A Geometrical Design Tool for Building Cost-Effective Layout-Aware n-Bit Quantum Gates Using the Bloch Sphere Approach

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Publication Details

Journal
Cureus Journal of Computer Science.
Published
2026-09-15
DOI
https://doi.org/10.7759/s44389-026-00279-5
Primary Topic
Quantum Computing Algorithms and Architecture
Type
article
Field-Weighted Citation Impact
0.00
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article

A Geometrical Design Tool for Building Cost-Effective Layout-Aware n-Bit Quantum Gates Using the Bloch Sphere Approach

Shanyan Chen, Ali Al-Shuwaili, Ali Al-Bayaty, Abbas AlZubaidi et al.
Cureus Journal of Computer Science.
Quantum Computing Algorithms and Architecture
article

A Geometrical Design Tool for Building Cost-Effective Layout-Aware n-Bit Quantum Gates Using the Bloch Sphere Approach

Shanyan Chen, Ali Al-Shuwaili, Ali Al-Bayaty, Abbas AlZubaidi, Marek Perkowski
article en

Abstract

The conventional design technique of any n-bit quantum gate is mainly achieved using the multiplication of unitary matrices for control qubits and target qubits, where and .These matrices represent quantum rotations by an n-bit quantum gate.For a quantum designer, such a conventional technique requires extensive computational time and effort, which may generate an n-bit quantum gate with too high quantum cost.In general, the Bloch sphere is only utilized as a visualization tool to verify the conventional design correctness for quantum rotations by a quantum gate.In contrast, this paper introduces a new concept of using the Bloch sphere as a "geometrical design tool" to build cost-effective n-bit quantum gates with lower quantum costs.This concept is termed the "Bloch sphere approach (BSA)."In BSA, a cost-effective n-bit quantum gate is built without using any multiplication of unitary matrices.Instead, the quantum rotations for such a gate are visually selected using the geometrical planar intersections of the Bloch sphere.The BSA can efficiently map m targets among controls for an n-bit quantum gate to satisfy the limited layout connectivity for the physical neighboring qubits of a superconducting quantum computer.Experimentally, n-bit quantum gates built using the BSA always have lower quantum costs than those for such gates built using the conventional quantum design techniques, by utilizing the same transpilation settings and the restricted layout connectivity of a real IBM superconducting quantum computer, where qubits.

Cureus Journal of Computer Science.
Portland State University (US), Capital Normal University (CN)
Sustainable cities and communities
Openalex Percentile: Top 8%
Quantum Computing Algorithms and Architecture
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