This document discusses the fundamentals of quantum computing, including key concepts such as qubits, quantum logic gates, and the differences between quantum and classical computation. It highlights the potential applications of quantum computing, including its capability to solve complex problems and the implications for cryptography, particularly with algorithms like Shor's algorithm. The author also addresses the current state of quantum computing technology and its future prospects.

1. USING MANY WORLDS OF
COMPUTE POWER
Quantum Computers exist, they are real and you can program them.
But what gives them their awesome power and what use will it be?

2. JAMES BIRNIE
● James Birnie, lead consultant @ ThoughtWorks since
June 2015
● http://www.jamesbirnie.com/
● jbirnie@thoughtworks.com
● Worked at a startup for 9 years
● Worked in software since 1996
● I suffer from Prosopagnosia

3. ThoughtMobile
hits the streets
ThoughtWorks
incorporated
1993
2000
2005
1996
2004
2006
2008
2010
2014
2016,
2017, 2018
2018
500+
ThoughtWorkers
ThoughtWorks
University
1st office outside U.S.
for distributed agile
25th book by
ThoughtWorkers
1st edition of
Technology Radar
3000+
ThoughtWorkers
AnitaB.org names
ThoughtWorks Top
Company for Women
Technologists
5000+
ThoughtWorkers
Named as one of the
fastest-growing private
companies for the fourth
consecutive year
TECHNOLOGY
EXCELLENCE
THEN, NOW
AND NEXT
ThoughtWorks has a reputation of
being on the forefront, defining the
tech principles used by the most
advanced organizations.
2001
Created the first Open
Source Continuous
Integration Server
2017
Apax Partners acquires
ThoughtWorks
Top 10 contributor
to open source

4. #1
in Agile and
Continuous Delivery
100+
books written

6. REAL QUANTUM COMPUTING
● Why Quantum computing?
● Quantum vs Classical, Bits vs Qubits
● State of the Quantum Computing Art
● What is this Many Worlds Thing?
● The Elephant in the Quantum Room

7. WHY QUANTUM
COMPUTING?
Why am I standing in front of an audience talking about a subject that a few months
ago I had at best a vague understanding of?

10. https://www.thoughtworks.com/radar/languages-and-frameworks

11. QUANTUM v CLASSICAL
QUBITS v BITS
How does a quantum computer work? How does a digital computer work? What do the
differences mean?

12. CLASSIC BIT
● Unit of binary information
● Can hold one of two states which we generally
represent as 0 and 1
● Usually stored as one of two distinct low voltages

13. LOGIC GATES COMPOSE INTO ARITHMETIC

14. QUBIT
● Two possible outcomes for the measurement
of a qubit - usually 0 and 1
● Observing the value “collapses” the state to
a single value
● Any quantum “thing” can be a qubit, such as an
electron, a photon or an ion
● Qubits can be in superposition,
holding both states simultaneously
https://en.wikipedia.org/wiki/Qubit

15. QUANTUM STATE - THE BLOCH SPHERE
● Quantum state is a complex valued
probability amplitude
● Probabilities of measuring the
different values are derived from the
quantum state
● This maps to a point on the Bloch
Sphere for a single qubit in a
pure state
By Smite-Meister - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=5829358
https://skillsmatter.com/skillscasts/11445-introduction-to-q-development-can-rob-use-entanglement-to-
thwart-heisenberg

16. QUANTUM LOGIC GATES
● Like classical logic gates they transform quantum
states into new quantum states
● Can act upon multiple Qubits - usually one or two
● Each gate degrades fidelity of the system
● Simplest is ID gate
● X, Y, Z gates rotate around an axis in
the Bloch sphere
● IBM Q-Experience defines 13 gates

18. QUANTUM COMPUTATION V CLASSICAL COMPUTATION
● Quantum circuits hold exponentially more information
at any given time for the same logical circuit size
● Quantum makes insoluble problems solvable in
reasonable time
● Quantum computers cannot meaningfully persist state
● Physical limitations of hardware limit the breadth and
depth of programs
● Quantum computers are
hard to program

21. Clementine’s Cat
Indifference...

22. Indifferent
Aloof
StandoffishArrogant Disinterested
Detached DistantUnresponsive

23. https://www.microsoft.com/en-us/quantum/development-kit

24. THE STATE OF THE
QUANTUM COMPUTING ART
What quantum computers are actually in existence? Can I use them? How would I
program a quantum computer? Does the Russian government have one?

