1. Introduction

Research on quantum neural machine learning has, until recently, mostly been a theoretical effort, anticipating a future where quantum computers would become available and sufficiently advanced to support quantum neural machine learning [1–5]. However, we now have quantum computers that are capable of implementing quantum artificial neural networks (QUANNs) experimentally, and one is able to access these computers via cloud. This brings QUANNs from the purely theoretical realm to the experimental realm, setting up the new stage for the expansion of quantum connectionism. In the current chapter, we address this issue, by implementing different QUANNs on IBM's quantum computers using the IBM Q Experience cloud-based access.

The chapter is divided into three sections. In Section 2, we address the basic properties of quantum neural computation, the connection with the quantum circuit computation model, and how different interpretations of quantum mechanics may address the basic computational dynamics involved.

In Section 3, we discuss how the IBM quantum computers can be considered QUANNs, illustrating with an example of a QUANN applied to the problem of the XOR Boolean function computation, implemented experimentally on two of IBM's devices (Section 3.1); afterward (Section 3.2), we turn to the experimental implementation of quantum robotics and quantum decision with a more complex form of quantum neural computation in the form of a variant of quantum neural reinforcement learning (QNRL), applied to a problem of decision under risk, where the agent must learn the optimal action that leads to the highest expected reward in a classical gamble.

The unit operator on the two-dimensional Hilbert space, spanned by the basis

ffiffi 2 p

� � (5)

<sup>2</sup> , using boldface letters to represent binary

<sup>2</sup> <sup>ν</sup> (6)

ν^j is ¼ sνj is , s ¼ 0, 1 (7)

<sup>H</sup>^ <sup>¼</sup> <sup>2</sup>πην^ (8)

ν^kj i s1s2…sd ¼ skνj i s1s2…sd (9)

ν^<sup>k</sup> (10)

skνj i s1s2…sd (11)

f g j i <sup>0</sup> ; j i<sup>1</sup> , is denoted by ^<sup>1</sup> <sup>¼</sup> j i <sup>0</sup> h j <sup>0</sup> <sup>þ</sup> j i<sup>1</sup> h j <sup>1</sup> which has the form of the identity

The Walsh-Hadamard transform unitary operator is, in turn, given by:

2 <sup>p</sup> <sup>¼</sup> <sup>1</sup>

We also use the usual notation for the ket vectors j i <sup>þ</sup> <sup>¼</sup> <sup>U</sup>^ WHj i <sup>0</sup> and

Besides the above notation, we denote the binary alphabet by A2 ¼ f g 0; 1 and

Using this notation, we are now ready to address some basic general properties

The basic computational unit of a QUANN is a neuron with a two-level firing

^ � <sup>σ</sup>^<sup>3</sup>

Therefore, the eigenvector 0j i corresponds to a neural activity where the firing frequency is 0 Hz, while the eigenvector 1j i corresponds to a neural activity where the firing frequency is 1 Hz. This means that there are two quantized energy levels associated with the artificial neuron, and these energy levels are obtained from the single neuron Hamiltonian, expressed in terms of the neural firing frequency oper-

Therefore, the eigenvector 0j i is associated with a neural firing energy level of 0 Joules, while the eigenvector 1j i is associated with a neural firing energy level of

For a neural network with d neurons, the neural firing activity can be addressed in terms of a neural field in the network, with the firing frequency field operators such that the k-th neuron neural firing operator ν^<sup>k</sup> obeys the eigenvalue equation:

and any pair of neural firing operators commute; that is, for k, l ¼ 1, 2, …, d,

ν^Tot ¼ ∑ d k¼1

> d k¼1

ν^k; ν^<sup>l</sup> ½ �¼ 0. Thus, the total neural firing frequency operator is given by:

which leads to the eigenvalue spectrum for the neural network:

ν^Totj i s1s2…sd ¼ ∑

<sup>ν</sup>^ <sup>¼</sup> <sup>1</sup>

<sup>U</sup>^ WH <sup>¼</sup> <sup>σ</sup>^<sup>1</sup> <sup>þ</sup> <sup>σ</sup>^<sup>3</sup> ffiffi

Quantum Neural Machine Learning: Theory and Experiments

DOI: http://dx.doi.org/10.5772/intechopen.84149

dynamics that can be described by the neural firing operator [5, 6]:

where ν is a neural firing frequency expressed in Hertz.

The eigenvectors for this operator are given by:

matrix.

j i � <sup>¼</sup> <sup>U</sup>^ WHj i<sup>1</sup> .

the set of d-length binary strings by A<sup>d</sup>

strings of length greater than 1.

of quantum neural computation.

ator as follows [5, 6]:

2πην Joules.

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The problem is first addressed in terms of the fundamental equations which employ quantum adaptive computation, namely quantum adaptive gates; then, we implement it experimentally on IBM's quantum computers and, afterward, we address the main Python code that was used to run the algorithm on these computers, thus, introducing quantum object-oriented programming (QOOP) and reflecting on its relevance for research on quantum artificial intelligence.

While, in Section 3.1, the main goal is to illustrate the implementation of QUANNs in a case where QUANNs exhibit a greater efficiency over classical ANNs, in Section 3.2, our main goal is not to address the speed-up of quantum algorithms over classical ones or even the greater efficiency of quantum algorithms over classical ones, but rather to provide for a reflection on the first steps for a possible future where quantum computation is incorporated in different (classical) robotic systems by way of the internet of things and cloud-based access to quantum devices, and the role that quantum adaptive computation may play in such a future.

In particular, in Section 3.2, we illustrate how a QUANN can become adaptive with respect to a problem that is given to it, in this case, a decision problem under risk, therefore, allowing us to address how QOOP can be employed to simulate an artificial agent, with a QUANN as its cognitive architecture, that must make a decision when presented a problem of classical decision under risk; therefore, our main goal in Section 3.2, from a computer science standpoint, is to address how a quantum artificially intelligent system decides when faced with a classical decision under risk problem, using QUANNs and QOOP.

In Section 4, we conclude with a chapter review and a reflection on future directions for cloud-based quantum-enabled technologies and QOOP.
