On the Satisfiability of Quantum Circuits of Small Treewidth

Oliveira, Mateus de Oliveira

doi:10.1007/978-3-319-20297-6_11

Cited by 2 publications

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“…The notion of treewidth has also caught attention from the circuit complexity community due to the fact that the satisfiability of read-once 1 Boolean circuits of constant treewidth can be determined in polynomial time [1,2,5,13,14,16,18]. Recently, nearquadratic lower bounds were shown for Boolean circuits of constant treewidth [9]. In the context of quantum computation, it has been shown that the satisfiability of read-once quantum circuits of constant treewidth can be determined in polynomial time [9].…”

Section: Introductionmentioning

confidence: 99%

“…Recently, nearquadratic lower bounds were shown for Boolean circuits of constant treewidth [9]. In the context of quantum computation, it has been shown that the satisfiability of read-once quantum circuits of constant treewidth can be determined in polynomial time [9]. Additionally, in a pioneering result, Markov and Shi have shown that quantum circuits of constant treewidth can be simulated with multiplicative precision in polynomial time [21].…”

Section: Introductionmentioning

confidence: 99%

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A Near-Quadratic Lower Bound for the Size of Quantum Circuits of Constant Treewidth

Oliveira

2018

Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms

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We show that any quantum circuit of treewidth t, built from r-qubit gates, requires at least Ω( ]. The proof of our lower bound follows by an extension of Nečiporuk's method to the context of quantum circuits of constant treewidth. This extension is made via a combination of techniques from structural graph theory, tensor-network theory, and the connected-component counting method, which is a classic tool in algebraic geometry. In particular, an essential key to proving our lower bound is the development of a new algorithm for tensor network contraction which may be of independent interest.

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