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

This work devise a quantum-mechanical algorithm that evolves a state, initially localized at the root, through the tree, and proves that if the classical strategy succeeds in reaching level $n$ in time polynomial in $n,$ then so does the quantum algorithm.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

A black box graph traversal problem that can be solved exponentially faster on a quantum computer than on a classical computer is constructed and it is proved that no classical algorithm can solve the problem in subexponential time.Expand

We solve a problem, which while not fitting into the usual paradigm, can be viewed as a quantum computation. Suppose we are given a quantum system with a Hamiltonian of the form $E|w〉〈w|$ where $|w〉$… 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

A general definition of quantum random walks on graphs is discussed and with a simple graph the possibility of very different behavior between a classical random walk and its quantum analog is illustrated.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

Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or… Expand