Improved Gap Estimates for Simulating Quantum Circuits by Adiabatic Evolution
Quantum Information Processing
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
A full characterization of quantum advice
Proceedings of the forty-second ACM symposium on Theory of computing
A study of heuristic guesses for adiabatic quantum computation
Quantum Information Processing
Testing non-isometry is QMA-complete
TQC'10 Proceedings of the 5th conference on Theory of quantum computation, communication, and cryptography
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
Commutative version of the local Hamiltonian problem and common eigenspace problem
Quantum Information & Computation
The complexity of stoquastic local Hamiltonian problems
Quantum Information & Computation
Locality bounds on hamiltonians for stabilizer codes
Quantum Information & Computation
The complexity of quantum spin systems on a two-dimensional square lattice
Quantum Information & Computation
Measuring 4-local qubit observables could probabilistically solve PSPACE
Quantum Information & Computation
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
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
Hardness of approximation for quantum problems
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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
ACM Transactions on Computation Theory (TOCT) - Special issue on innovations in theoretical computer science 2012
Efficient algorithms for universal quantum simulation
RC'13 Proceedings of the 5th international conference on Reversible Computation
The local Hamiltonian problem on a line with eight states is QMA-complete
Quantum Information & Computation
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The $k$-{\locHam} problem is a natural complete problem for the complexity class $\QMA$, the quantum analogue of $\NP$. It is similar in spirit to {\sc MAX-$k$-SAT}, which is $\NP$-complete for $k\geq 2$. It was known that the problem is $\QMA$-complete for any $k \geq 3$. On the other hand, 1-{\locHam} is in {\P} and hence not believed to be $\QMA$-complete. The complexity of the 2-{\locHam} problem has long been outstanding. Here we settle the question and show that it is $\QMA$-complete. We provide two independent proofs; our first proof uses only elementary linear algebra. Our second proof uses a powerful technique for analyzing the sum of two Hamiltonians; this technique is based on perturbation theory and we believe that it might prove useful elsewhere. Using our techniques we also show that adiabatic computation with 2-local interactions on qubits is equivalent to standard quantum computation.