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Quantum Information and Computing for Beginners: Basics of Qubit Transformations and Quantum Algorithms Cover

Quantum Information and Computing for Beginners: Basics of Qubit Transformations and Quantum Algorithms

Quantum Information & Computation
Volume 25 (2025): Issue 6 (December 2025)
By: Archit Dhingra  
Open Access
|Mar 2026

Figures & Tables

Figure 1.

Representation of |ψ〉 as a vector on the Bloch sphere.
Representation of |ψ〉 as a vector on the Bloch sphere.

Figure 2.

Pictorial representation of Hadamard gate in a circuit.
Pictorial representation of Hadamard gate in a circuit.

Figure 3.

Pictorial representation of the action of Φ gate on a qubit (or a quantum state). Here, in accordance with Equations (7) and (8), x = 0 or 1.
Pictorial representation of the action of Φ gate on a qubit (or a quantum state). Here, in accordance with Equations (7) and (8), x = 0 or 1.

Figure 4.

Pictorial representation of SWAP gate in a circuit.
Pictorial representation of SWAP gate in a circuit.

Figure 5.

Pictorial representation of SWAP\sqrt {SWAP} gate in a circuit.
Pictorial representation of SWAP\sqrt {SWAP} gate in a circuit.

Figure 6.

Some standard single and multiple bit gates (left), and the controlled-NOT (CNOT) gate along with its matrix representation (right). Adapted in part from ref. [1].
Some standard single and multiple bit gates (left), and the controlled-NOT (CNOT) gate along with its matrix representation (right). Adapted in part from ref. [1].

Figure 7.

H–CNOT combinational quantum circuit to produce |Φ+〉 when the input is |00〉.
H–CNOT combinational quantum circuit to produce |Φ+〉 when the input is |00〉.

Figure 8.

Representation of Deutsch–Jozsa algorithm as a quantum circuit, where ‘/n’ represents a set of n qubits. Adapted in part from ref. [1].
Representation of Deutsch–Jozsa algorithm as a quantum circuit, where ‘/n’ represents a set of n qubits. Adapted in part from ref. [1].

Figure 9.

A sample circuit representing quantum parallelism, where states on the left represent the input and |ψ〉 is given by Equation (16).1
A sample circuit representing quantum parallelism, where states on the left represent the input and |ψ〉 is given by Equation (16).1
DOI: https://doi.org/10.2478/qic-2025-0040 | Journal eISSN: 3106-0544 | Journal ISSN: 1533-7146
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Language: English
Page range: 773 - 783
Submitted on: Aug 29, 2025
|
Accepted on: Oct 31, 2025
|
Published on: Mar 9, 2026
Published by: Cerebration Science Publishing Co., Limited
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year
Keywords:
Hilbert space,
Bloch sphere,
quantum entanglement,
quantum algorithm,
quantum parallelism,
succinct quantum computing tutorial for university students
Related subjects:
Physics,
Quantum physics,
Mathematics,
Applied mathematics,
Computer sciences,
Computer sciences in the humanities,
Computer sciences,
Computer sciences in natural sciences

© 2026 Archit Dhingra, published by Cerebration Science Publishing Co., Limited
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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