dorsal/arxiv
View SchemaGeometric Phase Based Quantum Computation Applied to an NP-Complete Problem
| Authors | David R. Mitchell |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0508177 |
| URL | https://arxiv.org/abs/quant-ph/0508177 |
Abstract
We present a new approach to quantum computation involving the geometric phase. In this approach, an entire computation is performed by adiabatically evolving a suitably chosen quantum system in a closed circuit in parameter space. The problem solved is the determination of the solubility of a 3-SAT Boolean Satisfiability problem. The problem of non-adiabatic transitions to higher levels is addressed in several ways. The avoided level crossings are well defined and the interpolation can be slowed in this region, the Hamiltonian can be scaled with problem dimension resulting in a constant gap size and location, and the prescription here is sufficiently general as to allow for other suitably chosen Hamiltonians. Finally, we show that with $n$ applications of this approach, the geometric phase based quantum computation method may be used to find the solution to the 3-SAT problem in $n$ variables, a member of the NP-complete complexity class.
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"abstract": "We present a new approach to quantum computation involving the geometric\nphase. In this approach, an entire computation is performed by adiabatically\nevolving a suitably chosen quantum system in a closed circuit in parameter\nspace. The problem solved is the determination of the solubility of a 3-SAT\nBoolean Satisfiability problem. The problem of non-adiabatic transitions to\nhigher levels is addressed in several ways. The avoided level crossings are\nwell defined and the interpolation can be slowed in this region, the\nHamiltonian can be scaled with problem dimension resulting in a constant gap\nsize and location, and the prescription here is sufficiently general as to\nallow for other suitably chosen Hamiltonians. Finally, we show that with $n$\napplications of this approach, the geometric phase based quantum computation\nmethod may be used to find the solution to the 3-SAT problem in $n$ variables,\na member of the NP-complete complexity class.",
"arxiv_id": "quant-ph/0508177",
"authors": [
"David R. Mitchell"
],
"categories": [
"quant-ph"
],
"title": "Geometric Phase Based Quantum Computation Applied to an NP-Complete Problem",
"url": "https://arxiv.org/abs/quant-ph/0508177"
},
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