Graph Edge Pruning in Minor Embeddings to Reduce Physical Qubits
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Solution Overview
Problem
Current Quantum Annealer hardware requires excessive qubits due to NP-hard minor-embedding problems, leading to inefficient resource usage and suboptimal solution quality, as existing heuristics fail to provide exact mappings in practical time.
Innovation Solution
A post-processing approach that ranks and removes edges based on entanglement coefficients using Tarjan's algorithm to minimize the number of qubits needed, ensuring fewer qubits are used while maintaining solution quality for less sensitive QUBO problems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Loss of time
If heuristics are used for minor-embedding, then practical running time is reduced, but solution quality deteriorates and more qubits are used than needed
Solution Approach 1:
The patent applies preliminary action by performing edge removal operations before the final embedding is executed. The method pre-processes the graph by identifying and removing unnecessary edges based on entanglement coefficients, thereby preparing an optimized embedding that reduces qubit requirements while maintaining solution quality. This preliminary optimization prevents the need for post-processing corrections and ensures efficient resource utilization from the start.
2Manufacturing precision
If NP-hard minor-embedding problem is solved exactly, then optimal qubit mapping is achieved, but computational complexity becomes intractable
Solution Approach 1:
The patent applies the extraction principle by removing unnecessary edges from the graph based on entanglement coefficients. By extracting and eliminating edges that contribute minimally to the overall entanglement structure, the method simplifies the embedding problem while preserving the essential quantum correlations needed for accurate QUBO solution. This reduction in graph complexity makes the embedding tractable without sacrificing optimality.
Solution Approach 2:
The patent applies parameter changes by utilizing entanglement coefficients as a metric to guide edge removal decisions. By changing the parameter space from considering all possible edges to selectively removing edges below certain entanglement thresholds, the method transforms the intractable NP-hard problem into a manageable optimization task that maintains solution quality while reducing computational burden.
3Adaptability or versatility
If fully connected qubit architecture is implemented, then any input graph can be accommodated, but hardware complexity and resource requirements escalate exponentially
Solution Approach 1:
The patent applies preliminary action by pre-processing the input graph to identify and remove edges that would require excessive hardware connections. By performing edge removal based on entanglement coefficients before mapping to physical qubits, the method prepares an optimized graph representation that reduces the connectivity requirements of the quantum hardware while maintaining the ability to solve the original QUBO problem effectively.
Data Source
AI summary
One example method includes ranking all edges e of a graph G that was obtained using a minor embedding process performed on a graph topology Q, and the ranked edges are included in a list R, creating a graph G′ by copying G, and for each of the edges e, performing, for as long as a stop criterion has not been met, operations that include: identifying nodes and edges in the graph G′, removing, from the graph G′, any edges that meet an adjacency criterion, and placing the removed edges in a set B′ of edges, removing, from the list R, all edges of the B′ of edges, and removing, from the graph G′, the edge e.