Description
Book SynopsisThese three lectures cover a certain aspect of complexity and black holes, namely the relation to the second law of thermodynamics. The first lecture describes the meaning of quantum complexity, the analogy between entropy and complexity, and the second law of complexity. Lecture two reviews the connection between the second law of complexity and the interior of black holes. Prof. L. Susskind discusses how firewalls are related to periods of non-increasing complexity which typically only occur after an exponentially long time. The final lecture is about the thermodynamics of complexity, and “uncomplexity” as a resource for doing computational work. The author explains the remarkable power of “one clean qubit,” in both computational terms and in space-time terms.
This book is intended for graduate students and researchers who want to take the first steps towards the mysteries of black holes and their complexity.
Table of ContentsLecture I: Hilbert Space is Huge1 Preface2 How Huge?3 Volume of CP(N)4 Relative Complexity5 Dual Role of Unitaries6 Volume of SU(2K)7 Exploring SU(2K)7.1 Relative Complexity of Unitaries7.2 Complexity is Discontinuous8 Graph Theory Perspective8.1 Collisions and Loops9 The Second Law of Quantum Complexity9.1 Hamiltonian Evolution
II Lecture II: Black Holes and the Second Law of Complexity10 Preface11 The Black Hole-Quantum Circuit Correspondence11.1 Two Problems11.2 Circuits and Black Holes12 The Growth of Wormholes12.1 Properties of Growth12.2 Rindler Time and CV13 Exponential Time Breakdown of GR13.1 C=V14 Precursors14.1 The Epidemic Model14.2 Lyapunov and Rindler15 Precursors and Black Holes15.1 Instability of White Holes16 Complexity and Firewalls16.1 Firewalls are Fragile16.2 What Happens After Exponential Time?16.3 The Fragility of Complexity Equilibrium17 Do Typical States have Firewalls?17.1 AdS Black Holes17.2 Evaporating Black Holes
Lecture III: The Thermodynamics of Complexity18 Preface19 Negentropy20 Uncomplexity20.1 The Auxiliary System20.2 Combining Auxiliary Systems21 Uncomplexity as a Resource22 The Power of One Clean Qubit22.1 The Protocol22.2 Expending Uncomplexity and Negentropy23 Spacetime and Uncomplexity23.1 CA23.2 Geometric Interpretation of Uncomplexity
Conclusion
