dorsal/arxiv
View SchemaQuantum Computation by Adiabatic Evolution
| Authors | Edward Farhi, Jeffrey Goldstone, Sam Gutmann, Michael Sipser |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0001106 |
| URL | https://arxiv.org/abs/quant-ph/0001106 |
Abstract
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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"abstract": "We give a quantum algorithm for solving instances of the satisfiability\nproblem, based on adiabatic evolution. The evolution of the quantum state is\ngoverned by a time-dependent Hamiltonian that interpolates between an initial\nHamiltonian, whose ground state is easy to construct, and a final Hamiltonian,\nwhose ground state encodes the satisfying assignment. To ensure that the system\nevolves to the desired final ground state, the evolution time must be big\nenough. The time required depends on the minimum energy difference between the\ntwo lowest states of the interpolating Hamiltonian. We are unable to estimate\nthis gap in general. We give some special symmetric cases of the satisfiability\nproblem where the symmetry allows us to estimate the gap and we show that, in\nthese cases, our algorithm runs in polynomial time.",
"arxiv_id": "quant-ph/0001106",
"authors": [
"Edward Farhi",
"Jeffrey Goldstone",
"Sam Gutmann",
"Michael Sipser"
],
"categories": [
"quant-ph"
],
"title": "Quantum Computation by Adiabatic Evolution",
"url": "https://arxiv.org/abs/quant-ph/0001106"
},
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