Quantum Physics, Artificial Intelligence and Natural Language Processing

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Introduction

“Three Bodies,” a prequel to the three-body problem described in the science fiction novel “Three Bodies, the Three-Body Problem, and Machine Learning Technology” describes a breakthrough in modern physics: quantum theory.

In this article, I would like to give an overview of this quantum theory and its relation to artificial intelligence technology.

Quantum Physics

Quantum Physics is one of the fields of physics developed to elucidate phenomena and behaviors that cannot be explained within the framework of classical mechanics, and it is a theory that describes physical phenomena at microscopic scales (such as atoms and molecules). The basic concepts and main principles of quantum physics are described below.

Wave-Particle Duality: Quantum physics recognizes the existence of both particle-like and wave-like properties of matter, light, and so on. This characteristic of the simultaneous appearance of properties distinguished in classical mechanics has given rise to a variety of interpretations.
Wave Function: The wave function is a mathematical expression of the state of a quantum system that is complex-valued and dependent on variables such as time and position. The square of the absolute value of the wave function is interpreted as a probability density, representing the probability that the quantum system is in a certain state.
State Vector: The state of a quantum system is represented by a state vector. The state vector corresponds to the wave function and evolves over time in the state space of the quantum system. The state vector is represented as a vector in Hilbert space.
Schrödinger Equation: The Schrödinger equation is the fundamental equation for describing the time evolution of a quantum system. The Schrödinger equation determines the time evolution of the wavefunction, which is expressed using the time-dependent Hamiltonian operator and the state vector (wavefunction).
Observation and stochasticity: Observation plays an important role in quantum physics. Observation causes the state of a quantum system to collapse and a specific state to be determined. Probabilistic results can also be obtained in quantum physics, and the square of the absolute value of the wavefunction is interpreted as the probability distribution of the measured result.

These are some of the fundamental concepts of quantum physics. Quantum physica is an important theory for understanding and elucidating various phenomena, such as the behavior of particles and atomic nuclei, the structure of matter, and the properties of light, and is also an important foundation for applications such as quantum computers and quantum communications.

Philosophy of Quantum Physics

The aforementioned features of wave-grain duality and observation and stochasticity have given rise to a variety of interpretations and positions on quantum physics. The main perspectives among them are discussed below.

Copenhagen Interpretation: The Copenhagen interpretation is one of the most common interpretations of quantum physics. In this interpretation, a physical system has no definite state until it is observed and collapses stochastically upon observation. The observer observes a probabilistic outcome by interacting with the physical system, but does not account for the internal details of the physical system. The Copenhagen interpretation focuses on the role of the observer and the outcome of the observation.
Multi-world interpretation: The multi-world interpretation, also discussed in “Possible Worlds, Logic, Probability, and Artificial Intelligence” is another popular interpretation of quantum physics, proposed by Hugo Veristraum and Hugh Everett. In this interpretation, the probabilistic collapses produced by observations do not occur; rather, different universes corresponding to the observations are considered to exist in parallel. In other words, all possibilities are assumed to be realized simultaneously and the observer branches off into each universe.
Reaction interpretation: The reaction interpretation holds that a physical system has a definite state before it is observed and that observation reveals this state. In this interpretation, the physical system’s interaction with an observer triggers a definite reaction. The reaction interpretation is an attempt to explain the results of the observation on the basis of more classical physical laws, instead of explaining stochastic decay.

Such an interpretation is not far removed from the idea of parallel worlds in the Muryōsutra and Amitabha Sutras and the idea of “emptiness” described in Zen thought, which is discussed in “Zen Thought and History, Mahayana Buddhism, Path Thought, and Christianity” Quantum physics is also an opportunity for a world where anything is possible, as described in “Possible Worlds, Logic, Probability, and Artificial Intelligence.

Quantum Physics and Artificial Intelligence Technology

Quantum physics and artificial intelligence technologies have attracted much attention in recent years for their connections. Below we discuss some of the perspectives.

