This dissertation introduces a new type of quantum automata, their encoding and circuit realization. I concentrate on possible applications in robotics. Several methods and application of quantum automata and quantum circuit-based controllers for elementary robotic systems, with a focus on humanoid robot motion, emotion, and behavior generation are illustrated in detail. The research introduces several novel methodologies that bridge quantum computing principles with robotic control, aiming to overcome the limitations of classical deterministic and probabilistic approaches. The dissertation first presents a quantum-circuit-based framework for generating non-repetitive and expressive (e)motions in a humanoid robot actor, using superposition and entanglement to produce families of synchronized yet probabilistic behaviors. It then introduces a flowchart-based synthesis method for quantum automata using one-hot encoding, which significantly reduces quantum circuit cost by leveraging EXOR-based logic and restricting gate sets to NOT, CNOT, and Toffoli gates. Finally, the work expands into ternary quantum logic, developing hybrid quantum finite automata (QFA) using Chrestenson-family gates and uniformization ternary quantum gates, enabling more efficient pattern and language recognition with smaller state spaces. The key contributions of this dissertation are multifold. First, it presents the first practical implementation of a quantum-controlled humanoid robot for theatrical performance, demonstrating visually distinct, expressive, and entertaining behaviors that extend beyond the capabilities of classical control systems. Second, it introduces a direct synthesis methodology for quantum sequential circuits derived from high-level flowcharts, achieving up to a 95% reduction in quantum cost compared to existing design approaches. Third, the dissertation develops the generalized hybrid quantum finite automata (GHQFA), integrating ternary quantum logic with classical automata to enable complex pattern recognition and robotic gesture interpretation while requiring minimal quantum cost. Although the illustrative example of a robot car simulated in the CoppeliaSim environment is very simple based only on Chrestenson gates, the integration of all methods proposed herein establishes a foundation for controlling highly expressive humanoid robotic systems. Furthermore, the proposed models can be applied to real-world robotic tasks, including gesture recognition, motion synthesis, and adaptive behavior generation, with validation through both physical robotic performances and simulation studies. Finally, this work introduces an r-of-n encoding method that can enable to encode large machines for quantum circuits and can be integrated with the entanglement and superposition methods presented in this dissertation. This dissertation lays the groundwork for scalable and practical quantum-robotic systems, offering a pathway toward more intelligent, adaptive, and engaging robotic agents through quantum-enhanced control architectures.
This dissertation introduces a new type of quantum automata, their encoding and circuit realization. I concentrate on possible applications in robotics. Several methods and application of quantum automata and quantum circuit-based controllers for elementary robotic systems, with a focus on humanoid robot motion, emotion, and behavior generation are illustrated in detail. The research introduces several novel methodologies that bridge quantum computing principles with robotic control, aiming to overcome the limitations of classical deterministic and probabilistic approaches. The dissertation first presents a quantum-circuit-based framework for generating non-repetitive and expressive (e)motions in a humanoid robot actor, using superposition and entanglement to produce families of synchronized yet probabilistic behaviors. It then introduces a flowchart-based synthesis method for quantum automata using one-hot encoding, which significantly reduces quantum circuit cost by leveraging EXOR-based logic and restricting gate sets to NOT, CNOT, and Toffoli gates. Finally, the work expands into ternary quantum logic, developing hybrid quantum finite automata (QFA) using Chrestenson-family gates and uniformization ternary quantum gates, enabling more efficient pattern and language recognition with smaller state spaces. The key contributions of this dissertation are multifold. First, it presents the first practical implementation of a quantum-controlled humanoid robot for theatrical performance, demonstrating visually distinct, expressive, and entertaining behaviors that extend beyond the capabilities of classical control systems. Second, it introduces a direct synthesis methodology for quantum sequential circuits derived from high-level flowcharts, achieving up to a 95% reduction in quantum cost compared to existing design approaches. Third, the dissertation develops the generalized hybrid quantum finite automata (GHQFA), integrating ternary quantum logic with classical automata to enable complex pattern recognition and robotic gesture interpretation while requiring minimal quantum cost. Although the illustrative example of a robot car simulated in the CoppeliaSim environment is very simple based only on Chrestenson gates, the integration of all methods proposed herein establishes a foundation for controlling highly expressive humanoid robotic systems. Furthermore, the proposed models can be applied to real-world robotic tasks, including gesture recognition, motion synthesis, and adaptive behavior generation, with validation through both physical robotic performances and simulation studies. Finally, this work introduces an r-of-n encoding method that can enable to encode large machines for quantum circuits and can be integrated with the entanglement and superposition methods presented in this dissertation. This dissertation lays the groundwork for scalable and practical quantum-robotic systems, offering a pathway toward more intelligent, adaptive, and engaging robotic agents through quantum-enhanced control architectures.
