QAOA Parameter Selection via Bayesian Optimization
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Solution Overview
Problem
Current methods for solving discrete optimization problems, such as NP-complete problems, require checking all possible combinations, which is inefficient due to the exponential scaling of the solution space, making it challenging to find optimal solutions without exhaustive listing and checking.
Innovation Solution
The quantum approximate optimization algorithm (QAOA) combined with Bayesian optimization is used, where a quantum processor unit generates output values based on input parameters, and a Bayesian optimizer on classical processor units selects new input parameters for subsequent QAOA executions, efficiently sampling optimal solutions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If all possible combinations are checked to solve discrete optimization problems, then optimal solutions can be found, but the computational time and resources scale exponentially with problem size
Solution Approach 1:
The patent transforms the discrete optimization problem into a continuous parameter optimization problem by mapping binary variables to continuous angles (θ, φ) in quantum states. This allows the use of gradient-based optimization methods and quantum algorithms that operate in continuous space, avoiding exhaustive search of the exponential discrete state space while still finding optimal solutions through parameter tuning.
2Ease of operation
If random sampling is used to find feasible solutions, then the method is simple to implement, but a large number of samples are needed to find optimal solutions
Solution Approach 1:
The patent implements feedback loops where measurement results from quantum state preparations are used to update and refine the parameters (θ, φ) for subsequent iterations. Classical optimization algorithms process the measurement outcomes and feed back improved parameter values to the quantum system, creating an iterative refinement process that converges to optimal solutions much faster than random sampling.
Solution Approach 2:
The patent prepares quantum states with specific parameter configurations before measurement, based on problem structure analysis and initial optimization. This preliminary setup of quantum states with informed parameter choices, rather than random preparation, significantly increases the probability of finding optimal or near-optimal solutions in fewer samples.
Data Source
AI summary
In a general aspect, values of input parameters for a quantum approximate optimization algorithm (QAOA) are selected by a Bayesian optimizer. The QAOA can be configured to solve a combinatorial optimization problem (COP), such as Maximum Cut. A hybrid classical-quantum computing system can be used to execute the QAOA and select the input parameters.