Quantum computing offers potential advantages over classical computing by utilizing principles of quantum mechanics like superposition and entanglement. A quantum bit or "qubit" can represent more than the binary states of 0 and 1, allowing quantum computers to potentially solve certain problems like searching large databases and optimizing complex systems much faster than classical computers. Several algorithms like Grover's algorithm and Shor's algorithm demonstrate quantum computing's potential. Experimental quantum computers with a handful of qubits have been built by companies like IBM, D-Wave, and others. While still in early stages, quantum computing shows promise for applications in optimization problems in areas like healthcare, machine learning, materials science, and more.

1. FROM BITS TO QUBITS: CAN MEDICINE
BENEFIT FROM QUANTUM COMPUTING?
Mike Hogarth, MD, FACP, FACMI
mahogarth@ucdavis.edu
http://hogarth.ucdavis.edu

2. Early Classical Computers: “Colossus”
• The Z3, Atanasoff-Berry Computer
(ABC), and “Colossus”
– All developed independently of
each other
– All three used *binary*
arithmetic for processing
– Colossus (seen to the right)
developed by British
codebreakers in 1943 to help in
decryption
• *not* the machine built by
Alan Turing to decrypt
Enigma.

3. Early classical computing: ENIAC 1946
• ENIAC - Electronic Numerical
Integrator and Computer (1946-
1955)
– One of the earliest general-
purpose computer
– Performed *decimal* arithmetic
– 100Khz speed
– Multiplying two 10-digit
numbers took 2.8 seconds
– Used in the Manhattan Project

4. What is a “bit”?
● Term coined by Claude
Shannon in his paper A
Mathematical Theory of
Communication (1948)
● Claude Shannon also
founded digital circuit
design theory (1937)
● He attributed “bit” to John
Tukey of Bell Labs who
used it as a short for
‘binary information digit’

5. The solid state device - the transistor
• TRANSfer resISTOR
• Dec 16, 1947 - invented at
Bell Labs by William
Schockley, John Bardeen,
and Walter Brattain
• Provides a switch (on/off)
the replaced the vacuum
tube that could be
miniaturized and wasted less
heat

6. First transistor computer: CADET
• Harwell CADET
– Transistor Electronic
Digital Automatic
Computer - TEDAC (CADET
backwards)
– First fully transistorized
computer
– Dev. in 1951 by Harwell
Dekatron Computer
– Laid the foundations for
the industry and methods
for direct numerical
solutions

7. The boolean nature of transistors
The switch = transistor

8. Basic “logic gates”

9. Logic “circuits” and computation
A “half adder” with carry “out”. Adds
A and B and accounts for carry over
http://www.electronics-tutorials.ws/combination/comb_7.html

10. Integrated circuits that can “add”: A 4-bit binary adder
http://www.electronics-tutorials.ws/combination/comb_7.html

11. How classical computers ‘compute’ for you!
Addition
Multiplication
Square root
Intel i7 CPU ‘registers’

12. Computing with binary circuits and “gates”
http://www.electronics-tutorials.ws/combination/comb_1.html
“integrated circuit” using
transistors - CMOS 4071 with
four OR gates
“integrated circuit” using
transistors - 7408 with four
AND gates

13. A modern microcomputer - designed with integrated circuits

14. Moore’s Law - when will circuits become quantum
mechanical systems?
10 billion transistors!

15. There are also complex computations that cannot be done on classical computers
Time taken to run (N) as a function of the length of the input
Compute time
Input length
(digits for n)

16. Demonstrating the limits of classical computing with python...
Try 2 (2 to the 10 million)10000000
In python:
>>> 2**10000000 (use 7 zeros)
Does not return after 60 seconds….
Try 2 (2 to the 1 million)1000000
In python:
>>> 2**1000000 (1million -- use 6 zeros)
Returns a number in about 3-4 seconds

17. Improving on the “bit” and Moore’s law limitations
• What if you could have a “bit”
that could have more than
binary (“0” or “1”) states?
• What if you could have multi-
state bits with states that can
depend on other bits?