25. https://dilbert.com/strip/2012-04-17

26. MICROSOFT IS IN THE GAME...
https://www.cbronline.com/news/microsoft-set-5-year-quantum-computing
https://en.wikipedia.org/wiki/Majorana_fermion

27. RIGETTI QUANTUM ADVANTAGE PRIZE
https://techcrunch.com/2018/09/07/rigetti-announces-its-hybrid-quantum-computing-platform-and-a-1m-
prize/?guccounter=1
https://www.rigetti.com/

29. WHAT DO WE NEED TO BUILD A COMMERCIAL QUANTUM SOLUTION?
Scalable Qubit Foundation
Cryogenic Systems
Quantum - Classical Interface
Error Correction
Integration with Cloud Provider
Algorithms and Applications
These are
REALLY hard!
This is
expensive
This WILL
happen
This IS
happening

30. SO WHAT IS THIS MANY
WORLDS THING?
Hey Birnie, you promised us that you’d show us many worlds of compute power.
Where are these many worlds and how are they going to help us?

31. WE MADE A VIDEO AT THOUGHTWORKS LAST WEEK...
https://vimeo.com/327282856/21cae5df2c

32. SO LIGHT TRAVELS IN WAVES, RIGHT?

33. BUT WAIT, IT TURNS OUT LIGHT IS PARTICLES, PHOTONS..??
● It turns out that light ISN’T made up of waves after all
● Light consists of photons, these are particles that have
no mass but do have energy and momentum
● As light spreads out, it doesn’t
weaken, you just receive and
process photons less frequently
● Our eyes are not equipped to
see single photons although
some animal eyes are

34. BUT WE STILL SEE INTERFERENCE WITH ONLY ONE PHOTON...???
https://oneandother.io/articles/2016/5/12/the-double-slit-experiment

35. QUANTUM FOURIER TRANSFORM
● Transforms time domain into frequency domain
● Helps analyse interference between qubits
● Underpins a lot of quantum algorithms including Shor’s
algorithm for factorisation
● CANNOT be efficiently simulated on a
classical computer
● Implement using Hadamard and
controlled rotation gates
https://en.wikipedia.org/wiki/Quantum_Fourier_transform

36. MODELLING COMPLEX DYNAMICAL SYSTEMS
https://www.dwavesys.com/home

37. MODELLING COMPLEX DYNAMICAL SYSTEMS
https://newsroom.ibm.com/2019-01-08-New-IBM-Weather-System-to-Provide-
Vastly-Improved-Forecasting-Around-the-World

38. FINANCIAL APPLICATIONS
● Francis Lacan, Financial
Risk Management
solutions executive, IBM
● Marco Paini, Program
Manager and Quantum
Applications Lead,
QxBranch
https://www.meetup.com/London-Quantum-Computing-Meetup/events/255097947/

39. FINDING THE GROUND STATE OF A MOLECULE
Caffeine is about as complicated a molecule as can be
simulated accurately by classical computers
But organic chemistry has far more
complex molecules and sub-molecules

40. THE HABER-BOSCH PROCESS FOR NITROGEN FIXATION
https://en.wikipedia.org/wiki/Haber_process

41. THE ELEPHANT IN THE
(MANY) QUANTUM ROOMS
What is Shor’s algorithm? Why does it matter? Should I be worried about it ay time
soon? What can I do to avoid to prepare for a future without RSA?