Quantum Computing: Quantum computing is a technology that uses the principles of quantum physics to process information and eescribed in “Overview of Quantum Computers and Reference Information/Reference Books“. Quantum computing is a technology that uses the principles of quantum physics to process information, and differs from conventional computers in that it uses multi-state elements called qubits to perform calculations. While existing computers perform calculations based on two states (1 or 0), quantum computing can handle many states at once, and is expected to be applied to improving algorithms for artificial intelligence and solving advanced optimization problems.
Quantum Machine Learning: Quantum machine learning is an area of research that applies machine learning methods to quantum computers and quantum algorithms. Quantum machine learning techniques have the potential to enable more efficient learning and classification than conventional machine learning methods by taking advantage of the characteristics of quantum computers, and are expected to find faster and more efficient solutions for applications such as pattern recognition, optimization, and data analysis.
Quantum Sensing: Quantum sensing is a research area that utilizes the principles of quantum physics to realize highly sensitive sensing technology. This technology makes it possible to detect and measure minute changes and signals using quantum states and quantum effects, and in combination with artificial intelligence technology, is expected to lead to advanced processing such as sensor data analysis and pattern recognition, and to progress in application areas such as precision sensing and image recognition. This is expected to lead to advances in such application areas as precision sensing and image recognition.

Quantum Machine Learning and Quantum Algorithms

<Overview>

Quantum machine learning (QAM) is an area of research that combines ideas from quantum computing and quantum information processing with machine learning methods. QAM utilizes quantum algorithms and quantum data processing methods to achieve these goals.

<Quantum Algorithms>

Quantum Algorithms are algorithms that run on a quantum computer. Quantum computers have a different computational model from classical computers and use a basic unit of information called a qubit. Some representative quantum algorithms are described below.

Shor’s Algorithm: Shor’s algorithm is an algorithm for efficiently solving prime factorization problems. This algorithm has the potential to break the RSA cipher and some public key ciphers. Shor’s algorithm makes use of quantum computation concepts such as quantum Fourier transform and phase estimation.
Grover’s Algorithm: Grover’s algorithm is an algorithm for solving search problems at high speed. While classical search algorithms have a computational complexity of O(N), Grover’s algorithm has a computational complexity of O(√N), which makes it possible to efficiently find the desired data in a large database.
Algorithm for the Dual-Adaptivity Problem (Quantum Approximate Optimization Algorithm, QAOA): The dual-adaptivity problem is a type of optimization problem that is an approach with many practical applications. QAOA is a combinatorial optimization problem QAOA is an approximation algorithm for efficiently solving combinatorial optimization problems and can be used in conjunction with quantum annealing.

These quantum algorithms have different characteristics from classical algorithms and are expected to provide exponential speedups for certain problems, but to run these algorithms on real quantum computers, issues such as noise and error correction must be overcome, and they are still under research. However, to run these algorithms on an actual quantum computer, issues such as noise and error correction need to be overcome.

<Quantum Data Processing Methods>

Quantum data processing techniques refer to methods and techniques for manipulating, transforming, and controlling information on qubits in quantum information processing. Quantum data processing is an essential element in the realization of quantum algorithms and quantum computers, which aim to process quantum information in an efficient and reliable manner. Some typical quantum data processing methods are described below.

Quantum gating operations: Quantum gating is a fundamental technique for performing certain operations on qubits. Quantum gate operations are used to transform the state of a qubit or to control the interaction between qubits. Common quantum gates include Adamar gates, phase gates, and CNOT gates.
Quantum Measurement: Quantum measurement can be a technique to measure the state of a qubit in a particular basis and obtain the result. Quantum measurement is an important element in converting the state of a qubit into classical information and is used to verify the state of a qubit or to obtain the output of a quantum algorithm.
Quantum Entanglement: Quantum entanglement can be a method of interconnecting multiple qubits to create a combinatorial state. Entanglement is a powerful property of quantum computing, an approach that exploits correlations between qubits to enable parallel computation and high-speed information transfer.
Quantum Error Correction: Quantum bits are very sensitive to noise and errors, and quantum error correction refers to the development of methods and protocols to reduce errors. Quantum error correction includes quantum error correcting codes and quantum error correction algorithms.

<Other Quantum Machine Learning Approaches>

There are several other approaches to quantum machine learning in addition to those listed above, including

Quantum Reinforcement Learning: Quantum reinforcement learning is a method of applying the framework of reinforcement learning on a quantum computer. Reinforcement learning learns optimal behavior through an agent that learns by interacting with its environment. Quantum reinforcement learning uses quantum states and quantum gates to achieve fast learning and optimal policy discovery.
Quantum Supervised Learning: Quantum supervised learning is a generalization of classical supervised learning. While supervised learning uses labeled training data to build predictive models for unknown input data, quantum supervised learning aims to use quantum states or quantum gates as training data and apply quantum algorithms to build predictive models.
Quantum clustering: Quantum clustering can be a method for automatically grouping data. Usually, clustering is based on data similarity, but quantum clustering uses quantum states and quantum algorithms to perform clustering.

