Quantum Computation by Adiabatic Evolution

Details Quantum Computation by Adiabatic Evolution Quantum Computation by Adiabatic Evolution

2000-01-28

arxiv.org/abs/quant-ph/0001106v1

Physics

Quantum Physics

24 pages, 12 figures, LaTeX, amssymb,amsmath, BoxedEPS packages; email to farhi@mit.edu

Scientific paper

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 interpolates between an initial Hamiltonian, whose ground state is easy to construct, and a final Hamiltonian, whose ground state encodes the satisfying assignment. To ensure that the system evolves to the desired final ground state, the evolution time must be big enough. The time required depends on the minimum energy difference between the two lowest states of the interpolating Hamiltonian. We are unable to estimate this gap in general. We give some special symmetric cases of the satisfiability problem where the symmetry allows us to estimate the gap and we show that, in these cases, our algorithm runs in polynomial time.

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