Classical and Quantum Computation
Classical and Quantum Computation
The Complexity of the Local Hamiltonian Problem
SIAM Journal on Computing
Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation
SIAM Journal on Computing
The Power of Quantum Systems on a Line
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Computational Complexity
3-local Hamitonian is QMA-complete
Quantum Information & Computation
Minor-embedding in adiabatic quantum computation: I. The parameter setting problem
Quantum Information Processing
The detectability lemma and quantum gap amplification
Proceedings of the forty-first annual ACM symposium on Theory of computing
Spinto: high-performance energy minimization in spin glasses
Proceedings of the Conference on Design, Automation and Test in Europe
A study of heuristic guesses for adiabatic quantum computation
Quantum Information Processing
Complexity of Stoquastic Frustration-Free Hamiltonians
SIAM Journal on Computing
A promiseBQP-complete string rewriting problem
Quantum Information & Computation
Simplifying quantum double hamiltonians using perturbative gadgets
Quantum Information & Computation
The complexity of stoquastic local Hamiltonian problems
Quantum Information & Computation
Quantum Information & Computation
Consistency of local density matrices is QMA-Complete
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Complexity of commuting Hamiltonians on a square lattice of qubits
Quantum Information & Computation
QMA variants with polynomially many provers
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
The local Hamiltonian problem on a line with eight states is QMA-complete
Quantum Information & Computation
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The problem 2-LOCAL HAMILTONIAN has been shown to be complete for the quantumcomputational class QMA [1]. In this paper we show that this important problemremains QMA-complete when the interactions of the 2-local Hamiltonian are betweenqubits on a two-dimensional (2-D) square lattice. Our results are partially derived withnovel perturbation gadgets that employ mediator qubits which allow us to manipulatek-local interactions. As a side result, we obtain that quantum adiabatic computationusing 2-local interactions restricted to a 2-D square lattice is equivalent to the circuitmodel of quantum computation. Our perturbation method also shows how any stabilizerspace associated with a k-local stabilizer (for constant k) can be generated as anapproximate ground-space of a 2-local Hamiltonian.