• Publications
  • Influence
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
  • 603
  • 105
  • PDF
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
  • 849
  • 78
  • PDF
A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
A quantum system will stay near its instantaneous ground state if the Hamiltonian that governs its evolution varies slowly enough. This quantum adiabatic behavior is the basis of a new class ofExpand
  • 1,179
  • 59
  • PDF
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
  • 734
  • 47
  • PDF
Exponential algorithmic speedup by a quantum walk
TLDR
We construct a black box graph traversal problem that can be solved exponentially faster on a quantum computer than on a classical computer. Expand
  • 601
  • 34
  • PDF
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
  • 263
  • 26
  • PDF
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
  • 100
  • 12
  • PDF
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 isExpand
  • 97
  • 12
  • PDF
An Example of the Difference Between Quantum and Classical Random Walks
TLDR
A general definition of quantum random walks on graphs and illustrate with a simple graph the possibility of very different behavior between a classical random walk and its quantum analog. Expand
  • 319
  • 11
  • PDF
A Quantum Algorithm for the Hamiltonian NAND Tree
TLDR
We give a quantum algorithm for the binary NAND tree problem in the Hamil- tonian oracle model. Expand
  • 247
  • 8
  • PDF