Quantum computing and quadratically signed weight enumerators
Information Processing Letters
Quantum computation and quantum information
Quantum computation and quantum information
Feynman Lectures on Computation
Feynman Lectures on Computation
Adiabatic quantum state generation and statistical zero knowledge
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Complexity Limitations on Quantum Computation
COCO '98 Proceedings of the Thirteenth Annual IEEE Conference on Computational Complexity
Classical and Quantum Computation
Classical and Quantum Computation
Quantum information processing in continuous time
Quantum information processing in continuous time
Quantum Information Processing
The Complexity of the Local Hamiltonian Problem
SIAM Journal on Computing
A polynomial quantum algorithm for approximating the Jones polynomial
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
The Jones polynomial: quantum algorithms and applications in quantum complexity theory
Quantum Information & Computation
The complexity of quantum spin systems on a two-dimensional square lattice
Quantum Information & Computation
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We consider the following combinatorial problem. We are given three strings s, t, and t'of length L over some fixed finite alphabet and an integer m that is polylogarithmic inL. We have a symmetric relation on substrings of constant length that specifies whichsubstrings are allowed to be replaced with each other. Let Δ(n) denote the differencebetween the numbers of possibilities to obtain t from s, and t' from s after n ∈ Nreplacements. The problem is to determine the sign of Δ(m). As promises we have agap condition and a growth condition. The former states that |Δ(m)| ≥ εcm where ε isinverse polylogarithmic in L and c 0 is a constant. The latter is given by Δ(n) ≤ cnfor all n. We show that this problem is PromiseBQP-complete, i.e., it represents theclass of problems that can be solved efficiently on a quantum computer.