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IEICE Proceedings Series

Artificial Neural Network-inspired Quantum Adiabatic Evolution Algorithm with Energy Dissipation

Mitsunaga Kinjo, Shigeo Sato, Yuuki Nakamiya, Koji Nakajima

Published Oct 18, 2005• 0 citations
OpenAlex

Abstract

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.

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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.
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.
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.
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.
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.
The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.
There is increasing interest in quantum computing, because of its enormous computing potential. A small number of powerful quantum algorithms have been proposed to date; however, the development of new quantum algorithms for practical use remains essential. Parallel computing with a neural network has successfully realized certain unique functions such as learning and recognition; therefore, the introduction of certain neural computing techniques into quantum computing to enlarge the quantum computing application field is worthwhile. In this paper, a novel quantum associative memory (QuAM) is proposed, which is achieved with a quantum neural network by employing adiabatic Hamiltonian evolution. The memorization and retrieval procedures are inspired by the concept of associative memory realized with an artificial neural network. To study the detailed dynamics of our QuAM, we examine two types of Hamiltonians for pattern memorization. The first is a Hamiltonian having diagonal elements, which is known as an Ising Hamiltonian and which is similar to the cost function of a Hopfield network. The second is a Hamiltonian having non-diagonal elements, which is known as a neuro-inspired Hamiltonian and which is based on interactions between qubits. Numerical simulations indicate that the proposed methods for pattern memorization and retrieval work well with both types of Hamiltonians. Further, both Hamiltonians yield almost identical performance, although their retrieval properties differ. The QuAM exhibits new and unique features, such as a large memory capacity, which differs from a conventional neural associative memory.