Quantum Annealing Diversity Hamiltonian Sampling
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Solution Overview
Problem
Existing optimization methods often focus on finding a single near-optimal solution rather than generating a diverse set of solutions, which can lead to local extrema and limit the exploration of the solution space, particularly in applications where multiple good solutions are beneficial.
Innovation Solution
A method is introduced that involves generating a diversity Hamiltonian based on a subset of samples, combining it with the problem Hamiltonian, and using quantum annealing or Markov Chain Monte Carlo algorithms to sample values, thereby increasing the diversity of solutions obtained.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If existing optimization methods focus on finding a single near-optimal solution, then computational efficiency is improved, but solution diversity deteriorates
Solution Approach 1:
The patent segments the optimization process into multiple independent sampling iterations, where each iteration focuses on finding individual solutions. By dividing the solution search into discrete sampling steps and using diversity tracking to guide subsequent searches, the system maintains computational efficiency while generating diverse solutions across iterations.
Solution Approach 2:
The patent changes parameters dynamically by adjusting the diversity Hamiltonian weight and sampling temperature throughout the optimization process. These parameter modifications allow the system to balance between exploiting known good solutions and exploring new regions of the solution space, thereby maintaining both efficiency and diversity.
2Adaptability or versatility
If optimization methods explore the solution space extensively, then solution diversity is improved, but computational cost increases
Solution Approach 1:
The patent performs preliminary action by pre-calculating and storing diverse samples during initial sampling iterations. These pre-computed diverse samples are then used to guide subsequent optimization searches, reducing the need for extensive exploration in later stages and thereby lowering overall computational cost while maintaining solution diversity.
Solution Approach 2:
The system implements feedback mechanisms by continuously tracking the diversity of found solutions and using this information to adjust the diversity Hamiltonian weight. This feedback loop allows the optimization to adapt its exploration behavior, intensifying diversity search when solutions converge and reducing it when diverse solutions are found, thus optimizing computational resource usage.
3Adaptability or versatility
If a diversity Hamiltonian is added to the problem Hamiltonian, then solution diversity is improved, but problem complexity increases
Solution Approach 1:
The patent applies dynamics by making the diversity Hamiltonian weight a time-varying parameter that changes throughout the optimization process. The weight starts high to promote diversity exploration and gradually decreases to focus on solution quality, allowing the problem complexity to be managed dynamically rather than statically, thus balancing diversity and tractability.
Solution Approach 2:
The system applies partial action by selectively adding the diversity Hamiltonian term only when needed to maintain solution diversity, rather than always using the full combined Hamiltonian. This selective application reduces the effective problem complexity in stages where diversity is already sufficient, while applying it partially in stages where diversity needs enhancement.
Data Source
AI summary
Systems and methods for operating a computer system to generate samples having improved diversity are discussed. A processor receives a problem definition with a problem Hamiltonian defined over a set of variables and samples one or more values for the set of variables from the problem Hamiltonian, the one or more values for the set of variables comprising a first set of samples. At least a subset of the first set of samples is selected, and a diversity Hamiltonian based on the at least a subset of the first set of samples is generated. The problem Hamiltonian and the diversity Hamiltonian are combined to generate a combined Hamiltonian, and one or more values for the set of variables are sampled from the combined Hamiltonian, the one or more values for the set of variables comprising a second set of samples.