Quantum Physics and Natural Language Processing

Quantum physics and Natural Language Processing (NLP) are two different fields, but their connection has recently attracted attention in some research and applications. The relationship between quantum physics and natural language processing is described below.

<Quantum Language Modeling>

Quantum language modeling is a method of modeling and representing natural language by applying the principles of quantum physics. Unlike classical ideas based on conventional statistical language models (e.g., n-gram models and Transformer models described in “Overview of Transformer Models, Algorithms, and Examples of Implementations“), quantum language modeling uses quantum states and quantum operations to represent the meaning and structure of sentences, and is expected to capture more complex semantic relations and statistical properties of sentences. It is expected to capture more complex semantic relations and statistical properties of sentences.

In quantum language modeling, sentences and documents are treated as representations of quantum states, and quantum bit manipulations and quantum algorithms are used to construct language models, and a specific approach is to use quantum circuits to learn statistical patterns in sentences. A quantum circuit is a circuit that processes information by applying gate operations to qubits. In language modeling, quantum circuits are constructed to design quantum gates and take advantage of interactions between qubits in order to capture statistical patterns in sentences.

Quantum language modeling also makes it possible to use quantum algorithms to perform fast language processing. This would be, for example, using quantum phase estimation, one of the quantum algorithms, to efficiently detect specific patterns or grammatical rules in sentences, or applying quantum annealing to perform semantic analysis of sentences.

<Quantum Word Embeddings (QWE)>

Quantum Word Embeddings is a method of encoding the semantic representation of words and text using a quantum computing framework. While in ordinary natural language processing, words are embedded in a vector space, and words are mapped to the vector space to express meaning and relationships numerically, The meaning and relevance of words are represented by quantum states and quantum operations. This is expected to yield a richer semantic representation than conventional word embedding methods.

There are several methods of quantum word embedding. One approach is to represent a word as a state of qubits, for example, using n qubits to represent 2^n different states. According to this, each word is encoded in the state of these qubits, and the semantic similarity or association between words can be calculated based on their states.

Quantum word embedding can be applied to text processing and natural language processing tasks in the same way as regular word embedding. For example, by using quantum word embedding to calculate semantic similarity, it is possible to ascertain word relatedness and to use it for document classification and retrieval.

<Faster NLP Tasks Using Quantum Algorithms>

The aforementioned quantum algorithms may be used to achieve speedup and efficiency in some NLP tasks. This includes, for example, using quantum machines to accelerate processes such as search, classification, summarization, and clustering. The possibility of taking advantage of the characteristics of quantum algorithms to solve natural language processing tasks that are difficult for conventional algorithms is also being considered.

<Quantum Information Theory and Information Entropy>

Quantum information theory and information entropy are fundamental theories in the computation and transfer of information, but they also play an important role in natural language processing. This means, for example, that information entropy can be used to evaluate language models and calculate the amount of information, and the application of concepts and methods from quantum information theory is expected to create new perspectives and methods for processing and analyzing information.

These are still in the early stages of research with regard to quantum physics and natural language processing at this point, and there are no specific methods or techniques directly applying quantum physics that have been put into practical use. However, there is interest in the connection between the two, and future research and technological advances could lead to new developments and applications.

Reference Information and Reference Books

For more information on quantum computers, see “Overview of Quantum Computers and Reference Information/Reference Books. The National Institute of Informatics (NII) of the Research Organization of Information and Systems (RISO), an Inter-University Research Institute, has built a database of educational materials containing various contents related to quantum technology, such as diagrams, graphs, exercises, and program codes, and has made it available as the Quantum Technology Education Center for Advanced Studies. The database is open to the public as a center for advanced education in quantum technology.

As a reference book, a general reading is “Gendai Shiso, February 2020, Special Issue = Quantum Computers – A New Paradigm for Information Science and Technology“.

“Machine Learning with Quantum Computers”

“Quantum Computer Science: An Introduction“