An algorithm to find quantum templates

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.