Quantum Circuit Complexity

After decades of unhindered progress, classical computing has started facing significant hurdles both in terms of physical scalability and theoretical bounds of efficiency. Among the alternative models of computing, Quantum Computing, though proposed six decades ago, has recently started seeing potentials to progress beyond the limits of classical computing. This book discusses the theoretical bounds on the efficiency of low depth quantum circuits, one of the structurally simplest models of quantum computing. Three different properties are explored; universality in which one circuit can be used to simulate different circuits, fault detection in which certain kinds of faults in simple quantum gates can be detected and third, a fundamental theoretical limitation in the power of a popular quantum gate. These properties give us a better idea about simple quantum circuits, which are essentially building blocks for more complicated gadgets. The properties are analysed using novel techniques which will be useful to analyse other similar quantum circuits. Overall, this book will be useful to researchers of quantum circuit complexity and graduate students of theoretical computer science.