dorsal/arxiv
View SchemaAdiabatic quantum algorithms as quantum phase transitions: first versus second order
| Authors | Ralf Schützhold, Gernot Schaller |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0608017 |
| URL | https://arxiv.org/abs/quant-ph/0608017 |
| DOI | 10.1103/PhysRevA.74.060304 |
Abstract
In the continuum limit (large number of qubits), adiabatic quantum algorithms display a remarkable similarity to sweeps through quantum phase transitions. We find that transitions of second or higher order are advantageous in comparison to those of first order. With this insight, we propose a novel adiabatic quantum algorithm for the solution of 3-satisfiability (3-SAT) problems (exact cover), which is significantly faster than previous proposals according to numerical simulations (up to 20 qubits). These findings suggest that adiabatic quantum algorithms can solve NP-complete problems such as 3-SAT much faster than the Grover search routine (yielding a quadratic enhancement), possibly even with an exponential speed-up. PACS: 03.67.-a, 03.67.Lx, 73.43.Nq, 64.70.-p.
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"abstract": "In the continuum limit (large number of qubits), adiabatic quantum algorithms\ndisplay a remarkable similarity to sweeps through quantum phase transitions. We\nfind that transitions of second or higher order are advantageous in comparison\nto those of first order. With this insight, we propose a novel adiabatic\nquantum algorithm for the solution of 3-satisfiability (3-SAT) problems (exact\ncover), which is significantly faster than previous proposals according to\nnumerical simulations (up to 20 qubits). These findings suggest that adiabatic\nquantum algorithms can solve NP-complete problems such as 3-SAT much faster\nthan the Grover search routine (yielding a quadratic enhancement), possibly\neven with an exponential speed-up. PACS: 03.67.-a, 03.67.Lx, 73.43.Nq,\n64.70.-p.",
"arxiv_id": "quant-ph/0608017",
"authors": [
"Ralf Sch\u00fctzhold",
"Gernot Schaller"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.74.060304",
"title": "Adiabatic quantum algorithms as quantum phase transitions: first versus second order",
"url": "https://arxiv.org/abs/quant-ph/0608017"
},
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