2005/08/24 by David R. Mitchell, Mitchell, David R.
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0508177
5 pages, 2 figures
arxiv created 2005/08/24 · openalex publication_date 2005/08/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.