Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Quantum computation and quantum information
Quantum computation and quantum information
Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Consistency of the Adiabatic Theorem
Quantum Information Processing
Finding cliques by quantum adiabatic evolution
Quantum Information & Computation
Quantum accuracy threshold for concatenated distance-3 codes
Quantum Information & Computation
Reversible logic synthesis of k-input, m-output lookup tables
Proceedings of the Conference on Design, Automation and Test in Europe
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Exploiting the similarity between adiabatic quantum algorithms and quantum phasetransitions, we argue that second-order transitions - typically associated with broken orrestored symmetries - should be advantageous in comparison to first-order transitions.Guided by simple examples we construct an alternative adiabatic algorithm for the NPcompleteproblem Exact Cover 3. We show numerically that its average performance (forthe considered cases up to O{20} qubits) is better than that of the conventional scheme.The run-time of adiabatic algorithms is not just determined by the minimum value of thefundamental energy gap (between the ground state and the exited states), but also byits curvature at the critical point. The proposed symmetry-restoring adiabatic quantumalgorithm only contains contributions linear and quadratic in the Pauli matrices and canbe generalized to other problem Hamiltonians which are decomposed of terms involvingone and two qubits. We show how the factoring problem can be cast into such a quadraticform. These findings suggest that adiabatic quantum algorithms can solve a large classof NP problems much faster than the Grover search routine (which corresponds to afirst-order transition and yields a quadratic enhancement only).