Qubit Mapping via Coupling Graph Segmentation
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Solution Overview
Problem
Current qubit mapping methods using optimization problem-based approaches suffer from high time complexity due to excessively large circuit depths, which hinder the efficiency of quantum computing performance.
Innovation Solution
The method involves segmenting the coupling graph into multiple connected subgraphs, allowing for qubit permutations within each subgraph to reduce circuit depth and optimize qubit mapping, thereby controlling the circuit depth and reducing time complexity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If qubit mapping is performed using optimization problem-based method on the entire coupling graph, then the mapping completeness is improved, but the circuit depth becomes excessively large and time complexity increases
Solution Approach 1:
The coupling graph is divided into multiple connected subgraphs, and qubit mapping is performed independently on each subgraph. This segmentation reduces the overall circuit depth by limiting the permutation scope within each subgraph rather than across the entire coupling graph, thereby reducing time complexity while maintaining mapping completeness.
2Adaptability or versatility
If qubit permutation is performed under the limit of the entire coupling graph, then all qubits can be mapped, but the circuit depth becomes excessively large
Solution Approach 1:
The coupling graph is segmented into multiple connected subgraphs with controlled sizes. By performing qubit permutation within each subgraph rather than across the entire graph, the circuit depth is reduced while still achieving comprehensive qubit mapping coverage through the collective action of all subgraphs.
Solution Approach 2:
The problem is transformed from a single global permutation problem to multiple local permutation problems organized in a hierarchical structure. This dimensional change allows parallel processing of subgraphs and reduces the overall circuit depth by limiting the permutation scope at each level.
Data Source
AI summary
A qubit mapping method is performed by a computer device. The method includes: obtaining a coupling graph corresponding to a quantum device, each vertex in the coupling graph representing one qubit in the quantum device, an edge between two vertexes representing that a two-qubit gate is allowed to directly act on qubits corresponding to the two vertexes; generating at least two connected subgraphs based on the coupling graph, a quantity of vertexes of each connected subgraph being greater than or equal to 2 and less than or equal to a routing number of the coupling graph, and a sum of quantities of vertexes of the at least two connected subgraphs being equal to a constant multiple of a quantity of vertexes of the coupling graph; and performing qubit mapping on a logic circuit based on the at least two connected subgraphs, to obtain a corresponding hardware compilable circuit.