Three Lectures on Complexity and Black Holes

Paperback Engels 2020 9783030451080
Verwachte levertijd ongeveer 9 werkdagen

Samenvatting

These 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.

Specificaties

ISBN13:9783030451080
Taal:Engels
Bindwijze:paperback
Uitgever:Springer International Publishing

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Inhoudsopgave

Lecture I: Hilbert Space is Huge<div>1 Preface</div><div>2 How Huge?</div><div>3 Volume of CP(N)</div><div>4 Relative Complexity</div><div>5 Dual Role of Unitaries</div><div>6 Volume of SU(2K)</div><div>7 Exploring SU(2K)</div><div>7.1 Relative Complexity of Unitaries</div><div>7.2 Complexity is Discontinuous</div><div>8 Graph Theory Perspective</div><div>8.1 Collisions and Loops</div><div>9 The Second Law of Quantum Complexity</div><div>9.1 Hamiltonian Evolution</div><div><br></div><div>II Lecture II: Black Holes and the Second Law of Complexity</div><div>10 Preface</div><div>11 The Black Hole-Quantum Circuit Correspondence</div><div>11.1 Two Problems</div><div>11.2 Circuits and Black Holes</div><div>12 The Growth of Wormholes</div><div>12.1 Properties of Growth</div><div>12.2 Rindler Time and CV</div><div>13 Exponential Time Breakdown of GR</div><div>13.1 C=V</div><div>14 Precursors</div><div>14.1 The Epidemic Model</div><div>14.2 Lyapunov and Rindler</div><div>15 Precursors and Black Holes</div><div>15.1 Instability of White Holes</div><div>16 Complexity and Firewalls</div><div>16.1 Firewalls are Fragile</div><div>16.2 What Happens After Exponential Time?</div><div>16.3 The Fragility of Complexity Equilibrium</div><div>17 Do Typical States have Firewalls?</div><div>17.1 AdS Black Holes</div><div>17.2 Evaporating Black Holes</div><div><br></div><div>Lecture III: The Thermodynamics of Complexity</div><div>18 Preface</div><div>19 Negentropy</div><div>20 Uncomplexity</div><div>20.1 The Auxiliary System</div><div>20.2 Combining Auxiliary Systems</div><div>21 Uncomplexity as a Resource</div><div>22 The Power of One Clean Qubit</div><div>22.1 The Protocol</div><div>22.2 Expending Uncomplexity and Negentropy</div><div>23 Spacetime and Uncomplexity</div><div>23.1 CA</div><div>23.2 Geometric Interpretation of Uncomplexity</div><div><br></div><div>Conclusion </div>

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        Three Lectures on Complexity and Black Holes