paper we discuss a photon travelling through a Mach-Zehnder interferometer, focusing the description on the temporal profile of the wave function. We show that in this approach the delayed-choice experiments can be explained by the temporal overlap of the photon and the devices in the interferometer.

quant-ph↗