Quantum Cost Operator Updates for Low-Depth Combinatorial Optimization
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Solution Overview
Problem
Conventional quantum approximate optimization algorithms face challenges in accurately solving combinatorial optimization problems due to noise and the difficulty in increasing the number of circuit layers, leading to insufficient expression of arbitrary solutions in quantum states.
Innovation Solution
An information processing method that updates cost unitary operators in a quantum circuit by adding first-order terms with new variational parameters to enhance the ability to express arbitrary solutions without increasing the layer count, thereby improving accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the number of circuit layers is increased to improve solution accuracy, then the ability to express arbitrary solutions is improved, but noise and quantum bit errors increase
Solution Approach 1:
The patent segments the cost operator into multiple terms (first-order terms, second-order terms, and higher-order terms) and selectively includes only necessary terms in the quantum circuit. By dividing the cost operator analysis into judgment steps for each term type, the patent achieves accurate solution representation without requiring increased circuit layers, thus avoiding noise accumulation and quantum bit errors.
2Adaptability or versatility
If the number of circuit layers is increased to express arbitrary solutions, then solution representation capability is improved, but device complexity increases
Solution Approach 1:
The patent extracts and removes unnecessary higher-order terms from the cost operator based on judgment results. By taking out only the essential first-order and second-order terms that are needed for the specific combinatorial optimization problem, the patent simplifies the quantum circuit structure while maintaining the ability to express arbitrary solutions accurately.
Solution Approach 2:
Instead of increasing the layer dimension of the quantum circuit to improve solution expression capability, the patent transitions to another dimension by adjusting the composition of the cost operator (selecting which terms to include). This dimensional shift allows achieving the same goal through operator optimization rather than circuit depth increase.
3Measurement precision
If all terms in the cost operator are included to ensure complete problem representation, then problem accuracy is improved, but the number of variational parameters increases
Solution Approach 1:
The patent applies local quality by treating different terms in the cost operator differently based on their relevance to the specific problem. Instead of uniformly including all terms, the patent selectively includes first-order terms when needed and excludes higher-order terms when not necessary, optimizing the balance between problem representation accuracy and the number of variational parameters.
Data Source
AI summary
An information processing device judges, with respect to at least any one of multiple quantum bits in a quantum circuit, whether a corresponding first-order term is present in a cost operator. When the first-order term corresponding to any one of the plurality of quantum bits is not present the information processing device updates at least any one of the cost unitary operators so that the first-order term corresponding to the any one of the quantum bits and to which a new first variational parameter is assigned is included in the exponent part. The information processing device solves a combinatorial optimization problem based on multiple mixer unitary operators and the multiple cost unitary operators after updating at least the any one of the cost unitary operators.