Variable Freezing for Quantum Optimization Problems
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Solution Overview
Problem
Quantum computers require significant processing cycles to express complex real-world problems effectively, making it computationally expensive to determine optimal solutions, especially when dealing with Quadratic Unconstrained Binary Optimization (QUBO) matrices.
Innovation Solution
A method involving a classical computer to optimize QUBO problems by freezing variables, generating a contribution vector, and creating an equivalent optimization problem that can be solved using fewer quantum bits, thereby reducing the computational burden on quantum computers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the objective optimisation problem is expressed to a quantum computer in a resolvable manner, then the quantum computer can determine the optimal solution, but the processing cycles required to express the problem become computationally expensive
Solution Approach 1:
The patent applies preliminary action by performing variable freezing and contribution vector calculation on the classical computer before the quantum computation. This preprocessing step identifies and freezes variables that have minimal impact on the objective function, thereby reducing the problem size that needs to be solved by the quantum computer without compromising the overall optimisation accuracy.
Solution Approach 2:
The patent segments the optimisation problem by dividing the variables into frozen variables (those with minimal impact) and active variables (those that significantly affect the objective function). This segmentation allows the quantum computer to focus only on the essential variables, reducing the computational burden while maintaining solution quality.
2Measurement precision
If more variables are included in the quantum optimisation problem, then the solution accuracy improves, but the number of quantum bits required increases
Solution Approach 1:
The patent extracts and removes variables that have minimal contribution to the objective function by calculating contribution vectors and identifying variables below a threshold. These extracted variables are frozen and excluded from the quantum optimisation problem, thereby reducing the number of quantum bits required while preserving the essential problem characteristics needed for accurate solution.
3Productivity
If the problem is simplified to reduce quantum bit requirements, then the computational burden decreases, but the solution may lose accuracy
Solution Approach 1:
The patent changes parameters by transforming the original optimisation problem into an equivalent form through variable freezing and contribution vector calculation. This parameter transformation reduces the problem dimensionality and quantum bit requirements while maintaining the essential optimisation characteristics, achieving a balance between computational efficiency and solution accuracy.
Data Source
AI summary
A computer implemented method for optimising, an objective optimisation problem. The methods begins by receiving the objective optimisation problem. The objective optimisation problem is represented by an L×L objective matrix comprising a plurality of matrix components A set of frozen variables is received. The method determines a set of freezable matrix components corresponding to the set of frozen variables. Then, a contribution vector is determined based on the set of freezable matrix components and the set of frozen variables An equivalent optimisation problem is determined based on the contribution vector and the objective optimisation problem. The equivalent optimisation problem excludes the freezable matrix components such that the equivalent optimisation problem may be solved on a quantum computer using fewer quantum bits than the objective optimisation problem would require.