Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
Complexity: knots, colourings and counting
Complexity: knots, colourings and counting
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Quantum algorithms for solvable groups
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Quantum algorithms for some hidden shift problems
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Exponential algorithmic speedup by a quantum walk
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Classical and Quantum Computation
Classical and Quantum Computation
Approximate Counting and Quantum Computation
Combinatorics, Probability and Computing
A Subexponential-Time Quantum Algorithm for the Dihedral Hidden Subgroup Problem
SIAM Journal on Computing
Polynomial-time quantum algorithms for Pell's equation and the principal ideal problem
Journal of the ACM (JACM)
Inapproximability of the Tutte polynomial
Information and Computation
Simulating Quantum Computation by Contracting Tensor Networks
SIAM Journal on Computing
A Polynomial Quantum Algorithm for Approximating the Jones Polynomial
Algorithmica - Special Issue: Quantum Computation; Guest Editors: Frédéric Magniez and Ashwin Nayak
The Jones polynomial: quantum algorithms and applications in quantum complexity theory
Quantum Information & Computation
Estimating Jones polynomials is a complete problem for one clean qubit
Quantum Information & Computation
A new connection between quantum circuits, graphs and the Ising partition function
Quantum Information Processing
Simulating quantum computers with probabilistic methods
Quantum Information & Computation
Quantum algorithms for invariants of triangulated manifolds
Quantum Information & Computation
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We present a quantum algorithm that additively approximates the value of a tensor network to a certain scale. When combined with existing results, this provides a complete problem for quantum computation. The result is a simple new way of looking at quantum computation in which unitary gates are replaced by tensors and time is replaced by the order in which the tensor network is “swallowed.” We use this result to derive new quantum algorithms that approximate the partition function of a variety of classical statistical mechanical models, including the Potts model.