42. James Ellis
Clifford Cocks
Malcolm Williamson

43. Martin Hellman
Whitfield Diffie

44. Ronald Rivest
Len Adleman
Adi Shamir

45. PUBLIC KEY CRYPTOGRAPHY 101
● Find an algorithm that is easy to do in one direction and
hard to do backwards
○ Multiply two large primes
○ Discrete logarithms
○ Elliptic curve factorisation
● Factorisation of large numbers takes
sub-exponential time on a
classical computer

46. SHOR’S ALGORITHM TO FACTORISE N
1. Pick a random number a < N
2. Use Euclidean algorithm to find GCD of a and N
3. If this is not 1, you are done
4. Find the period r of the function a^x mod N
5. If r is odd OR a^r/2 = -1 mod N go back to step 1
6. gcd(ar/2 + 1, N) and gcd(ar/2 - 1, N) are both nontrivial factors of N. We are
done.
WHERE IS THE MAGIC IN ALL OF THIS?
https://www.youtube.com/watch?v=wUwZZaI5u0c
https://en.wikipedia.org/wiki/Shor%27s_algorithm

47. AN EXAMPLE OF SHOR’S ALGORITHM TO FACTORISE 15
Randomly choose a number LESS THAN 15: a = 4
GCD (4, 15) = 1
Period of 4^x mod 15 = 2
4^1 - 1 = 3, GCD(3, 15) = 3
4^1 + 1 = 5, GCD(5, 15) = 5
15 = 3 * 5

48. AN EXAMPLE OF SHOR’S ALGORITHM TO FACTORISE 1517
Randomly choose a number LESS THAN 1517: a = 10
GCD (10, 1517) = 1
Period of 10^x mod 1517 = 15 so this is an odd number go back to step 1
Randomly choose another number LESS THAN 1517: a = 14
GCD(14, 1457) = 1
Period of 14^x mod 1517 = 24 so move forward
14^12 - 1 = 56693912375295, GCD(56693912375295, 1517) = 37
14^12 + 1 = 56693912375297, GCD(56693912375297, 1517) = 41
1517 = 37 * 41

49. IMPLEMENTING SHOR IN A SPREADSHEET...

50. STEP 4 IS THE QUANTUM MAGIC
1. Pick a random number a < N
2. Use Euclidean algorithm to find GCD of a and N
3. If this is not 1, you are done
4. Use the quantum period finding routine to find the period r, the period of
the function a^x mod N
5. If r is odd OR a^r/2 = 1 mod N go back to step 1
6. gcd(ar/2 + 1, N) and gcd(ar/2 - 1, N) are both nontrivial factors of N. We are
done.
Finding the period of a function a^x mod N is exponential
complexity using a classical computer but the quantum period
finding routine has polynomial complexity

51. HERE’S ONE I MADE EARLIER...
https://github.com/JimBobBirnie/shor-by-james

52. AND ONE ANDREW MADE EARLIER...
https://github.com/AndrewBryer/shor-by-andrew

53. SO IS RSA DEAD?
● Implementing Shor’s algorithm requires at least twice
the number of qubits as the size of the key
● Factorising a 2048 bit key is estimated to require a
quantum computer with around 6000 qubits
● The biggest (publicly known) gate-logic quantum
computer has 72 qubits

54. WHAT DO I DO IF RSA IS DEAD?
● BB84 demonstrated in 1984 by Bennett and Brassard
● Some classical algorithms exist that will not be
vulnerable even to quantum attack
○ Lattice based encryption
○ Supersingular elliptic curve isogeny cryptography
○ Symmetric key quantum resistance
● Open Quantum Safe (OQS) was
started late in 2016
https://en.wikipedia.org/wiki/Post-quantum_cryptography

55. A BRIEF HISTORY LESSON
● Diffie and Hellman publish “multi user cryptographic techniques” in 1976
which is the precursor to what is thought to be the world’s first public key
cryptography system
● In 1977 Rivest, Shamir and Adleman publish the RSA algorithm and later
set up the RSA company and patent the algorithm in the US
● BUT….
● In 1997 it emerges that scientists working at GCHQ, James Ellis, Clifford
Cocks and Malcolm Williamson had created public key cryptography,
including an algorithm almost identical to RSA, “several years earlier”

56. SOME BOOKS I HAVE READ (OR NOT) THAT HELPED ALONG THE WAY

57. ANY QUESTIONS?
Does anybody have any questions?
Please feel free to ask. Please don’t get offended if I don’t know the answer.

58. QUANTUM STATE
What state does a single qubit hold? What about when you have multiple qubits
together in the same system? What happens when you measure state?

