What On Earth Is Quantum Computing? (And will it break all my encryption?)

As presented to BSides Columbus 2019.

You might have heard that quantum computers can break public key encryption. You might also have heard that you can buy a quantum computer today, or run programs on one via a cloud service. Yet TLS does not seem to be broken! What is going on? It's hard to tell, because most "explanations" of quantum computing are either marketing brochures or written for an audience of physics postdocs. This talk will clearly explain what we know about quantum computing today, and how it is relevant to software professionals now and in the near future. We'll focus on the security space in particular and discuss what quantum computers can do besides factor large integers. Come with questions, leave with a clear vision for how new computing technologies may change your work in the decades to come!

Transcript

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

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

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3. RSA
   

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

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5. ”
   “
   — 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
   

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

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7. 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
   

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8. 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
   

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

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10. CAST OF CHARACTERS
    

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

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

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

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14. COPROCESSORS
    CPU
    GPU
    TPU
    DSP
    Quantum
    

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15. ”
    “
    — 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
    

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

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17. 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]
    

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

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

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20. QUANTUM COMPUTER OPERATION ARGUMENTS
    QUBITS
    

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21. QUANTUM OPERATIONS
    QUANTUM
    OPERATION
    

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

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

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24. ”
    “
    — 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."
    

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

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26. NOISE
    

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

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28. 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
    

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

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30. 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
    

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

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32. ”
    “
    — 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.
    

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33. NISQ
    

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

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

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

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37. TOPOLOGICAL
    QUBITS
    Ester Dalvit / Nature
    

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38. PROGRAMMING A
    QUANTUM COMPUTER
    

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39. 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
    

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

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41. ”
    “
    — 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.
    

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42. 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)
    

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

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44. 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!
    

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45. 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)]
    

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46. 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!
    

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

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48. 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
    

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

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50. • 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
    

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51. C O N T A C T
    craig.stuntz@improving.com
    @craigstuntz
    http://paperswelove.org/chapter/columbus/
    https://speakerdeck.com/craigstuntz
    

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