Classical and Quantum Computation
Classical and Quantum Computation
Complexity of Stoquastic Frustration-Free Hamiltonians
SIAM Journal on Computing
Commutative version of the local Hamiltonian problem and common eigenspace problem
Quantum Information & Computation
The complexity of stoquastic local Hamiltonian problems
Quantum Information & Computation
The complexity of quantum spin systems on a two-dimensional square lattice
Quantum Information & Computation
Commuting quantum circuits: efficient classical simulations versus hardness results
Quantum Information & Computation
Product-state approximations to quantum ground states
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Guest column: the quantum PCP conjecture
ACM SIGACT News
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We consider the computational complexity of Hamiltonians which are sums of commuting terms acting on plaquettes in a square lattice of qubits, and we show that deciding whether the ground state minimizes the energy of each local term individually is in the complexity class NP. That is, if the ground states has this property, this can be proven using a classical certificate which can be efficiently verified on a classical computer. Different to previous results on commuting Hamiltonians, our certificate proves the existence of such a state without giving instructions on how to prepare it.