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A Quantum Approximate Optimization Algorithm
We introduce a quantum algorithm that produces approximate solutions for combinatorial optimization problems. The algorithm depends on a positive integer p and the quality of the approximationExpand
Quantum Computation by Adiabatic Evolution
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 thatExpand
Quantum supremacy using a programmable superconducting processor
TLDR
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
A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
TLDR
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
Quantum computation and decision trees
Many interesting computational problems can be reformulated in terms of decision trees. A natural classical algorithm is to then run a random walk on the tree, starting at the root, to see if theExpand
Exponential algorithmic speedup by a quantum walk
TLDR
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
Analog analogue of a digital quantum computation
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
Classification with Quantum Neural Networks on Near Term Processors
TLDR
A quantum neural network, QNN, that can represent labeled data, classical or quantum, and be trained by supervised learning, is introduced and it is shown through classical simulation that parameters can be found that allow the QNN to learn to correctly distinguish the two data sets. Expand
A Quantum Approximate Optimization Algorithm Applied to a Bounded Occurrence Constraint Problem
We apply our recent Quantum Approximate Optimization Algorithm to the combinatorial problem of bounded occurrence Max E3LIN2. The input is a set of linear equations each of which contains exactlyExpand
An Example of the Difference Between Quantum and Classical Random Walks
TLDR
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
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