59. The unit of information in a quantum computer is called a quantum bit or qubit. In contrast to classical bits, or
cbits, the value of qubits are not as easily defined as those of cbits. Where a cbit either has the value of 0 or
1, a qubit can exist in a superposition of the two values. Consequently a qubit can’t be said to have an actual
value, but rather a probability to be found in a certain state when measured. The measuring of qubits is
performed as the final step of a computation to produce an output in cbits. This destroys the quantum state. A
qubit can be described as a unit vector in a 2D complex vector space C 2 . In this paper the ket notation will
be used for describing the qubit vectors. A qubit in the zero state is written as |0⟩ and a qubit in the one state
as |1⟩. |0⟩ and |1⟩ are basis vectors in the 2D complex vector space C 2 . |0⟩ = ( 1 0 ) |1⟩ = ( 0 1 )

60. A Bloch sphere, seen in figure 2.1, can be used as a geometrical representation of the qubit. The
Bloch sphere is the space of all rays in C 2 [5]. The north pole of the sphere represents the |0⟩
state and the south pole represents the |1⟩ state. A state |ψ⟩ = α0 |0⟩ + α1 |1⟩ is represented as the
point (θ, ϕ) 3 4 CHAPTER 2. BACKGROUND on the sphere, where α0 = cos θ 2 and α1 = e iϕ sin
θ 2 [6]. The Bloch sphere can be useful for visualizing the state of a qubit and the effect of
transformations performed on the qubit. x y z φ θ 1 0 ψ Figure 2.1: Bloch sphere [7]
https://www.mathopenref.com/ray.html
This is the definition of a ray in complex vector space and shows why the Bloch Sphere is the
space of all rays

61. QUANTUM FOURIER TRANSFORM IN (VERY STYLISED) PICTURES
https://quantumcomputing.stackexchange.com/questions/2607/simplified-explanation-of-shor-qft-
transformation-as-thumbtack

62. MY TYPICAL CHROME BROWSER

63. LOTS OF CONFERENCE TALKS
https://web2day.co/

64. SATURDAY OCTOBER 5TH - THE QUANTUM HACK DAY
https://www.meetup.com/London-Quantum-Computing-Meetup/events/254156028/

65. https://www.youtube.com/watch?v=fFW36-CGkPY

66. CLASSIC LOGIC GATES
● Idealised or physical device applying a boolean function
● Performs a logical operation on one or more binary
inputs and produces one binary output
● An ideal logic gate would have zero rise time and
unlimited fan out
● Implemented with diodes or transistors
acting as electronic switches
● Modern computers can be considered to
be composed of ideal logic gates

67. CLIFFORD GROUP
● Clifford group of logic gates consists of X, Y, Z,
Hadamard, S, T and CNOT
● Only a limited set of states can result from applying
these transformations
● A circuit containing only Clifford transforms can be
simulated in polynomial time on a classical computer
● U1, U2, U3 gates makes all points
on the Block sphere accessible

68. MAJORANA TOPOLOGICAL QUBITS
https://en.wikipedia.org/wiki/Majorana_fermion

69. RIGETTI HAS AN OFFERING
https://www.rigetti.com/

70. FINDING THE PERIOD (SIMPLIFIED EXPLANATION)
● You need 2 quantum registers (input and output)
● The input register has 2N bits, the output register N bits
● The input register is a superposition (use Hadamard gates) of ALL the
values from 0 to about 2 x N
● Entangle the registers by performing a controlled exponential function
from the input to the output register
● Carry out the Quantum Fourier Transform on the input register
● Observe the input register, this yields a value that is a factor of the period r
of a modulo N
● Repeat until you have enough factors to deduce the value of r

71. LOTS OF MEETUPS
https://en.wikipedia.org/wiki/Majorana_fermion

72. HELLO QUANTUM
● Android and iOS application
● Puzzle solving game
● Visualises interactions
between 2 qubits
● Tutorials and information
on quantum logic
https://www.vysor.io/
https://helloquantum.mybluemix.net/

73. OTHER QUANTUM COMPUTING CONCEPTS
● Qubits can become entangled so that measuring one
will tell us the state of the other. The qubits that
interact in a CNOT gate are thus entangled.
● A unary operation (such as a single gate) can be
controlled by a control qubit.
● Any gate or compound operation necessarily has an
adjoint which is the complex conjugate transpose,
effectively an inverse function.
https://quantumexperience.ng.bluemix.net/qx/tutorial?sectionId=full-
user-guide&page=004-Quantum_Algorithms~2F110-

74. CLEMENTINE’S CAT
Who is Clementine? Why am I talking about her cat? Why wouldn’t I just use
Schrodinger’s cat to demonstrate a quantum program?

