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      Non-diagonal problem Hamiltonian for adiabatic quantum computation

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          Abstract

          Adiabatic quantum computation starts from embedding a computational problem into a Hamiltonian whose ground state encodes the solution to the problem. This problem Hamiltonian, \(H_{\rm p}\), is normally chosen to be diagonal in the computational basis, which is a product basis for qubits. We point out that \(H_{\rm p}\) can be chosen to be non-diagonal. To be more precise, we show how to construct \(H_{\rm p}\) in such a way that all its excited states are entangled with respect to the qubit tensor product structure, while the ground state is still of the product form and encodes the solution to the problem. We discuss how such non-diagonal problem Hamiltonians might improve the performance of the adiabatic quantum computation.

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          Most cited references 12

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          A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem

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            The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines

             Paul Benioff (1980)
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              Quantum Mechanical Models of Turing Machines That Dissipate No Energy

               Paul Benioff (1982)
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                Author and article information

                Journal
                23 November 2018
                Article
                1811.09453

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                quant-ph

                Quantum physics & Field theory

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