Unveiling Shor’s Algorithm through Peter Shor’s Narration — Day 19
Day19 of #Quantum30 Challenge
On the Day 19 of #Quantum30 Challenge, I got the pleasure to listen the story of Shor’s factoring algorithm in the words of Peter Shor himself. In this talk, the speaker, the infamous Dr. Peter Shor, delves into their recollections of the discovery of the factoring algorithm in the context of their academic journey and the historical developments in quantum computing.
The resource is “The Story of Shor’s Algorithm, Straight From the Source | Peter Shor” from the YouTube channel of Qiskit. The discussion is comprehensive and covers various key points:
Introduction and Background:
- The speaker introduces the topic of their talk, reflecting on their discovery of the factoring algorithm.
- They mention their connection to Caltech, where Richard Feynman was also present during their senior year.
- The speaker recalls attending a lecture by Feynman on “negative probability” and its relation to Bell’s theorem, showing Feynman’s interest in quantum mechanics.
Bell's Theorem and Negative Probability:
- The speaker explains Bell’s theorem, which demonstrates that quantum mechanics cannot be both local and realistic.
- Feynman’s exploration of Bell’s theorem led him to question the assumption that all probabilities must be between zero and one.
- Feynman’s “negative probability” concept aimed to work around this assumption, but he did not publish it due to potential implications on his reputation.
Discovering Quantum Computing:
- The speaker shares their early encounters with quantum computing through a talk by Charlie Bennett at Bell Labs.
- Bennett’s talk introduced the BB84 key distribution protocol and raised questions about its mathematical security.
Development of Quantum Computing Concepts:
- The speaker, along with John Preskill, developed a simple proof for the security of the BB84 protocol.
- They recall Umesh Vazirani’s talk on the Bernstein-Vazirani problem, which sparked their interest in finding more problems that quantum computers could solve efficiently.
Simon’s Problem and Quantum Algorithms:
- The speaker describes Dan Simon’s work on the period-finding problem using quantum algorithms.
- They discuss the relationship between Simon’s work and their own exploration of the discrete logarithm problem.
Factoring Algorithm Discovery:
- The speaker identifies the error in their original rejection of Simon’s paper, realizing its potential implications for the factoring problem.
- They describe their realization that the discrete logarithm and factoring problems are related and propose a quantum algorithm for factoring.
Spread of the Factoring Algorithm:
- The speaker highlights the rapid spread of news about their factoring algorithm discovery.
- They recall discussions and interviews at various conferences, including a significant interest from the NSA.
Quantum Error Correction Challenges:
- The speaker addresses the challenges of error correction in quantum computers, considering the no-cloning theorem.
- They explore various classical error correction techniques and their compatibility with quantum systems.
Quantum Error Correcting Codes—Initial Insights:
- The speaker introduces the concept of quantum error-correcting codes using repetition codes as an example.
- They mention the discovery of Asher Peres’ three-qubit code that corrects bit errors and its implications.
CSS Codes and More Complex Codes:
- The speaker describes the CSS codes developed in collaboration with Rob Calderbank and Andrew Steane.
- They discuss the quantum Hamming code, a generalization of the classical Hamming code.
- The speaker highlights the discovery of more complex codes by IBM and Los Alamos researchers.
Symmetry, Additive Codes, and Stabilizer Codes:
- The speaker delves into their exploration of the symmetry group of a five-qubit code.
- They explain the connection between the code and additive codes over the field with four elements.
- The speaker introduces the concept of stabilizer codes, named by Dan Gottesman, and their significance.
Conclusion and Gratitude:
- The speaker concludes by expressing gratitude for being part of the 40th anniversary celebration of the Endicott House Conference on Physics and Computation.
- The speaker expresses his hope to enjoy the rest of the celebration and reflect on the journey of quantum computing.
Throughout the talk, the speaker offers insights into their thought process, interactions with fellow researchers, and the evolution of quantum computing concepts. The narrative is filled with historical references, personal anecdotes, and technical explanations, providing a comprehensive overview of their journey and contributions to the field.
Thank you, readers! QuantumComputingIndia #Quantum30 #quantum #quantumtechnology #Science #Math #Mathematics #quantumphysics #physics