18. How we arrived at “quantum computing”
• Story begins before any concerns
about classical computing or
practical generalized applications
for quantum based computers
• Rolf Landauer - physicist, IBM
Fellow at IBM’s Thomas Watson
Research Center in NY
– First to highlight that computation
is physics at the hardware level
– One is harnessing physics to
perform information processing
– Landauer Principle -- energy must
be expended to erase information
Rolf Landauer (1927-1999)

19. Richard Feynman (1918-1988)
• Nobel prize in physics in 1965 - for work
on quantum electrodynamics and the
physics of elementary particles
• Invited keynote at MIT “First Conference
on the Physics of Computation”
• Feynman proposed simulating quantum
mechanical system using a computer
based on the same principles (a quantum
computer)

20. David Deutsch
• Originally described an experimental
computational system where:
• Submitted idea in 1978 in a paper sent to
Physics Review but was rejected. Did not re-
submit to other journals.
• Resubmitted paper after being invited to do
so - to International Journal of Theoretical
Physics in 1985. It is the seminal paper on
quantum computing today
“a conventional computer operating by quantum means that had some
additional quantum hardware that allowed it to do something extra”
(Deutch)
(age 62)

21. Key Concepts: Deutsch 1985

22. What physical things can be used as a
quantum “multi-state” bit for computing?
• Photon
• Atomic nucleus
• Electron
• Magnetic field

23. Electrons as multi-state “bits”
• An electron’s spin -- can only have two values (up/down) - like a bit
• In a quantum mechanical system, electron spin can be in many (probable) states at
once before it is measures (superposition)
• The fundamental quantum-mechanical nature of “spin” makes it an ideal candidate
for use as a quantum bit (qubit)
• Individual spins can be initialized, coherently controlled, and read out using a
variety of techniques (optical, electronic)

24. Welcome to the “qubit”
https://www.cbinsights.com/blog/quantum-computing-explainer/
● Concept originally introduced by
Stephen Wiesner (1983) in his proposal
for “quantum money”
● Term “qubit” attributed to Benjamin
Schumacher - invented in jest because
it sounded like “cubit”
● Schumacher described a way of
compressing states from a quantum
source of information so they require
less physical resources to store
○ “Schumacher compression”

25. 3-qubits and 8 states at the same time
https://www.doc.ic.ac.uk/~nd/surprise_97/journal/vol4/spb3/#1.1 Quantum computer basics

26. Three key features of quantum computation
• Superposition
• Entanglement
• Annealing

27. Quantum-mechanical systems
and improving on the “bit”
• Superposition
–A quantum-mechanical system can have a particle
be in multiple states at once!
–“Quantum bits” can be in a superposition of states
–Adds significant computational advantage to a
qubit over a bit
• 2 classical bits → a state representing either 0,1,2,3 (1
number at any time
• 2 qubits → can represent all 4 numbers at the same
time

28. Quantum Superposition
• The quantum mechanical
property that has an atom,
electron, or its spin, or its
magnetic field to be in two
‘positions’ (states) at the same
time

29. Entanglement
• Physical phenomenon that occurs when pairs of
particles are generated in ways that the quantum
state of each particle cannot be described
independently
• One must describe the quantum state for the
whole system (A Hamiltonian)
• Described by Einstein, Podolsky and Rosen (EPR) as
the “EPR Paradox”
– Einstein considered it “spooky”
– The “spin” of the particles are “entangled”
changing one, changes the other instantly
– Has been proven to happen with particles
even as far apart as 15m

30. Quantum Entanglement
• The ability of quantum systems to exhibit correlations
between states within a superposition
• If we have two qubits, each in superposition of 0 and 1, the
qubits are said to be entangled
• Seen as a powerful computational feature of quantum
computation
• Interference -- if we examine/measure one qubit’s state,
entanglement causes us to erase the rest

31. Quantum Annealing
• “a method for finding solutions to
combinatorial optimisation problems
and ‘ground states’ of systems”
• What it does at the quantum level --
finds the lowest energy state in a
system
• By letting a system cool and go
through sequential states, it will
“anneal”, one can find the lowest
energy state
• Uses equations that describe the
total energy of a system - a
“Hamiltonian”
Finnila, Gomez, Sebenik, Stenson, Doll. Quantum annealing: A new method for
minimizing multidimensional functions. Chem Physics Letters. 219(1994) 343-348

32. Annealing - reaching the lowest energy point with a
specially designed quantum computer

33. The physics of “annealing”

34. Results using Quantum Annealing

35. Practical applications for QA
• Combinatorial optimization - “traveling
salesman problem”
• Integer factorization (breaks RSA)
• Search in unsorted databases (Grover’s)
• Pattern recognition
• Protein folding

36. Classical vs. Quantum Gates

37. The fundamental Quantum NOT gate

38. A new truly ‘quantum’ gate

39. The “Hadamard” gate
• Hadamard gate - receives a qubit in state 0 as
input and can return a qubit as output that is in a
superposition of 0 and 1 (simultaneously)
• Consistent with Shrodinger’s principle --->
measuring a system in superposition collapses it
to 0 or 1 but probabilistically
– If the Hadamard gate gets a 0 as input, there
is a 50:50 chance of seeing a 0 or 1

