منابع مشابه
3-local Hamiltonian is QMA-complete
It has been shown by Kitaev that the 5-local Hamiltonian problem is QMA-complete. Here we reduce the locality of the problem by showing that 3-local Hamiltonian is already QMA-complete.
متن کاملThe local Hamiltonian problem on a line with eight states is QMA-complete
The Local Hamiltonian problem – estimating the ground state energy of a local Hamiltonian – is a natural problem in physics, and belongs to the complexity class QMA. QMA is the quantum analogue of NP. Languages in QMA have a quantum verifier: a polynomial-time quantum algorithm that takes (poly-sized) quantum states as witnesses. In quantum mechanics, the Hamiltonian of a system is the Hermitia...
متن کاملConsistency of Local Density Matrices Is QMA-Complete
Suppose we have an n-qubit system, and we are given a collection of local density matrices ρ 1 ,. .. , ρ m , where each ρ i describes a subset C i of the qubits. We say that the ρ i are " consistent " if there exists some global state σ (on all n qubits) that matches each of the ρ i on the subsets C i. This generalizes the classical notion of the consistency of marginal probability distribution...
متن کاملThe Bose-Hubbard Model is QMA-complete
The Bose-Hubbard model is a system of interacting bosons that live on the vertices of a graph. The particles can move between adjacent vertices and experience a repulsive on-site interaction. The Hamiltonian is determined by a choice of graph that specifies the geometry in which the particles move and interact. We prove that approximating the ground energy of the Bose-Hubbard model on a graph a...
متن کاملTesting Non-isometry Is QMA-Complete
Determining the worst-case uncertainty added by a quantum circuit is shown to be computationally intractable. This is the problem of detecting when a quantum channel implemented as a circuit is close to a linear isometry, and it is shown to be complete for the complexity class QMA of verifiable quantum computation. The main idea is to relate the problem of detecting when a channel is close to a...
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ژورنال
عنوان ژورنال: Quantum Information and Computation
سال: 2003
ISSN: 1533-7146,1533-7146
DOI: 10.26421/qic3.3-7