TY - JOUR

T1 - Neuromorphic quantum computation with energy dissipation

AU - Kinjo, Mitsunaga

AU - Sato, Shigeo

AU - Nakamiya, Yuuki

AU - Nakajima, Koji

PY - 2005/11

Y1 - 2005/11

N2 - Real parallel computing with a quantum computer attracts vast interest due to its extreme high potential. We propose a neuromorphic quantum computation algorithm based on an adiabatic Hamiltonian evolution with energy dissipation. This algorithm can be applied to problems if a cost function can be expressed in a quadratic form. This requirement results from the fact that our Hamiltonian is designed by following a method similar to an artificial neural network (ANN). The state of an ANN is often trapped at local minima, and the network outputs an error. Since the state of a quantum system with the proposed algorithm is always in the ground state according to the adiabatic theorem, it is not necessary to be concerned that the quantum state is trapped at local minima. However, there is no guarantee that a quantum algorithm based on an adiabatic Hamiltonian evolution with degeneration or level crossing is successfully executed. We show successful numerical simulation results with the proposed algorithm by introducing energy dissipation to keep the quantum state staying in the ground state, and then we show an application to the n-queen problem, which is one of the combinatorial optimization problems.

AB - Real parallel computing with a quantum computer attracts vast interest due to its extreme high potential. We propose a neuromorphic quantum computation algorithm based on an adiabatic Hamiltonian evolution with energy dissipation. This algorithm can be applied to problems if a cost function can be expressed in a quadratic form. This requirement results from the fact that our Hamiltonian is designed by following a method similar to an artificial neural network (ANN). The state of an ANN is often trapped at local minima, and the network outputs an error. Since the state of a quantum system with the proposed algorithm is always in the ground state according to the adiabatic theorem, it is not necessary to be concerned that the quantum state is trapped at local minima. However, there is no guarantee that a quantum algorithm based on an adiabatic Hamiltonian evolution with degeneration or level crossing is successfully executed. We show successful numerical simulation results with the proposed algorithm by introducing energy dissipation to keep the quantum state staying in the ground state, and then we show an application to the n-queen problem, which is one of the combinatorial optimization problems.

UR - http://www.scopus.com/inward/record.url?scp=28844487482&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=28844487482&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.72.052328

DO - 10.1103/PhysRevA.72.052328

M3 - Article

AN - SCOPUS:28844487482

VL - 72

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 5

M1 - 052328

ER -