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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, Joshua M. Lapan, A. Lundgren, Daniel Preda
- Physics, MedicineScience
- 20 April 2001

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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 ScienceSTOC '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

An Example of the Difference Between Quantum and Classical Random Walks

- Andrew M. Childs, E. Farhi, S. Gutmann
- Mathematics, Computer ScienceQuantum Inf. Process.
- 6 March 2001

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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

A Quantum Algorithm for the Hamiltonian NAND Tree

- E. Farhi, J. Goldstone, S. Gutmann
- Mathematics, Computer ScienceTheory Comput.
- 14 February 2007

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