Quantum computation of Fourier transforms over symmetric groups
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Generic quantum Fourier transforms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A new family of Cayley expanders (?)
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Applications of coherent classical communication and the schur transform to quantum information theory
Quantum Information & Computation
Synthesis of quantum-logic circuits
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Efficient Quantum Tensor Product Expanders and k-Designs
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Classical and quantum tensor product expanders
Quantum Information & Computation
Quantum Information & Computation
Exponential quantum speed-ups are generic
Quantum Information & Computation
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We give a simple recipe for translating walks on Cayley graphs of a group G into a quantum operation on any irrep of G. Most properties of the classical walk carry over to the quantum operation: degree becomes the number of Kraus operators, the spectral gap lower-bounds the gap of the quantum operation (viewed as a linear map on density matrices), and the quantum operation is efficient whenever the classical walk and the quantum Fourier transform on G are efficient. This means that using classical constantdegree constant-gap families of Cayley expander graphs on groups such as the symmetric group, we can construct efficient families of quantum expanders.