A Geometrical Design Tool for Building Cost-Effective Layout-Aware n-Bit Quantum Gates Using the Bloch Sphere Approach
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arXiv
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| Format: | Preprint |
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2026
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| author | Al-Bayaty, Ali Perkowski, Marek |
| author_facet | Al-Bayaty, Ali Perkowski, Marek |
| contents | The conventional design technique of any n-bit quantum gate is mainly achieved using unitary matrices multiplication, where n >= 2 and 1 <= m <= n-1 for m target qubits and n-m control qubits. 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 a too high quantum cost. 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 unitary matrices multiplication. 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 n-m controls for an n-bit quantum gate, to satisfy the limited layout connectivity for the physical neighboring qubits of a 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_00484 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Geometrical Design Tool for Building Cost-Effective Layout-Aware n-Bit Quantum Gates Using the Bloch Sphere Approach Al-Bayaty, Ali Perkowski, Marek Quantum Physics The conventional design technique of any n-bit quantum gate is mainly achieved using unitary matrices multiplication, where n >= 2 and 1 <= m <= n-1 for m target qubits and n-m control qubits. 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 a too high quantum cost. 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 unitary matrices multiplication. 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 n-m controls for an n-bit quantum gate, to satisfy the limited layout connectivity for the physical neighboring qubits of a 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. |
| title | A Geometrical Design Tool for Building Cost-Effective Layout-Aware n-Bit Quantum Gates Using the Bloch Sphere Approach |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.00484 |