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  3. Volume 7, Number 1, 2025
  4. Study of the Quantum Phase Influence on the Qubit State in Circuits With Hadamard Gates Connected in Series

Study of the Quantum Phase Influence on the Qubit State in Circuits With Hadamard Gates Connected in Series

CSN.
2025;
Volume 7, Number 1
: pp. 247 - 260
https://doi.org/10.23939/csn2025.01.247
Authors:
  1. T. I. Onyshkevych
  2. Valerii Hlukhov
1
Lviv Polytechnic National University, Department of Computer Engineering
2
Lviv Polytechnic National University, Ukraine

This paper presents a study of the influence of the quantum phase on the qubit state in circuits with Hadamard gates in series for further minimisation in software or hardware modelling.
The study is carried out using the Azure Quantum computing platform to simulate quantum algorithms and run quantum applications on dedicated hardware.
The study provides an overview of the qubit as a unit of quantum information, describes in detail the operation of the Hadamard gate, simulates the operation of a circuit of two Hadamard gates in series with initial inputs $|0\rangle$ and $|1\rangle$, and simulates the operation of a circuit with a sequential shift on $\frac{\pi}{4}$ and Hadamard gate inputs$|0\rangle$ and $|1\rangle$. In the course of the study, it was found how the same intermediate state of the qubit can have different outputs after the Hadamard gate, by means of phase. Also, the results of the schemes where the first Hadamard gate is replaced by a sequential shift on $\frac{\pi}{4}$.
The results obtained can be used to test the Hadamard gate model when creating its digital model.

Hadamard gate
quantum computing
quantum gates
superposition
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