What makes quantum computers SO powerful?

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A quantum computer in the next decade could crack the encryption our society relies on using Shor's Algorithm. Head to https://brilliant.org/veritasium to start your free 30-day trial, and the first 200 people get 20% off an annual premium subscription. The topic is especially relevant in the wake of Willow, the quantum computing chip unveiled by Google in December 2024. #quantumcomputing ▀▀▀ A huge thank you to those who helped us understand this complex field and ensure we told this story accurately - Dr. Lorenz Panny, Prof. Serge Fehr, Dr. Dustin Moody, Prof. Benne de Weger, Prof. Tanja Lange, PhD candidate Jelle Vos, Gorjan Alagic, and Jack Hidary. A huge thanks to those who helped us with the math behind Shor’s algorithm - Prof. David Elkouss, Javier Pagan Lacambra, Marc Serra Peralta, and Daniel Bedialauneta Rodriguez. ▀▀▀ References: Joseph, D., et al. (2022). Transitioning organizations to post-quantum cryptography. Nature, 605(7909), 237-243. - https://ve42.co/Joseph2022 Bernstein, D. J., & Lange, T. (2017). Post-quantum cryptography. Nature, 549(7671), 188-194. - https://ve42.co/Bernstein2017 An Insight, An Idea with Sundar Pichai - Quantum Computing, Wold Economic Forum via YouTube - https://ve42.co/QCWEFyt Migrating to Post-Quantum Cryptography, The White House - https://ve42.co/PQCWhiteHouse Kotas, W. A. (2000). A brief history of cryptography. University of Tennessee - https://ve42.co/Kotas2000 Hellman, M. (1976). New directions in cryptography. IEEE transactions on Information Theory, 22(6), 644-654. - https://ve42.co/Hellman1976 Rivest, R. L., Shamir, A., & Adleman, L. (1978). A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM, 21(2), 120-126. - https://ve42.co/Rivest1978 Kak, A. (2023). Lecture 12: Public-Key Cryptography and the RSA Algorithm - https://ve42.co/Kak2023 Calderbank, M. (2007). The RSA Cryptosystem: History, Algorithm, Primes. University of Chicago. - https://ve42.co/Calderbank2007 Cryptographic Key Length Recommendation, Keylength - https://ve42.co/KeyLength Coppersmith, D. (2002). An approximate Fourier transform useful in quantum factoring. arXiv preprint quant-ph/0201067. - https://ve42.co/Coppersmith2002 Quantum Fourier Transform, Qiskit - https://ve42.co/Qiskit Shor, P. W. (1994, November). Algorithms for quantum computation: discrete logarithms and factoring. In Proceedings 35th annual symposium on foundations of computer science (pp. 124-134). IEEE. - https://ve42.co/Shor1994 Shor’s algorithm, Wikipedia - https://ve42.co/ShorWiki Euler’s totient function, Wikipedia - https://ve42.co/EulerWiki Asfaw, A. (2020). Shor’s Algorithm Lecture Series, Qiskit Summer School - https://ve42.co/ShorYT How Quantum Computers Break Encryption, minutephysics via YouTube - https://ve42.co/PQCmpyt Breaking RSA Encryption - an Update on the State-of-the-Art, QuintessenceLabs - https://ve42.co/QuintessenceLabs O'Gorman, J., & Campbell, E. T. (2017). Quantum computation with realistic magic-state factories. Physical Review A, 95(3), 032338. - https://ve42.co/OGorman2017 Gidney, C., & Ekerå, M. (2021). How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits. Quantum, 5, 433. - https://ve42.co/Gidney2021 2021 Quantum Threat Timeline Report, Global Risk Institute - https://ve42.co/QuantumRisk The IBM Quantum Development Roadmap, IBM - https://ve42.co/IBMQC Post-Quantum Cryptography, Computer Security Resource Center (NIST) - https://ve42.co/CSRCPQC Alagic, G., et al. (2022). Status report on the third round of the NIST post-quantum cryptography standardization process. US Department of Commerce, NIST. - https://ve42.co/Alagic2022 Thijs, L. (2015). Lattice cryptography and lattice cryptanalysis - https://ve42.co/Thijs2015 ▀▀▀ Special thanks to our Patreon supporters: Tj Steyn, Meg Noah, Bernard McGee, KeyWestr, Elliot Miller, Jerome Barakos, M.D., Amadeo Bee, TTST, Balkrishna Heroor, Chris LaClair, John H. Austin, Jr., Eric Sexton, john kiehl, Anton Ragin, Diffbot, Gnare, Dave Kircher, Burt Humburg, Blake Byers, Evgeny Skvortsov, Meekay, Bill Linder, Paul Peijzel, Josh Hibschman, Mac Malkawi, Juan Benet, Ubiquity Ventures, Richard Sundvall, Lee Redden, Stephen Wilcox, Marinus Kuivenhoven, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi. ▀▀▀ Written by Casper Mebius & Derek Muller Edited by Trenton Oliver Filmed by Raquel Nuno Animated by Ivy Tello & Mike Radjabov Additional video/photos supplied by Getty Images & Pond5 Music from Epidemic Sound & Jonny Hyman Produced by Derek Muller, Petr Lebedev, & Emily Zhang