Preface
Theory of quantum information and computation has been extensively investigated
in the last two decades (see the textbook [121] by Nielsen and Chuang and the
references [25, 53, 144, 147, 148] for the first constructions or construction
methods of quantum codes shown in the literature; see also the papers [1, 2, 20, 21,
82, 122, 146] concerned with constructions of topological quantum codes, which
will not be investigated in this book). This book is written in order to familiarize
graduate or postgraduate students with respect to several constructions or construction methods of quantum codes as well as techniques of constructions of
quantum convolutional codes available in the literature. More precisely, we gathered great part of the most relevant papers that we have published concerning
quantum coding theory to present such results here, in form of book. To this end,
we utilize the well-known Calderbank–Shor–Steane (CSS) construction, the
Hermitian and the Steane enlargement construction to certain classes of classical
codes. These quantum codes have good parameters and they are introduced recently
in the literature. Furthermore, the book also presents several constructions of
families of asymmetric quantum codes with good parameters.
Keeping in mind a similar approach, the book also contains a careful description
of the procedures adopted to construct families of quantum convolutional codes. To
close the book, we introduce and construct families of asymmetric quantum convolutional codes (this concept was introduced in Ref. [102] (La Guardia, G.G.:
Asymmetric quantum convolutional codes. Quantum Inform. Processing 15, 167–
183 (2016)).
Although the book does not bring new didactic approach nor new form of
presentation, I tried to write it carefully, with accessible language and clear
explanations, in order to improve the quality and the accessibility of it. In my point
of view, the book has some advantages. The first one is to teach the reader certain
algebraic techniques of code construction that could improve the capacity of
abstraction of him/her. It is also an attempt to motivate the reader to perform their
own contributions from this area of research. Another important contribution is that
vii
Theory of quantum information and computation has been extensively investigated
in the last two decades (see the textbook [121] by Nielsen and Chuang and the
references [25, 53, 144, 147, 148] for the first constructions or construction
methods of quantum codes shown in the literature; see also the papers [1, 2, 20, 21,
82, 122, 146] concerned with constructions of topological quantum codes, which
will not be investigated in this book). This book is written in order to familiarize
graduate or postgraduate students with respect to several constructions or construction methods of quantum codes as well as techniques of constructions of
quantum convolutional codes available in the literature. More precisely, we gathered great part of the most relevant papers that we have published concerning
quantum coding theory to present such results here, in form of book. To this end,
we utilize the well-known Calderbank–Shor–Steane (CSS) construction, the
Hermitian and the Steane enlargement construction to certain classes of classical
codes. These quantum codes have good parameters and they are introduced recently
in the literature. Furthermore, the book also presents several constructions of
families of asymmetric quantum codes with good parameters.
Keeping in mind a similar approach, the book also contains a careful description
of the procedures adopted to construct families of quantum convolutional codes. To
close the book, we introduce and construct families of asymmetric quantum convolutional codes (this concept was introduced in Ref. [102] (La Guardia, G.G.:
Asymmetric quantum convolutional codes. Quantum Inform. Processing 15, 167–
183 (2016)).
Although the book does not bring new didactic approach nor new form of
presentation, I tried to write it carefully, with accessible language and clear
explanations, in order to improve the quality and the accessibility of it. In my point
of view, the book has some advantages. The first one is to teach the reader certain
algebraic techniques of code construction that could improve the capacity of
abstraction of him/her. It is also an attempt to motivate the reader to perform their
own contributions from this area of research. Another important contribution is that
vii