QUANTUM COMPUTING? WHAT ON EARTH IS AND WILL IT BREAK ALL MY ENCRYPTION? CRAIG STUNTZ ∈ IMPROVING https://speakerdeck.com/craigstuntz 

THE PROMISE https://commons.wikimedia.org/wiki/File:Quantum-computer-Chalmers_2017.jpg 

RSA 

ECDSA RSA DSA https://arxiv.org/pdf/1804.00200.pdf 

” “ — Richard Feynman …nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical, and by golly it’s a wonderful problem, because it doesn’t look so easy. https://people.eecs.berkeley.edu/~christos/classics/Feynman.pdf 

https://github.com/krishnakumarsekar/awesome-quantum-machine-learning 

HOWEVER! • TLS does not seem to be broken • Cryptographically relevant quantum computers don’t exist (yet) • Quantum supremacy not (yet) shown • Classical algorithms keep getting better! • No “universal” speedup • Theoretical advantages of quantum computers are not well understood • Many popular articles on quantum computing are mostly marketing 

YOU SHOULD CARE ANYWAY • Advantages are potentially huge • New cryptosystems take years to vet and implement; need to start now • Whether or not they’re implementable, there is at least some potential for new physics, which is cool 

“CLASSICAL” COMPUTING https://commons.wikimedia.org/wiki/File:Vax_11-780_(2).jpg 

CAST OF CHARACTERS 

PROGRAMMER CC-A by https://www.wocintechchat.com/ 

LIBRARY AUTHOR — OR — CRYPTOGRAPHER https://www.flickr.com/photos/ibm_research_zurich/16138523887/ 

HARDWARE DESIGNER https://commons.wikimedia.org/wiki/File:Quantum_Computing;_Ion_Trapping_(5941055642).jpg 

COPROCESSORS CPU GPU TPU DSP Quantum 

” “ — Neil C. Thompson & Svenja Spanuth The migration of computing from a general purpose technology to a fragmented one will fundamentally alter it… In particular, we expect the gains from computing improvement to be become much more unequal, to the detriment of many. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3287769 

NUTS AND BOLTS https://www.flickr.com/photos/63059536@N06/5941039382 

HOW CLASSICAL COMPUTERS WORK https://commons.wikimedia.org/wiki/File:ABasicComputer.gif LDR EAX, ADR_VAR1 LDR EBX, ADR_VAR2 ADD EAX, EBX STR EAX, [ECX] 

CLASSICAL COMPUTER OPERATION ARGUMENTS REGISTERS https://commons.wikimedia.org/wiki/File:RF-remote-control-dip-switch-calculator.png 

HOW QUANTUM COMPUTERS WORK https://commons.wikimedia.org/wiki/File:H_CNOTGate.png Qubits Quantum Gates 

QUANTUM COMPUTER OPERATION ARGUMENTS QUBITS 

QUANTUM OPERATIONS QUANTUM OPERATION 

QUANTUM OPERATIONS QUANTUM OPERATION 1 2 |0⟩ + 1 2 |1⟩ |0⟩ |1⟩ MEASURE 

ENTANGLEMENT / INTERFERENCE http://www.smbc-comics.com/comic/the-talk-3 

” “ — Holly Cummins "Mixing together waves so that wrong answers cancel themselves out is very different from how classical computers work, but it is something many of us have experienced in the macroscopic world. For example, noise cancelling headphones work by adding extra noise to existing noise." 

INTERFERENCE https://www.flickr.com/photos/brewbooks/309494512 ✅ ❌ 

NOISE 

COMPUTATIONAL COMPLEXITY Detail from image by Dr. Gabriel Robins, http://www.cs.virginia.edu/~robins/cs3102/ 

SOME PROBLEMS SEEM HARD; SOME WE KNOW ARE HARD WHAT IS A HARD PROBLEM, ACTUALLY? • General solution impossible • Entscheidungsproblem — think Turing • Solution exists but is exponentially hard • Traveling salesman problem • Efficient solutions exist • Greatest common divisor • “Hmm, actually, we’re not sure!” • Finding factors of products of large prime numbers 

https://www.quantamagazine.org/teenager-finds-classical-alternative-to-quantum-recommendation-algorithm-20180731/ 

SOME PROBLEMS SEEM HARD; SOME WE KNOW ARE HARD WHAT IS A HARD PROBLEM, ACTUALLY? https://commons.wikimedia.org/wiki/File:BQP_complexity_class_diagram.svg 

UNDER THE HOOD BUILDING AND PROGRAMMING A QUANTUM COMPUTER https://www.wpafb.af.mil/News/Article-Display/Article/1250638/ 

” “ — Lance Fortnow The basic ability to do Fourier transformation, that’s at the heart of the power of quantum, at least most of the algorithms we know. 

