Global Qubit Placement Using Layered Graph Crossing Reduction
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Solution Overview
Problem
Conventional methods for qubit placement in quantum computing environments are computationally expensive or impractical due to the time complexity of identifying optimal global placement, leading to increased execution time and resource consumption.
Innovation Solution
A computer-implemented method using graph processing algorithms, such as the Sugiyama algorithm and barycenter heuristic, to optimize qubit placement by reducing edge crossings and minimizing swap operations, resulting in near-optimal global qubit placement.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional methods are used for identifying optimal global qubit placement, then qubit placement accuracy is improved, but computational time complexity increases significantly
Solution Approach 1:
The patent segments the qubit placement optimization problem into multiple layers representing different time slices, where each layer contains nodes representing qubit groups. This segmentation transforms the complex global optimization problem into a structured multi-layer graph problem that can be processed more efficiently using the Sugiyama algorithm, thereby reducing computational time while maintaining placement accuracy.
Solution Approach 2:
The patent changes the representation parameters by transforming the qubit placement problem into a graph theory framework with specific parameters: nodes representing qubit groups, edges representing connections between time slices, and layers representing temporal progression. This parameter transformation enables the application of efficient graph processing algorithms that reduce computational complexity while preserving the essential optimization objectives.
2Productivity
If optimal global qubit placement is achieved, then execution time of quantum programs is reduced, but computational resources required for placement optimization increase
Solution Approach 1:
The patent performs preliminary qubit placement optimization by constructing and processing the layered graph structure before actual quantum program execution. The Sugiyama algorithm is applied in advance to determine optimal qubit groupings and positions across time slices, creating a pre-optimized placement strategy that reduces execution time during actual quantum computation without requiring continuous computational resources during runtime.
Solution Approach 2:
The patent creates a graphical model (layered graph) that copies and represents the quantum program's qubit placement requirements in a simplified, processable format. This graph copy allows classical computers to efficiently simulate and optimize placement strategies without directly manipulating the actual quantum state, thereby reducing the computational burden on quantum resources while achieving optimal placement.
3Object-generated harmful factors
If the number of edge crossings in layered graph is reduced, then qubit swap operations are minimized, but graph processing complexity increases
Solution Approach 1:
The patent extracts the essential structural relationships from the quantum program and represents them in a layered graph format, separating the optimization problem from the detailed quantum operations. By taking out only the critical connectivity information and temporal relationships into the graph structure, the patent enables the application of efficient graph drawing algorithms that minimize edge crossings (and thus swap operations) without requiring complex processing of the entire quantum program detail.
Data Source
AI summary
Embodiments of the present disclosure provide for efficient global qubit placement within a quantum computing environment for a quantum program. Some embodiments utilize a graph-based approach to represent positions in a quantum computing environment, and optimize the graph layout using a graph processing algorithm to rearrange layers of a graph and reduce edge crossings. A layered graph associated with minimum cost is selected and utilized as an efficient layered graph for purposes of global qubit placement at various time steps of execution. Embodiments provide satisfactory approximations that avoid the NP-hard nature of this task to significantly reduce compilation time to a solution for global qubit placement as opposed to optimal global qubit placement while additionally identifying solutions that significantly reduce overall execution time and computing resource usage.