QUBO Slack Variable Computation for Qubit-Efficient Annealing
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Solution Overview
Problem
The limited number of qubits in quantum annealers and the increased memory burden in digital annealers due to the linear increase in slack variables for inequality constraints in quantum computing applications restrict the size of solvable problems and affect solution quality.
Innovation Solution
A computing method utilizing the framework of Reinforcement Learning (RL) and the Q-Learning algorithm to find slack variables in the QUBO form, reducing the number of qubits or memory burden in quantum and digital annealers, thereby enhancing the ability to solve complex problems accurately.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If slack variables are added to inequality constraints to convert them into quadratic penalty terms, then the constraints can be satisfied, but the number of qubits required increases linearly with the number of inequalities
Solution Approach 1:
The patent extracts and separates the slack variable determination from the main optimization problem. Instead of treating all variables equally in the QUBO formulation, the method identifies and isolates slack variables as a distinct component that can be optimized separately using reinforcement learning, thereby reducing their impact on the total qubit count.
Solution Approach 2:
The patent applies preliminary action by using reinforcement learning to pre-determine or pre-optimize the slack variable values before the main quantum annealing process. The Q-learning algorithm learns optimal slack variable assignments in advance, allowing the subsequent quantum optimization to focus only on the original decision variables, thus reducing the required qubit count.
2Adaptability or versatility
If the number of slack variables increases to handle more inequality constraints, then more constraints can be modeled, but the memory burden in digital annealers increases
Solution Approach 1:
The patent extracts the slack variable optimization from the main problem formulation and handles it separately through reinforcement learning. This separation allows the system to model complex constraints without proportionally increasing the memory burden, as the slack variables are determined through a more efficient RL-based approach rather than being fully integrated into the QUBO matrix.
Solution Approach 2:
The patent changes the parameter representation by using a Q-learning function that maps states to slack variable values. Instead of directly encoding all slack variables in the QUBO formulation, the method uses learned parameters from reinforcement learning to determine slack variable assignments, thereby reducing the memory requirements while maintaining constraint modeling capability.
3Reliability
If more qubits are allocated to slack variables, then inequality constraints can be handled, but the problem size that can be processed is restricted
Solution Approach 1:
The patent extracts slack variable determination from the main QUBO problem and handles it through reinforcement learning. This extraction allows inequality constraints to be satisfied without allocating excessive qubits to slack variables, thereby preserving more qubits for the actual problem variables and increasing the overall problem size capacity.
Solution Approach 2:
The patent applies preliminary action by using Q-learning to determine slack variable values before the main quantum optimization. This preliminary determination of slack variables reduces the need to allocate qubits for them during the actual problem solving, thereby increasing the number of qubits available for processing larger problems.
Data Source
AI summary
A computing method for obtaining slack variables in an objective function is applied to a quantum computing device. Through the use of the reinforcement learning method, a first function is obtained. Through the first function, the slack variables solution of the problem's objective function in the QUBO form are found. Consequently, the objective function in the QUBO form is optimized to be used for quantum annealers or digital annealers. Since the number of variables in the objective function is significantly reduced, the complexity of the problem is directly reduced. Furthermore, the annealer has the capability to handle more complex problems and find a high-quality solution more efficiently and accurately. Consequently, the purpose of obtaining the optimal value of the objective function can be achieved.