
An improved planar graph product structure theorem
Dujmović, Joret, Micek, Morin, Ueckerdt and Wood [J. ACM 2020] proved th...
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qTorch: The Quantum Tensor Contraction Handler
Classical simulation of quantum computation is necessary for studying th...
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Improved bounds for the excludedminor approximation of treedepth
Treedepth, a more restrictive graph width parameter than treewidth and p...
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ConstantDepth and SubcubicSize Threshold Circuits for Matrix Multiplication
Boolean circuits of McCullochPitts threshold gates are a classic model ...
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Classical algorithms for quantum mean values
We consider the task of estimating the expectation value of an nqubit t...
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Benchmarking treewidth as a practical component of tensornetworkbased quantum simulation
Tensor networks are powerful factorization techniques which reduce resou...
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Stabilizer Circuits, Quadratic Forms, and Computing Matrix Rank
We show that a form of strong simulation for nqubit quantum stabilizer ...
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Fast simulation of planar Clifford circuits
A general quantum circuit can be simulated in exponential time on a classical computer. If it has a planar layout, then a tensornetwork contraction algorithm due to Markov and Shi has a runtime exponential in the square root of its size, or more generally exponential in the treewidth of the underlying graph. Separately, Gottesman and Knill showed that if all gates are restricted to be Clifford, then there is a polynomial time simulation. We combine these two ideas and show that treewidth and planarity can be exploited to improve Clifford circuit simulation. Our main result is a classical algorithm with runtime scaling asymptotically as n^ω/2<n^1.19 which samples from the output distribution obtained by measuring all n qubits of a planar graph state in given Pauli bases. Here ω is the matrix multiplication exponent. We also provide a classical algorithm with the same asymptotic runtime which samples from the output distribution of any constantdepth Clifford circuit in a planar geometry. Our work improves known classical algorithms with cubic runtime. A key ingredient is a mapping which, given a tree decomposition of some graph G, produces a Clifford circuit with a structure that mirrors the tree decomposition and which emulates measurement of the quantum graph state corresponding to G. We provide a classical simulation of this circuit with the runtime stated above for planar graphs and otherwise n t^ω1 where t is the width of the tree decomposition. The algorithm also incorporates a matrixmultiplicationtime version of the GottesmanKnill simulation of multiqubit measurement on stabilizer states, which may be of independent interest.
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