Identity circuits can be used as templates to minimize reversible circuits. This paper describes an algorithm to find all quantum templates with 3 qubits. The algorithm is used to find all templates with up to 8 gates. The method first finds a quantum identities of 3 qubits, template matching is used to verify if the identity is a template. Experiments show the significance of templates the new to reduce the quantum costs of benchmark circuits.
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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