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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 approximation
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 that
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.
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 the
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.
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 $|w〉$
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 exactly
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.
Quantum Adiabatic Evolution Algorithms versus Simulated Annealing
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
A Quantum Algorithm for the Hamiltonian NAND Tree
TLDR
A quantum algorithm for the binary NAND tree problem in the Hamil- tonian oracle model using a continuous time quantum walk with a running time proportional to p N is given.
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