Abstract Quantum automata can solve certain problems with a smaller state space than classical automata. We developed a quantum finite automaton using ternary rotation quantum gates and the Chrestenson family of ternary quantum gates. The main idea of this paper is to show how to combine rotation ternary quantum circuit-based Quantum Finite Automaton and quantum reversible circuit-based Deterministic Finite Automaton to build a more powerful machine. The combined machine can enable more complex language and pattern recognition. The developed quantum finite automaton and resulting combined machine can be used for robotics applications such as language, gesture, and motion recognition.
This study explores how quantum computing can reshape the intelligence, adaptability, and learning capacity of humanoid robotics. It examines how quantum principles such as superposition and entanglement allow robots to process and evaluate information in parallel, leading to faster, more flexible responses than those built on classical computing. The paper connects ideas from quantum machine learning (QML), quantum optimization, and quantum reinforcement learning (QRL) to practical scenarios in humanoid robotics, where rapid reasoning and context awareness are essential. Within a hybrid quantum-classical framework, the study outlines how these methods can enhance robotic perception, decision-making, and natural-language interaction, making cognitive robotics more adaptive in complex domains such as healthcare, manufacturing, and disaster response. Rather than presenting a full solution, this work defines a pathway for integrating quantum algorithms into real robotic architectures. The results indicate that combining quantum computing with humanoid robotics through hybrid quantum-classical systems could lead to a new stage of robotic intelligence machines able to handle uncertainty, learn continuously, and reason in ways that reflect deeper, more human-like awareness.
This textbook provides a comprehensive foundation for the emerging interdisciplinary field of quantum robotics. It systematically addresses the core question of how quantum computational principles can be formulated to address fundamental challenges in robotics: planning, optimization, perception, and control. The work is structured to build a rigorous bridge between the abstract mathematics of quantum information and the concrete computational problems of autonomous systems. The first part establishes the necessary foundations, introducing the computational models of quantum circuits alongside the classical formulations of robotic kinematics, dynamics, and state estimation. The second part is dedicated to quantum algorithmic primitives, with detailed exposition on quantum search, quantum linear algebra, and quantum optimization algorithms. Each algorithmic chapter explicitly maps these primitives to robotic problem classes, such as motion planning, sensor data processing, and trajectory optimization, discussing both potential advantages and current practical constraints. The third part focuses on system integration and forward-looking perspectives. It explores quantum machine learning models for robotic learning, outlines hybrid quantum-classical computer architectures required for real-world applications, and rigorously examines the ethical and societal implications of increasingly capable quantum-optimized autonomous systems. The textbook concludes with practical appendices detailing software tools, benchmark problems, and problem sets. Designed for graduate students and researchers in robotics, computer science, and quantum engineering, this book emphasizes clear problem formulation, realistic resource analysis, and verifiable claims. Its goal is to equip the next generation of scientists and engineers with the principles and critical perspective needed to advance the field beyond theoretical potential into practical, validated technology.
