CHAPTER 1
Introduction
A robot is a physical hardware embodied agent, situated and operating in an uncertain and dynamic real-world environment [Matarić, 2007]. Typical robots have sensors by which they can perceive their environment’s state (as well as their own), manipulators for acting in and affecting their environment, electronic hardware capable of real-time computation and control, and sophisticated software algorithms.
The software algorithms are the “brains” of the robot, providing the principles for sensing, planning, acting, and learning with respect to the environment. These algorithms enable the robot to represent the joint robot-environment state and reason over sensor uncertainties and environment dynamics. A key hurdle to the development of more intelligent robotics has traditionally been computational tractability and scalability of algorithms. Robotic planning quickly becomes computationally infeasible for classical implementations as the time horizon for which an optimal plan must be formulated is increased. Classical robotic learning suffers from the curse of dimensionality. As dimensionality of sensor percept data increases and the hypothesis space over which it is interpreted becomes large, there exist fewer and fewer algorithms that can operate well to make sense of the sensor data while still being efficient.
The technological capabilities of classical robots are thus often pillared on fundamental development in systems and algorithms. Advances in sub-fields of robotics such as perception, planning, machine learning, and control push the intelligence periphery of what robots can do. The field of quantum robotics explores the applications of quantum principles to enhance software, hardware, and algorithmic capability in these areas.
1.1 WHAT DOES QUANTUM ROBOTICS STUDY?
Quantum robotics explores the application of the principles of quantum mechanics, quantum computing, quantum algorithms, and related fields to robotics. The quantum world is expected to provide many possible benefits to robot hardware and software intelligence capability.
Quantum computing theory predicts significant asymptotic speed ups in the worst-case time complexity for many classical algorithms used by robots to solve computational problems. Techniques such as quantum parallelism, Grover’s algorithm, and quantum adiabatic optimization may improve asymptotic performance on classically NP-complete computational problems for robots.
Qubit (“quantum bit”) representation of data is thought to be more scalable and power efficient than traditional binary bit representation of data. This may allow for gains in the processing of large amounts of data by robotic systems. While there are key limitations with storing and extracting data from a quantum memory, there are expected benefits even with the fundamental limitations. Whether the benefits are mostly for model building in offline mode or extend to real-time operation remains to be seen, but the potential for impact is surely there. In addition, the potential energy efficiency of quantum-scale circuitry and qubit hardware may bring down the power consumed by robotic systems.
Aside from providing potential computational software and hardware advantages for robots operating in classical environments, quantum approaches unlock new possibilities for robot sensing and control in environments governed by quantum dynamics. Quantum mechanical principles may be useful in engineering new quantum sensors and creating new quantum robot controllers that can operate on matter at a quantum scale. Many of the classical filtering algorithms (such as Kalman Filters or Hidden Markov Models) have quantum analogues and expected improvements in dealing with uncertainty, representational power, and with operating in quantum environments.
Quantum robotics is as much about science as it is engineering, and the emphasis of our field is on plausible science. Most quantum algorithms have highly specific conditions under which they work. Recognizing the rigorous scientific limitations of quantum methods is important for appropriate application in robotics.
1.2 AIM AND OVERVIEW OF OUR WORK
Our book serves as a roadmap for the emerging field of quantum robotics, summarizing key recent advances in quantum science and engineering and discussing how these maybe beneficial to robotics. We provide both a survey of the underlying theory (of quantum computing and quantum algorithms) as well as an overview of current experimental implementations being developed by academic and commercial research groups. Our aim is to provide a starting point for readers entering the world of quantum robotics and a guide for further exploration in sub-fields of interest. From reading our exposition, we hope that a better collective understanding of quantum robotics will emerge.
In general, our work is written for an audience familiar with robotic algorithms. While our book provides brief introductions to classical methods commonly used in robotic planning, learning, sensing, and control, the reader may wish to brush up on the prerequisites from other readily available robotic textbooks. Our work does not, however, presume any prior knowledge of quantum mechanics or quantum computing.
In Chapter 2, we provide background on relevant concepts in quantum mechanics and quantum computing that may be useful for quantum robotics. From there, the survey delves into key concepts in quantum search algorithms (Chapter 3) that are built on top of the quantum computing primitives. Speedups (and other algorithmic advantages) resulting from the quantum world are also investigated in the context of robot planning (Chapter 4), machine learning (Chapter 5), and robot controls and perception (Chapter 6). Our survey explores how algorithms commonly used for robots are expected to change when implemented with quantum mechanisms. We survey the literature for time and space complexity differences, key changes in underlying properties, and possible tradeoffs in scaling commonly used robotic techniques in quantum media. Our book also highlights some of the current implementations of quantum engineering mechanisms (Chapter 7) as well as current limitations. Finally, we conclude with a holistic summary of potential benefits to robotics from quantum mechanisms (Chapter 8).
1.3 QUANTUM OPERATING PRINCIPLES
Quantum approaches can be difficult to understand. Their mathematics can be quite nuanced and esoteric to the uninitiated reader. Even someone who is a talented robotics engineer and master of traditional mathematically intense robotic methods may struggle! To make quantum approaches easier to comprehend, our book boils each technique we discuss down to its essential Quantum Operating Principles (QOPs).
QOPs is a presentation style we introduce to make the assumptions of quantum approaches clearer. Many of the more sophisticated algorithms are really just applications of a few fundamental quantum principles.
Whenever we discuss a quantum improvement for a robot, we do so in relation to the classical techniques used in robotics. For the quantum technique, we attempt to highlight its fundamental QOPs and the potential advantages of the quantum technique to the classical method. At the end of each chapter, we also include a table of QOPs that different quantum methods discussed in the chapter use. We hope that these explanations will make the reader’s journey into quantum robotics smoother.
Quantum robotics (and quantum computing at large) are fields whose fundamentals are still in flux. They are exciting fields with daily new insights and discoveries. However, the best ways to engineer quantum systems are still being debated. Because of the rapid movement of the field, we believe that the best student of quantum robotics is one that understands the fundamental assumptions of different methods. If tomorrow a particular quantum theory were to accumulate more evidence, the algorithms and techniques based on it would be more likely to be used in the future for robots. Conversely, if a particular quantum theory is proven false, it is good to know which techniques in the literature will not pan out. Our goal with the QOPs breakdown is to help readers understand the spectra of possible truth in the quantum world, since there is not yet certainty.
In the next section, we introduce the basics of the current theory of quantum mechanics. Later sections will apply these QOP concepts to robotic search and planning, machine learning, sensing, and controls.