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- W1956774414 abstract "A canonical result about satisfiability theory is that the 2-SAT problem can be solved in linear time, despite the NP-hardness of the 3-SAT problem. In the quantum 2-SAT problem, we are given a family of 2-qubit projectors $Pi_{ij}$ on a system of $n$ qubits, and the task is to decide whether the Hamiltonian $H=sum Pi_{ij}$ has a 0-eigenvalue, or it is larger than $1/n^alpha$ for some $alpha=O(1)$. The problem is not only a natural extension of the classical 2-SAT problem to the quantum case, but is also equivalent to the problem of finding the ground state of 2-local frustration-free Hamiltonians of spin $frac{1}{2}$, a well-studied model believed to capture certain key properties in modern condensed matter physics. While Bravyi has shown that the quantum 2-SAT problem has a classical polynomial-time algorithm, the running time of his algorithm is $O(n^4)$. In this paper we give a classical algorithm with linear running time in the number of local projectors, therefore achieving the best possible complexity." @default.
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- W1956774414 date "2015-08-25" @default.
- W1956774414 modified "2023-09-25" @default.
- W1956774414 title "Linear time algorithm for quantum 2SAT" @default.
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- W1956774414 doi "https://doi.org/10.48550/arxiv.1508.06340" @default.
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