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IEEE International Symposium on Multiple-Valued Logic (ISMVL)

Speed-up of Neuromorphic Adiabatic Quantum Computation by Local Adiabatic Evolution

Mitsunaga Kinjo, Katsuhiko Shimabukuro

Published May 1, 2011• 1 citation
Publisher

Abstract

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.

DOI
10.1109/ismvl.2011.63

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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.
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.
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.
The training of neural networks (NNs) is a computationally intensive task requiring significant time and resources. This article presents a novel approach to NN training using adiabatic quantum computing (AQC), a paradigm that leverages the principles of adiabatic evolution to solve optimization problems. We propose a universal AQC method that can be implemented on gate quantum computers, allowing for a broad range of Hamiltonians and thus enabling the training of expressive neural networks. We apply this approach to various neural networks with continuous, discrete, and binary weights. The study results indicate that AQC can very efficiently evaluate the global minimum of the loss function, offering a promising alternative to classical training methods.
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.Request access from your librarian to read this chapter's full text.
QUBO problems are NP-hard and have wide applications in optimization, including finance, logistics, machine learning, and combinatorial problems. However, classical algorithms employed for solving them can often get stuck in local minima. This paper presents an Adiabatic Quantum Computing (AQC) approach towards finding an optimal solution for QUBO problems. The QUBO problem has been first encoded into Hamiltonians. The adiabatic theorem has been used to achieve success of an AQC solution with a rate which is found to be dependent on relative gap between the ground state and first exited state of the Hamiltonian.
The computation time in adiabatic quantum computing (AQC) is determined by the time limit of the adiabatic evolution, which in turn depends on the evolution path.In this research we have used the variational method to find an optimized path.For the simplest case involving a single qubit and for the most general path involving one or more independent interpolating functions, the result is path independent.This result does not change when there is an extra Hamiltonian term.We have also applied these two scenarios in AQC to a Hadamard gate.Adding an extra Hamiltonian gives a non-trivial result compared to the normal AQC, however it does not result in a speed-up.Moreover, we show that in these two scenarios we can choose an arbitrary path provided that it satisfies the boundary conditions.