Learning is a criticai aspect of any intelligent cognitive system. How can this be done within a QIP approach? This is a relatively new field, but some progress has already been achieved (Ivancevic & Ivancevic, 2010). There are at least three ways to accomplish learning using quantum principles. One way is to update the agent's belief state based on experience (Schack et al ., 2001), as done in Bayesian learning models (Griffiths et al ., 2008). A second way is to update the weights in a unitary matrix using gradient descent of an error function (Zak & Williams, 1998), as done in connectionist learning models (Rumelhart & McClelland, 1986). A third way is to update the amplitudes assigned to control U gate actions based on rewards and punishments (Dong et al ., 2010), as done with reinforcement learning algorithms (Sutton & Barto, 1998). This chapter reviews all three approaches. Quantum state updating based on experience For the first type of quantum learning model, consider how to update an agent's belief state based on experience. In Chapter 4 we presented a quantum model for probability judgments, and in that chapter the initial belief state denoted |ψ⟩ was given or assumed to be already known in advance – when new facts were presented, inferences were made from the known state |ψ⟩ using Luder's rule. However, where does this initial state |ψ⟩ come from? Now we examine how this initial state |ψ⟩ can be learned or estimated from experience. Principles borrowed from quantum state tomography can be used to model the estimation of a quantum state (Schack et al ., 2001).
Learning is a criticai aspect of any intelligent cognitive system. How can this be done within a QIP approach? This is a relatively new field, but some progress has already been achieved (Ivancevic & Ivancevic, 2010). There are at least three ways to accomplish learning using quantum principles. One way is to update the agent's belief state based on experience (Schack et al ., 2001), as done in Bayesian learning models (Griffiths et al ., 2008). A second way is to update the weights in a unitary matrix using gradient descent of an error function (Zak & Williams, 1998), as done in connectionist learning models (Rumelhart & McClelland, 1986). A third way is to update the amplitudes assigned to control U gate actions based on rewards and punishments (Dong et al ., 2010), as done with reinforcement learning algorithms (Sutton & Barto, 1998). This chapter reviews all three approaches. Quantum state updating based on experience For the first type of quantum learning model, consider how to update an agent's belief state based on experience. In Chapter 4 we presented a quantum model for probability judgments, and in that chapter the initial belief state denoted |ψ⟩ was given or assumed to be already known in advance – when new facts were presented, inferences were made from the known state |ψ⟩ using Luder's rule. However, where does this initial state |ψ⟩ come from? Now we examine how this initial state |ψ⟩ can be learned or estimated from experience. Principles borrowed from quantum state tomography can be used to model the estimation of a quantum state (Schack et al ., 2001).
Introduction In many situations, learning from the results of measurements can be regarded as updating one's probability distributions over certain variables. According to Bayesians, this updating should be carried out according to the rule of conditionalization. In the theory of quantum mechanics, there is a rule that tells us how to update the state of a system, given observation of a measurement result. The state of a quantum system is closely related to probability distributions over potential measurements. Therefore we might expect there to be some relation between Bayesian conditionalization and the quantum state-update rule. There have been several suggestions that the state change just is Bayesian conditionalization, appropriately understood, or that it is closely analogous. Bub was the first to make the connection between quantum measurement and Bayesian conditionalization in a 1977 paper, using an approach based on quantum logic. The connection is renewed in discussions by Fuchs and also Jacobs in 2002, where again the analogy between the quantum state update and Bayesian conditionalization is pointed out. At the same time, Fuchs draws attention to a disanalogy – namely that there is an “extra unitary” transformation as part of the measurement in the quantum case. In this chapter, I will first review the proposals of Bub, Jacobs, and Fuchs. I will then show that the presence of the extra unitaries in quantum measurement leads to a difference between classical and quantum measurement in terms of information gain, drawing on results by Nielsen and Fuchs and Jacobs.
