Contents

Preface

Acknowledgments

Notation

1Introduction

1.1What does Quantum Robotics Study?

1.2Aim and Overview of our Work

1.3Quantum Operating Principles

2Relevant Background on Quantum Mechanics

2.1Qubits and Superposition

2.2Quantum States and Entanglement

2.3Schrödinger Equation and Quantum State Evolution

2.4Quantum Logic Gates and Circuits

2.4.1Reversible Computing and Landauer’s Principle

2.4.2Notable Quantum Gates

2.4.3Quantum Circuit for Fast Fourier Transform

2.5Quantum Computing Mechanisms

2.5.1Quantum Parallelism

2.5.2Challenges with Quantum Parallelism

2.5.3Grover’s Search Algorithm

2.5.4Adiabatic Quantum Optimization

2.5.5Adiabatic Hardware and Speedups

2.5.6Shor’s Quantum Factorization Algorithm

2.5.7Quantum Teleportation

2.6Quantum Operating Principles (QOPs) Summary

2.7Chapter Summary

3Quantum Search

3.1Uninformed Grover Tree Search

3.2Informed Quantum Tree Search

3.3Application of Quantum Annealing to STRIPS Classical Planning

3.3.1Classical STRIPS Planning

3.3.2Application of Quantum Annealing to STRIPS Planning

3.4Chapter Summary

4Quantum Agent Models

4.1Classical Markov Decision Processes

4.2Classical Partially Observable Markov Decision Processes

4.3Quantum Superoperators

4.4Quantum MDPs

4.5QOMDPs

4.6Classical Reinforcement Learning Models

4.6.1Projection Simulation Agents

4.6.2Reflective Projection Simulation Agents

4.7Quantum Agent Learning

4.8Multi-armed Bandit Problem and Single Photon Decision Maker

4.9Chapter Summary

5Machine Learning Mechanisms for Quantum Robotics

5.1Quantum Operating Principles in Quantum Machine Learning

5.1.1Quantum Memory

5.1.2Quantum Inner Products and Distances

5.1.3Hamiltonian Simulation

5.1.4QOPs Summary for Quantum Machine Learning

5.2Quantum Principal Component Analysis (PCA)

5.2.1Classical PCA Analysis

5.2.2Quantum PCA Analysis

5.2.3Potential Impact of Quantum PCA on Robotics

5.3Quantum Regression

5.3.1Least Squares Fitting

5.3.2Quantum Approaches to Curve Fitting

5.3.3Potential Impact of Quantum Regression on Robotics

5.4Quantum Clustering

5.4.1Classical Cluster Analysis

5.4.2Quantum Cluster Analysis

5.4.3Potential Impact of Quantum Clustering on Robotics

5.5Quantum Support Vector Machines

5.5.1Classical SVM Analysis

5.5.2Quantum SVM Analysis

5.5.3Potential Impact of Quantum SVMs on Robotics

5.6Quantum Bayesian Networks

5.6.1Classical Bayesian Network Structure Learning

5.6.2Bayesian Network Structure Learning using Adiabatic Optimization

5.6.3Potential Impact of Quantum Bayesian Networks on Robotics

5.7Quantum Artificial Neural Networks

5.7.1Classical Artificial Neural Networks

5.7.2Quantum Approaches to Artificial Neural Networks

5.7.3Potential Impact of Quantum Artificial Neural Networks to Robotics

5.8Manifold Learning and Quantum Speedups

5.8.1Classical Manifold Learning

5.8.2Quantum Speedups for Manifold Learning

5.8.3Potential Impact of Quantum Manifold Learning on Robotics

5.9Quantum Boosting

5.9.1Classical Boosting Analysis

5.9.2QBoost

5.9.3Potential Impact of Quantum Boosting on Robotics

5.10Chapter Summary

6Quantum Filtering and Control

6.1Quantum Measurements

6.1.1Projective Measurements

6.1.2Continuous Measurements

6.2Hidden Markov Models and Quantum Extension

6.2.1Classical Hidden Markov Models

6.2.2Hidden Quantum Markov Models

6.3Kalman Filtering and Quantum Extension

6.3.1Classic Kalman Filtering

6.3.2Quantum Kalman Filtering

6.4Classical and Quantum Control

6.4.1Overview of Classical Control

6.4.2Overview of Quantum Control Models

6.4.3Bilinear Models (BLM)

6.4.4Markovian Master Equation (MME)

6.4.5Stochastic Master Equation (SME)

6.4.6Linear Quantum Stochastic Differential Equation (LQSDE)

6.4.7Verification of Quantum Control Algorithms

6.5Chapter Summary

7Current Strategies for Quantum Implementation

7.1DiVincenzo Definition

7.2Mosca Classification

7.3Comparison of DiVincenzo and Mosca Approaches

7.4Quantum Computing Physical Implementations

7.5Case Study Evaluation of D-Wave Machine

7.6Toward General Purpose Quantum Computing and Robotics

7.7Chapter Summary

8Conclusion

ACheatsheet of Quantum Concepts Discussed

Bibliography

Authors’ Biographies

Index