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Circulant matrices are an important family of operators, which have a widerange of applications in science and engineering related fields. They are ingeneral non-sparse and non-unitary. In this paper, we present efficient quantumcircuits to implement circulant operators using fewer resources and with lowercomplexity than existing methods. Moreover, our quantum circuits can be readilyextended to the implementation of Toeplitz, Hankel, and block circulantmatrices. Efficient quantum algorithms to implement the inverses and productsof circulant operators are also provided.

Efficient quantum circuits for dense and non-unitary operators