Scott Aaronson is a professor of computer science at University of Texas at Austin and director of its Quantum Information Center. Previously he received his PhD at UC Berkeley and was a faculty member at MIT in Electrical Engineering and Computer Science from 2007-2016. Scott has won numerous prizes for his research on quantum computing and complexity theory, including the Alan T Waterman award in 2012 and the ACM Prize in Computing in 2020. In addition to being a world class scientist, Scott is famous for his highly informative and entertaining blog Schtetl Optimized, which has kept the scientific community up to date on quantum hype for nearly the past two decades.

In this episode, Scott Aaronson gives a crash course on quantum computing, diving deep into the details, offering insights, and clarifying misconceptions surrounding quantum hype.

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Part I. Introduction (Personal)
00:00 : Biography
01:02 : Shtetl Optimized and the ways of blogging
09:56 : Sabattical at OpenAI, AI safety, machine learning
10:54 : "I study what we can't do with computers we don't have"

Part II. Introduction (Technical)
22:57 : Overview
24:13 : SMBC Cartoon: "The Talk". Summary of misconceptions of the field
33:09 : How all quantum algorithms work: choreograph pattern of interference
34:38 : Outline

Part III. Setup
36:10 : Review of classical bits
40:46 : Tensor product and computational basis
42:07 : Entanglement
44:25 : What is not spooky action at a distance
46:15 : Definition of qubit
48:10 : bra and ket notation
50:48 : Superposition example
52:41 : Measurement, Copenhagen interpretation

Part IV. Working with Qubits
57:02 : Unitary operators, quantum gates
59;03: Correction: The matrix denoted as "Hadamard gate" is actually a 45 degree rotation matrix. The Hadamard gate differs from this matrix by a sign flip in the last column. See 1;11;00 for the Hadamard gate.
1:03:34 : Philosophical aside: How to "store" 2^1000 bits of information.
1:08:34 : CNOT operation
1:09:45 : Quantum circuits
1:11:00 : Hadamard gate
1:12:43 : Circuit notation, XOR notation
1:14:55 : Subtlety on preparing quantum states
1:16:32 : Building and decomposing general quantum circuits: Universality
1:21:30 : Complexity of circuits vs algorithms
1:28:45 : How quantum algorithms are physically implemented
1:31:55 : Equivalence to quantum Turing Machine

Part V. Quantum Speedup
1:35:48 : Query complexity (black box / oracle model)
1:39:03 : Objection: how is quantum querying not cheating?
1:42:51 : Defining a quantum black box
1:45:30 : Efficient classical f yields efficient U_f
1:47:26 : Toffoli gate
1:50:07 : Garbage and quantum uncomputing
1:54:45 : Implementing (-1)^f(x))
1:57:54 : Deutsch-Jozsa algorithm: Where quantum beats classical
2:07:08 : The point: constructive and destructive interference

Part VI. Complexity Classes
2:08:41 : Recap. History of Simon's and Shor's Algorithm.
2:14:42 : BQP
2:18:18 : EQP
2:20:50 : P
2:22:28 : NP
2:26:10 : P vs NP and NP-completeness
2:33:48 : P vs BQP
2:40:48 : NP vs BQP
2:41:23 : Where quantum computing explanations go off the rails

Part VII. Quantum Supremacy
2:43:46 : Scalable quantum computing
2:47:43 : Quantum supremacy
2:51:37 : Boson sampling
2:52:03 : What Google did and the difficulties with evaluating supremacy
3:04:22 : Huge open question

Further Reading:
Scott Aaronson's Lecture Notes: https://www.scottaaronson.com/qclec.pdf
Scott Aaronson's Blog: https://scottaaronson.blog/
Nielsen & Chuang. Quantum Computation and Quantum Information

#quantumcomputing #quantum #quantumphysics #math #physics #computerscience #complexity

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