Efficient quantum circuits for Schur and Clebsch-Gordan transforms

D Bacon, I Chuang, A W Harrow

Research output: Working paper

99 Citations (Scopus)


The Schur basis on n d-dimensional quantum systems is a generalization of the total angular momentum basis that is useful for exploiting symmetry under permutations or collective unitary rotations. We present efficient (size poly(n,d,log(1/\epsilon)) for accuracy \epsilon) quantum circuits for the Schur transform, which is the change of basis between the computational and the Schur bases. These circuits are based on efficient circuits for the Clebsch-Gordan transformation. We also present an efficient circuit for a limited version of the Schur transform in which one needs only to project onto different Schur subspaces. This second circuit is based on a generalization of phase estimation to any nonabelian finite group for which there exists a fast quantum Fourier transform.
Translated title of the contributionEfficient Quantum Circuits for Schur and Clebsch-Gordan Transforms
Original languageEnglish
PublisherUniversity of Bristol
Number of pages4
Publication statusPublished - 2004

Bibliographical note

Other identifier: CSTR-05-007


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