A new connection between quantum circuits, graphs and the Ising partition function
Quantum Information Processing
Limiting negations in bounded treewidth and upward planar circuits
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Quantum Computation and the Evaluation of Tensor Networks
SIAM Journal on Computing
Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design
Quantum Information Processing
Classical simulation of quantum computation, the Gottesman-Knill theorem, and slightly beyond
Quantum Information & Computation
Simulating quantum computers with probabilistic methods
Quantum Information & Computation
Constant-optimized quantum circuits for modular multiplication and exponentiation
Quantum Information & Computation
A complete dichotomy rises from the capture of vanishing signatures: extended abstract
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Quantum Information & Computation
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The treewidth of a graph is a useful combinatorial measure of how close the graph is to a tree. We prove that a quantum circuit with $T$ gates whose underlying graph has a treewidth $d$ can be simulated deterministically in $T^{O(1)}\exp[O(d)]$ time, which, in particular, is polynomial in $T$ if $d=O(\log T)$. Among many implications, we show efficient simulations for log-depth circuits whose gates apply to nearby qubits only, a natural constraint satisfied by most physical implementations. We also show that one-way quantum computation of Raussendorf and Briegel (Phys. Rev. Lett., 86 (2001), pp. 5188-5191), a universal quantum computation scheme with promising physical implementations, can be efficiently simulated by a randomized algorithm if its quantum resource is derived from a small-treewidth graph with a constant maximum degree. (The requirement on the maximum degree was removed in [I. L. Markov and Y. Shi, preprint:quant-ph/0511069].)