A Quantum Approximate Optimization Algorithm
- E. Farhi, J. Goldstone, S. Gutmann
- Computer Science, Mathematics
- 14 November 2014
A quantum algorithm that produces approximate solutions for combinatorial optimization problems that depends on a positive integer p and the quality of the approximation improves as p is increased, and is studied as applied to MaxCut on regular graphs.
Quantum Computation by Adiabatic Evolution
- E. Farhi, J. Goldstone, S. Gutmann, M. Sipser
- 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…
Quantum computation and decision trees
- E. Farhi, S. Gutmann
- Computer Science, Mathematics
- 27 June 1997
This work devise a quantum-mechanical algorithm that evolves a state, initially localized at the root, through the tree, and proves that if the classical strategy succeeds in reaching level $n$ in time polynomial in $n,$ then so does the quantum algorithm.
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, Computer ScienceScience
- 20 April 2001
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.
Exponential algorithmic speedup by a quantum walk
- Andrew M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, D. Spielman
- Computer ScienceSymposium on the Theory of Computing
- 24 September 2002
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
- E. Farhi, S. Gutmann
- 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 $|w〉$…
A Quantum Approximate Optimization Algorithm Applied to a Bounded Occurrence Constraint Problem
- E. Farhi, J. Goldstone, S. Gutmann
- Mathematics, Computer Science
- 18 December 2014
This paper applies the recent Quantum Approximate Optimization Algorithm to the combinatorial problem of bounded occurrence Max E3LIN2 and shows that the level one QAOA will efficiently produce a string that satisfies $\left(\frac{1}{2} + 1}{101 D^{1/2}\, l n\, D}\right)$ times the number of equations.
An Example of the Difference Between Quantum and Classical Random Walks
- Andrew M. Childs, E. Farhi, S. Gutmann
- Physics, MathematicsQuantum Information Processing
- 6 March 2001
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
- E. Farhi, J. Goldstone, S. Gutmann
- Physics
- 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…
Quantum Algorithms for Fixed Qubit Architectures
- E. Farhi, J. Goldstone, S. Gutmann, H. Neven
- Physics
- 17 March 2017
Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or…
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