This book discusses modern approaches and challenges of computer-aided
design (CAD) of quantum circuits with a view to providing compact
representations of quantum functionality. Focusing on the issue of
quantum functionality, it presents Quantum Multiple-Valued Decision
Diagrams (QMDDs - a means of compactly and efficiently representing and
manipulating quantum logic. For future quantum computers, going well
beyond the size of present-day prototypes, the manual design of quantum
circuits that realize a given (quantum) functionality on these devices
is no longer an option. In order to keep up with the technological
advances, methods need to be provided which, similar to the design and
synthesis of conventional circuits, automatically generate a circuit
description of the desired functionality. To this end, an efficient
representation of the desired quantum functionality is of the essence.
While straightforward representations are restricted due to their
(exponentially) large matrix descriptions and other decision
diagram-like structures for quantum logic suffer from not
comprehensively supporting typical characteristics, QMDDs employ a
decomposition scheme that more naturally models quantum systems. As a
result, QMDDs explicitly support quantum-mechanical effects like phase
shifts and are able to take more advantage of corresponding
redundancies, thereby allowing a very compact representation of relevant
quantum functionality composed of dozens of qubits. This provides the
basis for the development of sophisticated design methods as shown for
quantum circuit synthesis and verification.
