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Quantum Information Processing

Practical circuit optimization algorithm for quantum simulation based on template matching

Yuxiang Liu, Zaichen Zhang, Yi Yong Hu, Fan‐Xu Meng, Tian Luan, Xianchao Zhang, Xutao Yu

Published Feb 1, 2024• 5 citations
Publisher
DOI
10.1007/s11128-023-04252-2

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Quantum circuits are often generated by decomposing gates from networks with classical reversible gates. Only in rare cases, the results are minimal. Post-optimization methods, such as template matching, are employed to reduce the quantum costs of circuits. Quantum templates are derived from identity circuits. All minimal realizations, within certain limitations, can be embedded into templates. Due to this property, templates matching has the potential to reduce quantum costs of circuits. However, one of the difficulties in finding templates matches is due to the mobility of the gates within the circuit. Thus far, template matching procedures have employed heuristics to reduce the search space. This article presents an in-depth study of exact template matching with a set of algorithms. A graph structure with the corresponding circuits facilitates the discovery of potential sequences of templates to be matched, and how exact minimization of circuits can be accomplished. The significance of the proposed method is verified in benchmarks optimization.

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This paper shows how to find the optimal quantum circuits for all 3-qubit functions with an exhaustive search. A circuit for a given function is said to be optimal, if no realization with fewer gates exists. It is important to have the optimal results for all three-input functions, since they can serve as benchmarks when evaluation heuristic optimization algorithms. The optimal results generated, are compared with optimized quantum circuits obtained from post synthesis algorithms. It is observed that the published templates do not lead to optimal results. Experimental results show, that optimal circuits can seldom be obtained with template matching. On average the optimal size of a 3-qubit circuit is 10.0, where as template matching only achieves an average of 11.9 gates. It is shown that this is due to the fact that not all templates have been discovered. The paper concludes with some directions for further research.

IEEE International Symposium on Multiple-Valued Logic (ISMVL)•May 1, 2012•5 citations
Quantum circuits are often generated by decomposing gates from networks with classical reversible gates. Only in rare cases, the results are minimal. Post-optimization methods, such as template matching, are employed to reduce the quantum costs of circuits. Quantum templates are derived from identity circuits. All minimal realizations, within certain limitations, can be embedded into templates. Due to this property, templates matching has the potential to reduce quantum costs of circuits. However, one of the difficulties in finding templates matches is due to the mobility of the gates within the circuit. Thus far, template matching procedures have employed heuristics to reduce the search space. This article presents an in-depth study of exact template matching with a set of algorithms. A graph structure with the corresponding circuits facilitates the discovery of potential sequences of templates to be matched, and how exact minimization of circuits can be accomplished. The significance of the proposed method is verified in benchmarks optimization.
The execution of quantum algorithms requires two key considerations. On the one hand, it should meet the connectivity constraint requirements of quantum circuit mapping for quantum architectures, and on the other hand, it needs to consider reducing the probability of errors in the execution of quantum circuits as much as possible. This paper proposes a novel optimization technique based on template matching that to satisfy both requirements. The template matching optimization method can significantly reduce the number of gates in a quantum circuit and further enhance its practicality. It stands as advanced optimization technology available today. Our method optimizes quantum logic circuits mapped onto quantum architecture by initially selecting their linear substructure. We then zone the circuit according to the gate dependency graph and optimize each block through template matching. Finally, we reorganize the circuit to obtain the optimized version as the final result. Our proposed method is amenable to various quantum architectures. To evaluate its efficacy, we conduct a comparative analysis with the t|ket⟩ and Qiskit compiler using a set of benchmark test circuits. Specifically, compare to the t|ket⟩ compiler method, the highest average optimization rate of our method can reach 25.75%. Compare with the Qiskit compiler method, the highest average optimization rate can reach 32.72%. Overall, our approach has significant optimization advantages.
This paper shows how to find the optimal quantum circuits for all 3-qubit functions with an exhaustive search. A circuit for a given function is said to be optimal, if no realization with fewer gates exists. It is important to have the optimal results for all three-input functions, since they can serve as benchmarks when evaluation heuristic optimization algorithms. The optimal results generated, are compared with optimized quantum circuits obtained from post synthesis algorithms. It is observed that the published templates do not lead to optimal results. Experimental results show, that optimal circuits can seldom be obtained with template matching. On average the optimal size of a 3-qubit circuit is 10.0, where as template matching only achieves an average of 11.9 gates. It is shown that this is due to the fact that not all templates have been discovered. The paper concludes with some directions for further research.