NISQ 

ION TRAPS https://jqi.umd.edu/news/future-ion-traps 

SUPER- CONDUCTING QUBITS https://www.flickr.com/photos/ibm_research_zurich/26093923343 

QUANTUM ANNEALING https://commons.wikimedia.org/wiki/File:DWave_128chip.jpg 

TOPOLOGICAL QUBITS Ester Dalvit / Nature 

PROGRAMMING A QUANTUM COMPUTER 

Q# using (qubits = Qubit[2]) { for (test in 1..count) { Set (initial, qubits[0]); Set (Zero, qubits[1]); H(qubits[0]); CNOT(qubits[0], qubits[1]); let res = M (qubits[0]); if (M (qubits[1]) == res) { set agree = agree + 1; } #$ Count the number of ones we saw: if (res == One) { set numOnes = numOnes + 1; } } Set(Zero, qubits[0]); Set(Zero, qubits[1]); } https://docs.microsoft.com/en-us/quantum/quickstart?view=qsharp-preview&tabs=tabid-vs2017 

ABOUT THAT CRYPTO THING https://www.flickr.com/photos/usnistgov/5941059262/ 

” “ — Scott Aaronson If you take just one piece of information from this blog: Quantum computers would not solve hard search problems instantaneously by simply trying all the possible solutions at once. 

ONE WAY FUNCTIONS HOW DOES RSA WORK? • Given two numbers, it’s easy to find their product • But given a product, it’s much harder to find its prime factorization • If the factors are two prime numbers, then the factorization is unique, so this is even harder, and harder still if the prime numbers are very large (thousands of bits) 

THE PERIOD OF A FUNCTION https://commons.wikimedia.org/wiki/File:Sine.svg 

FIND THE PRIME FACTORS OF A PRODUCT EFFICIENTLY SHOR’S ALGORITHM • Classical part: Do some fairly simple arithmetic (finding the greatest common denominator of a couple of numbers) • Quantum part: Find the period of a function • Classical part: Do some more fairly simple arithmetic • Because we have small quantum computers, we can currently use Shor’s algorithm only to factor small numbers, like 15 • Despite these small numbers, Shor’s algorithm clearly works! 

GROVER’S ALGORITHM SEARCH PROBLEMS, REVISITED • Unlike Shor’s algorithm, works with general functions, not just finding products of primes • Slower than Shor’s algorithm, but much faster than classical search • Aaronson quote is still correct; we are not searching “instantaneously” by “trying all the possible solutions at once” [O( N)] 

QUANTUM RESISTANT CRYPTO • It may take 10-15 years to gain confidence in a novel cryptosystem • Many symmetric algorithms like AES are believed to be quantum resistant • A number of possibly quantum resistant asymmetric cryptosystems are under development and analysis • Some experiments have failed! 

SO HOW CLOSE ARE WE? https://www.flickr.com/photos/ellenm1/7847402208 

USEFUL QUANTUM COMPUTING • “Quantum supremacy” • Faster than a classical computer • A moving target, since classical hardware and algorithms keep improving • Perhaps 50+ entangled qubits? • “Goodbye, RSA” • Thousands of entangled, logical qubits 

FURTHER READING CC-A by https://www.wocintechchat.com/ 

• Surveys • A Beginner’s Guide to Quantum Computing and Q#, blog post by Frances Tibble • Quantum Computing in the NISQ era and beyond, report by John Preskill • Quantum Computing since Democritus, book by Scott Aaronson • Quantum Computing: Progress and Prospects, report by the National Academies of Sciences, Engineering, and Medicine • Specific areas • CECPQ2, blog post by Adam Langley on post-quantum experiments in Chrome • “Major Quantum Computing Advance Made Obsolete by Teenager,” Quanta article • “Graduate Student Solves Quantum Verification Problem,” Quanta article 

C O N T A C T [email protected] @craigstuntz http://paperswelove.org/chapter/columbus/ https://speakerdeck.com/craigstuntz