The astounding acceleration in Artificial Intelligence and Quantum Computing advances naturally gives rise to a line of research, which unrolls the potential advantages of quantum computing on classical Machine Learning tasks, known as Quantum Machine Learning or Quantum Machine Intelligence. The typical objectives are either (1) exploring the potential quantum advantages on classical learning tasks or (2) levering well-established classical ML algorithms to tackle quantum-related problems on Noisy Intermediate-Scale Quantum (NISQ) devices. Along the second research direction, we study Quantum Neural Networks (QNNs) to accomplish the purpose of Bayesian learning. By observing a wide range of studies on QNNs, in which the sole training method is based on frequentist training, we find that Bayesian learning benefits QNNs from two aspects. First, Bayesian-trained models enjoy a high level of generalization due to the prior and posterior distribution usage compared to frequentist training, which will be justified by this paper’s theoretical study of model capacity. Second, Bayesian Inference offers epistemic uncertainty estimation, which merits the decision-making process. It is worth mentioning that frequentist-trained QNNs generally lack this desirable property. Under the Bayesian training procedure, our derived models can be considered a new class of QNNs (called BayesianQNNs) which possesses both desirable properties of Bayesian Inference while maintaining comparable predictive performance as frequentist counterparts. The proposed Bayesian Quantum Neural Networks is justified by empirical evidence from numerical experiments.
The key approaches for machine learning, particularly learning in unknown probabilistic environments, are new representations and computation mechanisms. In this paper, a novel quantum reinforcement learning (QRL) method is proposed by combining quantum theory and reinforcement learning (RL). Inspired by the state superposition principle and quantum parallelism, a framework of a value-updating algorithm is introduced. The state (action) in traditional RL is identified as the eigen state (eigen action) in QRL. The state (action) set can be represented with a quantum superposition state, and the eigen state (eigen action) can be obtained by randomly observing the simulated quantum state according to the collapse postulate of quantum measurement. The probability of the eigen action is determined by the probability amplitude, which is updated in parallel according to rewards. Some related characteristics of QRL such as convergence, optimality, and balancing between exploration and exploitation are also analyzed, which shows that this approach makes a good tradeoff between exploration and exploitation using the probability amplitude and can speedup learning through the quantum parallelism. To evaluate the performance and practicability of QRL, several simulated experiments are given, and the results demonstrate the effectiveness and superiority of the QRL algorithm for some complex problems. This paper is also an effective exploration on the application of quantum computation to artificial intelligence.
Applying quantum computing techniques to machine learning has attracted widespread attention recently and quantum machine learning has become a hot research topic. There are three major categories of machine learning: supervised, unsupervised, and reinforcement learning (RL). However, quantum RL has made the least progress when compared to the other two areas. In this study, we implement the well-known RL algorithm Q learning with a quantum neural network and evaluate it in the grid world environment. RL is learning through interactions with the environment, with the aim of discovering a strategy to maximize the expected cumulative rewards. Problems in RL bring in unique challenges to the study with their sequential nature of learning, potentially long delayed reward signals, and large or infinite size of state and action spaces. This study extends our previous work on solving the contextual bandit problem using a quantum neural network, where the reward signals are immediate after each action.
Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT industry. In the last couple of years, researchers investigated if quantum computing can help to improve classical machine learning algorithms. Ideas range from running computationally costly algorithms or their subroutines efficiently on a quantum computer to the translation of stochastic methods into the language of quantum theory. This contribution gives a systematic overview of the emerging field of quantum machine learning. It presents the approaches as well as technical details in an accessable way, and discusses the potential of a future theory of quantum learning.
How can quantum theory be used to model human performance on complex information processing tasks? Quantum computing and quantum information theory is relatively new, but it is already a highly developed field (Nielsen and Chuang, 2000). The concept of a quantum computer was introduced by Feynman in 1982 (Feynman, 1982). Soon afterwards, a universal quantum computer was formulated by David Deutsch in 1989 using quantum gates, which he demonstrated could perform computations not possible with classic Turing machines, including generating genuine random numbers and performing parallel calculations within a single register. Subsequently, new quantum algorithms were discovered by Peter Schor in 1984 and Lov Grover in 1997 that could solve important computational problems, such as factoring and searching, faster than any known Turing machine. However, all of these accomplishments were designed for actual quantum computers, and only very small versions have been realized so far. Moreover, if we are not working under the assumption that the brain is a quantum computer, then what has all of this to do with information processing by humans? The answer is that quantum information processing theory provides new and powerful principles for modelling human performance. Currently, there are three general approaches to modelling information processing with humans. One is based on production rule systems such as used in Act-R (Anderson, 1993), EPIC (Meyer & Kieres, 1997), and Soar (Laird et al ., 1987); a second is neural network (Grossberg, 1982) and connectionist network (Rumelhart & McClelland, 1986) models; and a third is Bayesian models (Griffiths et al ., 2008).