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- Publications
- Influence
A Quantum Approximate Optimization Algorithm
- E. Farhi, J. Goldstone, S. Gutmann
- Mathematics, Physics
- 14 November 2014
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… Expand
Quantum Computation by Adiabatic Evolution
- E. Farhi, J. Goldstone, S. Gutmann, M. Sipser
- Mathematics, Physics
- 28 January 2000
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
A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
- E. Farhi, J. Goldstone, S. Gutmann, J. Lapan, A. Lundgren, D. Preda
- Physics, Medicine
- Science
- 20 April 2001
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 of… Expand
Quantum computation and decision trees
- E. Farhi, S. Gutmann
- Physics
- 27 June 1997
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… Expand
Exponential algorithmic speedup by a quantum walk
- Andrew M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, D. Spielman
- Mathematics, Computer Science
- STOC '03
- 24 September 2002
TLDR
Analog analogue of a digital quantum computation
- E. Farhi, S. Gutmann
- Physics, Mathematics
- 6 December 1996
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
A Quantum Approximate Optimization Algorithm Applied to a Bounded Occurrence Constraint Problem
- E. Farhi, J. Goldstone, S. Gutmann
- Mathematics, Physics
- 18 December 2014
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… Expand
Quantum Adiabatic Evolution Algorithms versus Simulated Annealing
- E. Farhi, J. Goldstone, S. Gutmann
- Physics, Mathematics
- 8 January 2002
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
An Example of the Difference Between Quantum and Classical Random Walks
- Andrew M. Childs, E. Farhi, S. Gutmann
- Mathematics, Computer Science
- Quantum Inf. Process.
- 6 March 2001
TLDR
A Quantum Algorithm for the Hamiltonian NAND Tree
- E. Farhi, J. Goldstone, S. Gutmann
- Mathematics, Computer Science
- Theory Comput.
- 14 February 2007
TLDR