TY - GEN

T1 - Learning method for a quantum bit network

AU - Osakabe, Yoshihiro

AU - Sato, Shigeo

AU - Kinjo, Mitsunaga

AU - Nakajima, Koji

AU - Akima, Hisanao

AU - Sakuraba, Masao

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2016.

PY - 2016

Y1 - 2016

N2 - Quantum computing (QC) has attracted much attention due to its enormous computing power, but proposed algorithms so far are not sufficient for practical use. Therefore, if a quantum computer could obtain algorithms by itself, the applicable field of QC would be extended greatly. In this study, we investigate a learning method for a quantum bit network (QBN) by utilizing the analogy between an artificial neural network and a QBN as described in the previous reports [1, 2]. According to this analogy, we can relate a synaptic weight matrix with a Hamiltonian. We propose a quantum version of Hebb learning as follows; we enhance both excitatory and inhibitory couplings according to the probability that arbitrary two quantum bits (qubits) take the same or opposite states when a QBN outputs a desired pattern. As a first step, we trained a QBN shown in Fig. 1 to learn the XOR problem. We updated the Hamiltonian only when the hidden qubit took the state “1” in order to break symmetry because the network always learns a pair of symmetric patterns whether these patterns are desired or not. A typical successful learning result is shown in Fig. 2. Though the success rate of learning with various initial Hamiltonians reaches only 50%, this preliminary result indicates certain possibility for implementing learning function with a QBN.

AB - Quantum computing (QC) has attracted much attention due to its enormous computing power, but proposed algorithms so far are not sufficient for practical use. Therefore, if a quantum computer could obtain algorithms by itself, the applicable field of QC would be extended greatly. In this study, we investigate a learning method for a quantum bit network (QBN) by utilizing the analogy between an artificial neural network and a QBN as described in the previous reports [1, 2]. According to this analogy, we can relate a synaptic weight matrix with a Hamiltonian. We propose a quantum version of Hebb learning as follows; we enhance both excitatory and inhibitory couplings according to the probability that arbitrary two quantum bits (qubits) take the same or opposite states when a QBN outputs a desired pattern. As a first step, we trained a QBN shown in Fig. 1 to learn the XOR problem. We updated the Hamiltonian only when the hidden qubit took the state “1” in order to break symmetry because the network always learns a pair of symmetric patterns whether these patterns are desired or not. A typical successful learning result is shown in Fig. 2. Though the success rate of learning with various initial Hamiltonians reaches only 50%, this preliminary result indicates certain possibility for implementing learning function with a QBN.

KW - Hebb learning

KW - Quantum computing

UR - http://www.scopus.com/inward/record.url?scp=84987934968&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84987934968&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84987934968

SN - 9783319447773

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 558

EP - 559

BT - Artificial Neural Networks and Machine Learning - 25th International Conference on Artificial Neural Networks, ICANN 2016, Proceedings

A2 - Villa, Alessandro E.P.

A2 - Masulli, Paolo

A2 - Rivero, Antonio Javier Pons

PB - Springer Verlag

T2 - 25th International Conference on Artificial Neural Networks, ICANN 2016

Y2 - 6 September 2016 through 9 September 2016

ER -