Quantum computation and quantum information
Quantum computation and quantum information
Generic quantum Fourier transforms
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A polynomial quantum algorithm for approximating the Jones polynomial
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Computing with highly mixed states
Journal of the ACM (JACM)
The quantum Schur and Clebsch-Gordan transforms: I. efficient qudit circuits
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation
SIAM Journal on Computing
The Princeton Companion to Mathematics
The Princeton Companion to Mathematics
Quantum computation beyond the circuit model
Quantum computation beyond the circuit model
Estimating Jones and Homfly polynomials with one clean qubit
Quantum Information & Computation
Estimating Jones polynomials is a complete problem for one clean qubit
Quantum Information & Computation
The computational complexity of linear optics
Proceedings of the forty-third annual ACM symposium on Theory of computing
Classical simulation of dissipative fermionic linear optics
Quantum Information & Computation
Commuting quantum circuits: efficient classical simulations versus hardness results
Quantum Information & Computation
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In topological quantum computation the geometric details of a particle trajectory areirrelevant; only the topology matters. Taking this one step further, we consider a model ofcomputation that disregards even the topology of the particle trajectory, and computesby permuting particles. Whereas topological quantum computation requires anyons,permutational quantum computation can be performed with ordinary spin-1/2 particles,using a variant of the spin-network scheme of Marzuoli and Rasetti. We do not knowwhether permutational computation is universal. It may represent a new complexityclass within BQP. Nevertheless, permutational quantum computers can in polynomialtime approximate matrix elements of certain irreducible representations of the symmetricgroup and approximate certain transition amplitudes from the Ponzano-Regge spin foammodel of quantum gravity. No polynomial time classical algorithms for these problemsare known.