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

TL;DR

This paper introduces the Bloch sphere approach (BSA), a geometrical design method for constructing cost-effective n-bit quantum gates that reduces quantum costs by visualizing rotations without matrix multiplication.

Contribution

The paper presents a novel geometrical design technique using the Bloch sphere to build lower-cost n-bit quantum gates, bypassing traditional matrix multiplication methods.

Findings

BSA produces quantum gates with lower quantum costs than conventional methods.

The approach efficiently maps control and target qubits respecting physical layout constraints.

Experimental results confirm the cost reduction achieved by BSA.

Abstract

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.