Graph Embedding for Adiabatic Quantum Optimization
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Solution Overview
Problem
Current adiabatic quantum computation methods face limitations in mapping problem graphs onto hardware graphs due to limited qubit connectivity and faulty qubits, leading to inefficiencies and constraints in solving optimization problems.
Innovation Solution
The development of unique graph embedding techniques, such as the Iterative Method and Edge Placement Method, which allow for more efficient mapping of problem graphs onto physical graphs, overcoming limitations by iteratively improving node positions and strategically placing edges to reduce chain length and qubit usage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional minor embedding techniques are used to map problem graphs onto hardware graphs, then the mapping can be achieved with existing hardware constraints, but the number of physical qubits required increases and chain length increases
Solution Approach 1:
The patent segments the embedding process into multiple stages: initial placement, iterative optimization, and refinement phases. Each stage focuses on specific aspects of the mapping problem, allowing systematic reduction of qubit usage while maintaining mapping validity.
Solution Approach 2:
The patent employs dynamic optimization algorithms that continuously adjust the embedding configuration during execution. The iterative methods dynamically reposition logical qubits and reconfigure chains based on current hardware state, enabling adaptive reduction of physical qubit requirements.
2Reliability
If conventional minor embedding techniques are used to map problem graphs onto hardware graphs, then the mapping can be achieved with existing hardware constraints, but the chain length increases reducing efficiency
Solution Approach 1:
The patent performs preliminary placement of logical qubits in optimal positions before finalizing the embedding. This preliminary action considers future chain formation and minimizes expected chain lengths, preventing suboptimal configurations from developing.
Solution Approach 2:
The iterative optimization methods incorporate feedback loops that monitor chain length metrics and adjust the embedding configuration accordingly. Each iteration uses information from previous iterations to refine the mapping and reduce chain lengths systematically.
3Adaptability or versatility
If the TRIAD method is used to embed arbitrary graphs into hardware graph, then any problem graph up to a certain size can be embedded, but the method is inefficient and constrains the problem graph to a particular limiting size
Solution Approach 1:
The patent changes key parameters of the embedding process, including the objective function weights, optimization constraints, and placement strategies. These parameter adjustments enable the system to adapt to different problem sizes and hardware configurations while maintaining high efficiency.
Solution Approach 2:
The patent introduces additional optimization dimensions beyond simple graph mapping, considering temporal aspects of the embedding process and multiple objective functions simultaneously. This multi-dimensional approach enables both versatility and efficiency.
4Measurement precision
If Klymko et al. method is used to determine all problem graphs that can be embedded into hardware graph, then complete enumeration is achieved, but the method lacks scalability and tends to be useful only for small hardware graphs
Solution Approach 1:
The patent extracts the essential features needed for embedding determination without performing complete enumeration. By identifying key structural properties and using heuristic filtering, the method achieves practical completeness for large graphs without the exponential complexity of exhaustive methods.
Data Source
AI summary
Methods are provided for implementing schemes for embedding a particular optimization problem into a particular hardware solution employing unique graph embedding techniques. The disclosed methods implement an adiabatic quantum optimization in a quantum computing device or a quantum processor. Heuristics for graph minor embedding are employed to map a problem graph structure of a particular binary unconstrained optimization problem onto a physical graph structure (topology) of the quantum computing device or quantum processor to provide an optimized hardware implementation. Known constraints that are presented with current schemes in their application to particular hardware solutions are avoided, including limited qubit connectivity and the presence of faulty qubits.