Quantum computing is an emerging technology that has the potential to change the perspectives and applications of computing in general. A wide range of applications are enabled: from faster algorithmic solutions of classically still difficult problems to theoretically more secure communication protocols. A quantum computer uses the quantum mechanical effects of particles or particle-like systems, and a major similarity between quantum and classical computers consists of both being abstracted as information processing machines. Whereas a classical computer operates on classical digital information, the quantum computer processes quantum information, which shares similarities with analog signals. One of the central differences between the two types of information is that classical information is more fault-tolerant when compared to its quantum counterpart. Faults are the result of the quantum systems being interfered by external noise, but during the last decades quantum error correction codes (QECC) were proposed as methods to reduce the effect of noise. Reliable quantum circuits are the result of designing circuits that operate directly on encoded quantum information, but the circuit’s reliability is also increased by supplemental redundancies, such as sub-circuit repetitions. Reliable quantum circuits have not been widely used, and one of the major obstacles is their vast associated resource overhead, but recent quantum computing architectures show promising scalabilities. Consequently the number of particles used for computing can be more easily increased, and that the classical control hardware (inherent for quantum computation) is also more reliable. Reliable quantum circuits haev been investigated for almost as long as general quantum computing, but their limited adoption (until recently) has not generated enough interest into their systematic design. The continuously increasing practical relevance of reliability motivates the present thesis to investigate some of the first answers to questions related to the background and the methods forming a reliable quantum circuit design stack. The specifics of quantum circuits are analysed from two perspectives: their probabilistic behaviour and their topological properties when a particular class of QECCs are used. The quantum phenomena, such as entanglement and superposition, are the computational resources used for designing quantum circuits. The discrete nature of classical information is missing for quantum information. An arbitrary quantum system can be in an infinite number of states, which are linear combinations of an exponential number of basis states. Any nontrivial linear combination of more than one basis states is called a state superposition. The effect of superpositions becomes evident when the state of the system is inferred (measured), as measurements are probabilistic with respect to their output: a nontrivial state superposition will collapse to one of the component basis states, and the measurement result is known exactly only after the measurement. A quantum system is, in general, composed from identical subsystems, meaning that a quantum computer (the complete system) operates on multiple similar particles (subsystems). Entanglement expresses the impossibility of separating the state of the subsystems from the state of the complete system: the nontrivial interactions between the subsystems result into a single indivisible state. Entanglement is an additional source of probabilistic behaviour: by measuring the state of a subsystem, the states of the unmeasured subsystems will probabilistically collapse to states from a well defined set of possible states. Superposition and entanglement are the building blocks of quantum information teleportation protocols, which in turn are used in state-of-the-art fault-tolerant quantum computing architectures. Information teleportation implies that the state of a subsystem is moved to a second subsystem without copying any information during the process. The probabilistic approach towards the design of quantum circuits is initiated by the extension of classical test and diagnosis methods. Quantum circuits are modelled similarly to classical circuits by defining gate-lists, and missing quantum gates are modelled by the single missing gate fault. The probabilistic approaches towards quantum circuits are facilitated by comparing these to stochastic circuits, which are a particular type of classical digital circuits. Stochastic circuits can be considered an emulation of analogue computing using digital components. A first proposed design method, based on the direct comparison, is the simulation of quantum circuits using stochastic circuits by mapping each quantum gate to a stochastic computing sub-circuit. The resulting stochastic circuit is compiled and simulated on FPGAs. The obtained results are encouraging and illustrate the capabilities of the proposed simulation technique. However, the exponential number of possible quantum basis states was translated into an exponential number of stochastic computing elements. A second contribution of the thesis is the proposal of test and diagnosis methods for both stochastic and quantum circuits. Existing verification (tomographic) methods of quantum circuits were targeting the reconstruction of the gate-lists. The repeated execution of the quantum circuit was followed by different but specific measurement at the circuit outputs. The similarities between stochastic and quantum circuits motivated the proposal of test and diagnosis methods that use a restricted set of measurement types, which minimise the number