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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.

### Most cited references12

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

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### Quantum Mechanical Models of Turing Machines That Dissipate No Energy

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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