A quantum algorithm that produces approximate solutions for combinatorial optimization problems that depends on a positive integer p and the quality of the approximation improves as p is increased, and is studied as applied to MaxCut on regular graphs.Expand

We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that… Expand

For the small examples that the authors could simulate, the quantum adiabatic algorithm worked well, providing evidence that quantum computers (if large ones can be built) may be able to outperform ordinary computers on hard sets of instances of NP-complete problems.Expand

This work considers an alternative search algorithm based on a continuous-time quantum walk on a graph and shows that full {radical}(N) speedup can be achieved on a d-dimensional periodic lattice for d>4.Expand

A method is proposed to calculate quantum numbers on solitons in quantum field theory. The method is checked on previously known examples and, in a special model, by other methods. It is found, for… Expand

This paper applies the recent Quantum Approximate Optimization Algorithm to the combinatorial problem of bounded occurrence Max E3LIN2 and shows that the level one QAOA will efficiently produce a string that satisfies $\left(\frac{1}{2} + 1}{101 D^{1/2}\, l n\, D}\right)$ times the number of equations.Expand

SummaryThe conditions for the existence of non-perturbative type « superconductor » solutions of field theories are examined. A non-covariant canonical transformation method is used to find such… Expand

We explain why quantum adiabatic evolution and simulated annealing perform similarly in certain examples of searching for the minimum of a cost function of n bits. In these examples each bit is… Expand