40. Quantum Algorithms

41. Grover’s Algorithm
• Lou Grover 1996
• Uses qubits in superposition to compute
‘searches’ much faster than classical
computers
• “Searches” = generalized search
–Finding an item in an *unstructured* list

42. Grover’s -- find item “w” in a list of N items
https://www.youtube.com/watch?v=hK6BBluTGhU
O - operation
N - number of items in the list

43. https://www.youtube.com/watch?v=hK6BBluTGhU
Grover’s algorithm is a quantum algorithm that will perform
search in less time -- lowers it by the square root of the
total items in the list

44. How does it work?
• It puts all the qubits in multiple possible positions
(superpositions)
• 3 steps
– Step 1: Hadamard gates - puts qubits in superpositions (all possible
positions for x)
• Makes the qubits have a uniform amount of energy
– Step 2: Oracle function - flips amplitude of only the item being
searched
– Step 3: Hadamard gates after Oracle function - applies state change
to the qubits and amplifies the value of the item being searched
– Repeat steps 2 and 3 until amplitude reaches ket “w”, meaning
probability is high the result is correct

45. Grover: Step 1
https://www.youtube.com/watch?v=hK6BBluTGhU
Use Hadamard gate to
put all qubits into
superpositions with the
same energy state

46. Grover: Step 2
https://www.youtube.com/watch?v=hK6BBluTGhU
Flip spin amplitude of
the item of interest in
the list

47. Grover: Step 3
https://www.youtube.com/watch?v=hK6BBluTGhU
Use another
Hadamard gate to re-
flip the item of interest
and amplify spin -
repeat steps 2-3 until
amplitude reaches a
high enough reliability
level

48. Peter Shor’s Algorithm and Prime Numbers
https://science.mit.edu/research/faculty/shor-peter-williston
Look out RSA
encryption!!

49. Quantum Logic “gates”

50. Quantum Computing at IBM
Free access to IBM
16-qubit machine
IBM Quantum
Computing Service

51. IBM Q - crowd-sourcing quantum
computing

52. IBM Q Composer

53. IBM 5-qubit Quantum Computer
Real IBM
Quantum Chip
(5 qubit)

54. You can run Grover’s on the IBM too!

55. Implementing algorithms using
“gates” in a drag and drop ‘composer’

56. D-Wave - the first commercial quantum computer

57. The D-Wave quantum transistor - the SQUID
● Superconducting QUantum Interference
Device (SQUID)
● Made of niobium, becomes
superconducting at low temperatures
● A very sensitive magnetometer that can
measure very subtle magnetic fields,
based on superconducting loops
containing Josephson junctions
● The transistor behavior:
● The SQUID stores two magnetic
fields, which either point up (+1) or
down (-1)
● Each SQUID is a qubit that can be
controlled and put into a
superposition of the two states

58. D-Wave
Coupling
● Multi-qubit D-Wave processor has qubits
connected to each other through couplers
● Couplers cause qubits to influence each other
● Mathematically, these elements couple
together qubits, set as variables, providing
parallelized solutions to multi-dimensional
computation
○ Ie, optimization problems where changing
one element requires re-computing of
the others
● Readout device attached to each qubit -
inactive during computation (do not affect
qubit behavior), but read output once
computation has finished
8 qubit loops with 16 couplers ‘connecting’
each qubit with 4 others

59. D-Wave - hardware at a glance

61. Quantum Programming in
Quipper

62. Utility of Quantum Computing

63. Quantum computing in medicine

64. Optimization problems in healthcare
• Anything that requires a high number of
variables and their combinations -- massive
variable problems = “optimization problems”
• Best ED throughput
• Best treatment strategies through pattern
matching

65. Deep Learning Model and Quantum Annealing

66. Correctly identifying handwritten numbers

67. Deep learning for digital pathology

68. FDA and Deep Learning

69. Proteins and modeling structure
• Understanding how proteins fold
• Modeling malfunctioning proteins and their physical structures
http://www.atelier.net/en/trends/articles/quantum-computing-set-revolutionise-health-sector_437915

70. Optimizing Radiation Dosimetry

71. “Quantum Informatics”
• A new field of information science that
optimizes applied information processing
using quantum computing devices
• Just an idea/concept -- what do you think?

72. Quantum Computers in the News

73. UK National Quantum Program

74. Rapidly Evolving Quantum Computing Designs

75. Quantum Commercial Ecosystem

76. Questions?