76. https://github.com/JimBobBirnie/clementines-cat.git

77. WRITING QUANTUM CODE
● https://quantumexperience.ng.bluemix.net/qx/editor
● https://developer.ibm.com/code/2017/05/17/developers-guide-to-
quantum-qiskit-sdk/
● https://docs.microsoft.com/en-us/quantum/quantum-
writeaquantumprogram?view=qsharp-preview&tabs=tabid-vscode
● https://docs.microsoft.com/en-us/quantum/quantum-qr-
intro?view=qsharp-preview
● https://marketplace.visualstudio.com/items?itemName=quantum.quantu
m-devkit-vscode

78. WILL WE EVER HAVE USEFUL QUANTUM COMPUTERS?
● Optimistic View - 2023
● Realistic View - 2048
● Pessimistic View - NEVER!
https://superposition.com/2018/02/08/mathematician-gil-
kalai-says-quantum-computers-will-never-work/

79. QUANTUM FOURIER TRANSFORM
● Transforms time domain into frequency domain
● Underpins a lot of quantum algorithms including Shor’s
algorithm for factorisation
● CANNOT be efficiently simulated on a
classical computer
● Shor used Hadamard and
controlled rotation gates
https://en.wikipedia.org/wiki/Quantum_Fourier_transform

80. QUANTUM FOURIER TRANSFORM
https://www.youtube.com/watch?v=fFW36-CGkPY

81. FINDING THE PERIOD
Shor's period-finding algorithm relies heavily on superposition. To compute
the period of a function we evaluate the function at all points simultaneously.
Quantum physics does not allow us to access all this information directly,
though. A measurement will yield only one of all possible values, destroying
all others.
We have to transform the superposition to another state that will return the
correct answer with high probability. This is achieved by the Quantum Fourier
Transform.
https://quantumexperience.ng.bluemix.net/qx/tutorial?sectionId=full-user-
guide&page=004-Quantum_Algorithms~2F110-Shor%27s_algorithm
https://www.futurelearn.com/courses/intro-to-quantum-
computing/0/steps/31577

82. ANDREW BRYER
● Andrew Bryer, graduate consultant @ ThoughtWorks
since late 2018
● Studied Maths and Computer Science at University of
Birmingham
● Interested in Quantum Computing
and Post Quantum Cryptography
● Dissertation about Ring Learning
With Errors
http://www.dgalindo.es/mscprojects/bryer.pdf

84. YOU WANT ME TO MAKE A STRATEGY…???

86. QUBIT
● Two possible outcomes for the measurement
of a qubit - usually 0 and 1
● Observing the value “collapses”
the state to a single value
● Lots of physical implementations
● Qubits can be in superposition,
holding both states at the
same time
https://en.wikipedia.org/wiki/Qubit

87. IBM Q EXPERIENCE
● Publicly accessible quantum computer
● Easy to set up an account
● Can compose quantum scores and
persist them
● Can execute programs on a real
5 qubit quantum computer
● Quantum simulator also available
https://quantumexperience.ng.bluemix.net/qx/community

89. https://dilbert.com/strip/2012-04-17

90. PUBLIC KEY CRYPTOGRAPHY 101
● Find an algorithm that is easy to do in one direction and
hard to do backwards
○ Multiply two large primes (and keep the primes secret)
○ Discrete logarithms
○ Elliptic curve factorisation
● Don’t tell anybody the secret bit
● Factorisation of large numbers takes
sub-exponential time on a
classical computer

91. MAGIC #1; STEP 6 EXPLAINED (NOT QUANTUM MAGIC)

92. IMPLEMENTING SHOR - CLASSICAL V QUANTUM

93. QUANTUM KEY DISTRIBUTION
https://en.wikipedia.org/wiki/Quantum_key_distribution

95. THE ELEPHANT IN THE QUANTUM ROOM!!

96. She still
doesn’t
care!!!