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Physical Review A

Neuromorphic quantum computation with energy dissipation

Mitsunaga Kinjo, Shigeo Sato, Yuuki Nakamiya, Koji Nakajima

Published Nov 23, 2005• 15 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.72.052328

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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 nnn-queen problem, which is one of the combinatorial optimization problems.
Farhi et al. have proposed an adiabatic quantum computation (AQC), which can be applied to NP-problems if one can know an appropriate Hamiltonian for a target problem. We have proposed a neuromorphic adiabatic quantum computation (NAQC) as the AQC with energy dissipation and an efficient method for designing a final Hamiltonian in consideration of the analogy with a neural network. The NAQC can be applied to optimization problems if its cost function can be expressed in a quadratic form. And successful operations have been confirmed by numerical simulations. In addition, local adiabatic evolution for quantum search have proposed by Roland et al. in order to speed-up the calculation time. In this paper, we show preliminary results for NAQC with local adiabatic evolution by numerical simulations.
An ANN(artificial neural network)-inspired quantum adiabatic evolution algorithm, which is a new quantum computation algorithm based on both the ANNlike method and the adiabatic Hamiltonian evolution, has been proposed for solving a combinatorial optimization problem. However, it has been known that the adiabatic evolution algorithm can not be applied to a quantum system with degenerated states during the evolution of a Hamiltonian. In order to remove this limitation, we propose an improved ANN-inspired algorithm with energy dissipation and discuss how to use this algorithm for solving an optimization problem.
A quantum computer employing a single quantum as a qubit executes real parallel computation. Several algorithms have been proposed for quantum computation. However, these algorithms are applicable only to a limited number of applications. Therefore, a general purpose algorithm should be studied and developed for practical use in the near future. We focus on the adiabatic evolution algorithm in order to incorporate an artificial neural network(ANN)-like method and discuss how to use this algorithm for solving an optimization problem.
Quantum computation algorithms indicate possibility that non-deterministic polynomial time problems can be solved much faster than classical methods. We have proposed a neuromorphic quantum computation algorithm based on adiabatic quantum computation, in which an analogy to an artificial neural network is considered in order to design a Hamiltonian. However, in the neuromorphic AQC, the relation between its computation time and success rate has not been clear. In this paper, we study residual energy and the probability of correct answers as a function of computation time. The residual energy behaves as expected from the adiabatic theorem. On the other hand, the success rate strongly depends on energy level crossings of excited states during Hamiltonian evolution. The results indicate that computation time must be adjusted according to a target problem.
A quantum computer employing a single quantum as a qubit executes real parallel computation and has various applications. Several algorithms have been proposed for quantum computation. However, these algorithms are applicable only to a limited number of applications. Therefore, a general purpose algorithm should be studied and developed for practical use in the near future. In this paper, we focus on the adiabatic evolution algorithm for general purpose quantum computation and discuss how to use this algorithm for solving an optimization problem. We show a new algorithm incorporating an artificial neural network (ANN)-like method in order to compose another Hamiltonian. The new algorithm is helpful for reducing computation cost and is easy to implement. Successful simulation results are shown.
The advantage of quantum mechanical dynamics in information processing has attracted much interest, and dedicated studies on quantum computation algorithms indicate that a quantum computer has remarkable computational power in certain tasks. Quantum properties such as quantum superposition and quantum tunneling are worth studying because they may overcome the weakness of gradient descent method in classical neural networks. Also, the technique established for neural networks can be useful for developing a quantum algorithm. In this chapter, first the authors show the effectiveness of incorporating quantum dynamics and then propose neuromorphic adiabatic quantum computation algorithm based on the adiabatic change of Hamiltonian. The proposed method can be viewed as one of complex-valued neural networks because a qubit operates like a neuron. Next, the performance of the proposed algorithm is studied by applying it to a combinatorial optimization problem. Finally, they discuss the learning ability and hardware implementation.