of circuit executions. The obtained simulation results show that the proposed validation methods improve the feasibility of quantum circuit tomography for small and medium size circuits. A third contribution of the thesis is the algorithmic formalisation of a problem encountered in teleportation-based quantum computing architectures. The teleportation results are probabilistic and require corrections represented as quantum gates from a particular set. However, there are known commutation properties of these gates with the gates used in the circuit. The corrections are not applied as dynamic gate insertions (during the circuit’s execution) into the gate-lists, but their effect is tracked through the circuit, and the corrections are applied only at circuit outputs. The simulation results show that the algorithmic solution is applicable for very large quantum circuits. Topological quantum computing (TQC) is based on a class of fault-tolerant quantum circuits that use the surface code as the underlying QECC. Quantum information is encoded in lattice-like structures and error protection is enabled by the topological properties of the lattice. The 3D structure of the lattice allows TQC computations to be visualised similarly to knot diagrams. Logical information is abstracted as strands and strand interactions (braids) represent logical quantum gates. Therefore, TQC circuits are abstracted using a geometrical description, which allows circuit input-output transformations (correlations) to be represented as geometric sub-structures. TQC design methods were not investigated prior to this work, and the thesis introduces the topological computational model by first analysing the necessary concepts. The proposed TQC design stack follows a top-down approach: an arbitrary quantum circuit is decomposed into the TQC supported gate set; the resulting circuit is mapped to a lattice of appropriate dimensions; relevant resulting topological properties are extracted and expressed using graphs and Boolean formulas. Both circuit representations are novel and applicable to TQC circuit synthesis and validation. Moreover, the Boolean formalism is broadened into a formal mechanism for proving circuit correctness. The thesis introduces TQC circuit synthesis, which is based on a novel logical gate geometric description, whose formal correctness is demonstrated. Two synthesis methods are designed, and both use a general planar representation of the circuit. Initial simulation results demonstrate the practicality and performance of the methods. An additional group of proposed design methods solves the problem of automatic correlation construction. The methods use validity criteria which were introduced and analysed beforehand in the thesis. Input-output correlations existing in the circuit are inferred using both the graph and the Boolean representation. The thesis extends the TQC state-of-the-art by recognising the importance of correlations in the validation process: correlation construction is used as a sub-routine for TQC circuit validation. The presented cross-layer validation procedure is useful when investigating both the QECC and the circuit, while a second proposed method is QECC-independent. Both methods are scalable and applicable even to very large circuits. The thesis completes with the analysis of TQC circuit identities, where the developed Boolean formalism is used. The proofs of former known circuit identities were either missing or complex, and the presented approach reduces the length of the proofs and represents a first step towards standardising them. A new identity is developed and detailed during the process of illustrating the known circuit identities. Reliable quantum circuits are a necessity for quantum computing to become reality, and specialised design methods are required to support the quest for scalable quantum computers. This thesis used a twofold approach towards this target: firstly by focusing on the probabilistic behaviour of quantum circuits, and secondly by considering the requirements of a promising quantum computing architecture, namely TQC. Both approaches resulted in a set of design methods enabling the investigation of reliable quantum circuits. The thesis contributes with the proposal of a new quantum simulation technique, no
Today's robots are controlled with classical computers that make decisions based on algorithms designed for a classical computing architecture.However, the amount of data increases continuously -a fact which pushes classical computers that control these robots to their limits.In comparison to classical computing, fundamentally different concepts of physics are the basis of quantum computing and thereby quantum computing has the potential to solve specific computational problems more efficiently.In addition to the aforementioned complications, the subgroup of robots that are subject to the research of this paper, namely humanoid robots, not only need more computational capacity but also require an algorithmic design based on a behavioral model which avoids causing antipathy when interacting with human beings.Using a real quantum computer with quantum phenomena such as superposition, entanglement, and quantum parallelism, new behavioral models and algorithms can be designed to improve human robot interaction and speed up machine learning processes.This paper promotes a hybrid-controlled robot using the combination of a classical computer-and quantum computer.With four quantum circuits to define a behavioral model and three different quantum machine learning algorithms we show the advantage of the hybrid-controlled robot.