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

Quantum supremacy is demonstrated using a programmable superconducting processor known as Sycamore, taking approximately 200 seconds to sample one instance of a quantum circuit a million times, which would take a state-of-the-art supercomputer around ten thousand years to compute.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 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

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 work introduces a quantum neural network, QNN, that can represent labeled data, classical or quantum, and be trained by supervised learning, and shows through classical simulation that parameters can be found that allow the QNN to learn to correctly distinguish the two data sets.Expand

The application of the Google Sycamore superconducting qubit quantum processor to combinatorial optimization problems with the quantum approximate optimization algorithm (QAOA) is demonstrated and an approximation ratio is obtained that is independent of problem size and for the first time, that performance increases with circuit depth.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