Quantum computation of Fourier transforms over symmetric groups
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
Classical and Quantum Computation
Classical and Quantum Computation
Decoherence, control, and symmetry in quantum computers
Decoherence, control, and symmetry in quantum computers
Generic quantum Fourier transforms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A Subexponential-Time Quantum Algorithm for the Dihedral Hidden Subgroup Problem
SIAM Journal on Computing
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Proceedings of the 2005 Asia and South Pacific Design Automation Conference
Applications of coherent classical communication and the schur transform to quantum information theory
Simple construction of quantum universal variable-length source coding
Quantum Information & Computation
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IEEE Transactions on Information Theory
Remote preparation of quantum states
IEEE Transactions on Information Theory
Weak Fourier-Schur sampling, the hidden subgroup problem, and the quantum collision problem
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Permutational quantum computing
Quantum Information & Computation
How a Clebsch-Gordan transform helps to solve the Heisenberg hidden subgroup problem
Quantum Information & Computation
Synthesis of quantum circuits for d-level systems by using cosine-sine decomposition
Quantum Information & Computation
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We present an efficient family of quantum circuits for a fundamental primitive in quantum information theory, the Schur transform. The Schur transform on n d-dimensional quantum systems is a transform between a standard computational basis to a labelling related to the representation theory of the symmetric and unitary groups. If we desire to implement the Schur transform to an accuracy of ε-1, then our circuit construction uses a number of gates which is polynomial in n, d and log(ε-1). The key tool in our construction is a poly(d, log n, log(ε-1)) algorithm for the ud Clebsch-Gordan transform. Our efficient circuit construction renders numerous protocols in quantum information theory computationally tractable and yields a new possible approach to quantum algorithms which is distinct from the standard paradigm of the quantum Fourier transform.