Quantum Computing Reality Check

QUANTUM COMPUTING REALITY CHECK
Demystifying a world of the weird and unexpected
Prof Peter Cochrane
www.petercochrane.com

Why QC ?
The big deal
Without QC we will never understand:
-Life
-Physics
-Biology
-Climate
-Ecologies
-Chemistry
-Cosmology
-Complexity
-Non-Linearity
-Quantum Mechanics
-Many-Body Problems
-++++++++++++++++++

Why QC ?
The big deal
Without QC we will never understand:
-Life
-Physics
-Biology
-Climate
-Ecologies
-Chemistry
-Cosmology
-Complexity
-Non-Linearity
-Quantum Mechanics
-Many-Body Problems
-++++++++++++++++++
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W I L D C L A I M S
Quantum Computers will:
- Access all bank accounts
- Instantly decrypt credit cards
- Replace all our digital machines
- Make quantum encryption mandatory
- Give high precision and certain answers
- Shrink down to become desktop machines
- Solve all our problems today and in the future
- Simulate the known universe with less than 300 Qbits
- xxx
- Improve your sex life

W I L D C L A I M S
Quantum Computers will:
- Access all bank accounts
- Instantly decrypt credit cards
- Replace all our digital machines
- Make quantum encryption mandatory
- Give high precision and certain answers
- Shrink down to become desktop machines
- Solve all our problems today and in the future
- Simulate the known universe with less than 300 Qbits
- xxx
- Improve your sex life
X

KNOWN UNIVERSE
An incomplete definition
Best Estimates ~ 1078 to 1082 Atoms/Protons
Ball Park: Say 1080 ‘Particles’ ~ 2240
So 300 Qbits => 2300 instantaneously defined ‘states’

KNOWN UNIVERSE
An incomplete definition
Best Estimates ~ 1078 to 1082 Atoms/Protons
Ball Park: Say 1080 ‘Particles’ ~ 2240
So 300 Qbits => 2300 instantaneously defined ‘states’
X

Q U A N T U M S U P R E M E C Y
No one complete definition - many shades
Key numbers; IFF we can engineer them!
50 Qbits => 250 ≈ 1015 ≈ 1PBit …. 54 Qbits > 1PByte
70 Qbits => 270 ≈ 1021 ≈ 1ZBit …. 74 Qbits > 1ZByte
70 Qbits Machine can fundamentally perform computations
impossible on any other machine

T H E G O T C H A !
Q u a n t u m S u p r e m a c y ? ?

H M M R E A L L Y !
Q u a n t u m S u p r e m a c y ? ?
Google 53 Qbits
Selected Problem
Best Estimate of
Super Computer
Processing Time
P r o b l e m
S p e c i f i c
S o l u t i o n &
C o m p u t a t i o n
G e n e r a l
P u r p o s e
S o l u t i o n s &
C o m p u t a t i o n
The largest chemical simulation on a
quantum computer to date…but not
all that impressive…energy state min!

KEY CONCEPTS
A d u a l i t y o f s t a t e s
A cat is locked in a box
with a device that that
w i l l k i l l i t a t s o m e
random time….
Before we open to box - all
we can say it that it may
be dead or alive with equal
probability 50% : 50% !
Schrödinger’s Cat
Famously dead and alive
at the same time!

KEY CONCEPTS
A d u a l i t y o f s t a t e s
A cat is locked in a box
with a device that that
w i l l k i l l i t a t s o m e
random time….
Before we open to box - all
we can say it that it may
be dead or alive with equal
probability 50% : 50% !
1
0
Schrödinger’s Cat
Famously dead and alive
at the same time!
HOLD THAT
THOUGHT

K E Y C O N C E P T S
Q u a n t u m e n t a n g l e m e n t
Communication and/or
Action @ a Distance
with no visible/known/
explainable means of
connection..
…demonstrated at
over 100km!

K E Y C O N C E P T S
Q u a n t u m e n t a n g l e m e n t
Einstein
Spooky Action
at a distance
still A MYSTERY
Communication and/or
Action @ a Distance
with no visible/known/
explainable means of
connection..
…demonstrated at
over 100km!

C O N C E P T U A L I S A T I O N
By analogy with a situation we understand
U n s t a b l e
S t a t e
S t a b l e
S t a t e
If the magnets are free floating they will move to the
lowest energy/stress/pressure state of alignment

C O N C E P T U A L I S A T I O N
By analogy with a situation we understand
U n s t a b l e
S t a t e
S t a b l e
S t a t e
If the magnets are free floating they will move to the
lowest energy/stress/pressure state of alignment
All the fields
and forces can
be measured
accuratelyWe can define
and describe all
of them
well
Mathematically
But we still do
not know
what
they are
exactly

WHAT WE KNOW FOR SURE (?)
W h a t o u r e x p e r i m e n t s / m e a s u re m e n t s re ve a l
Gravity - (g) = The weakest force in the universe but occurs in massive
concentrations - only attracts - acts over vast distances
Weak Nuclear Force - (1025 x g) = Only acts at a sub atomic scale and is
responsible for radioactive decay
ElectroMagnetic Force - (1036 x g) = Acts over vast distances but occurs in
very low concentrations - attracts and repels
Strong Nuclear Force - (1038 x g) = Only acts at a sub atomic nucleus scale
attracts & repels - very low concentrations

WHAT WE KNOW FOR SURE (?)
W h a t o u r e x p e r i m e n t s / m e a s u re m e n t s re ve a l
Gravity - (g) = The weakest force in the universe but occurs in massive
concentrations - only attracts - acts over vast distances
Weak Nuclear Force - (1025 x g) = Only acts at a sub atomic scale and is
responsible for radioactive decay
ElectroMagnetic Force - (1036 x g) = Acts over vast distances but occurs in
very low concentrations - attracts and repels
Strong Nuclear Force - (1038 x g) = Only acts at a sub atomic nucleus scale
attracts & repels - very low concentrations
Are we still
missing
something
WE NEED A GUT
that tells us
how
t hey are
all related

SOME COMPUTING BASICS
Digital Computers:
Binary Bit = 1 or 0 with 100% probability
Binary States = ’n bits’ gives 2n possible states
Digital Process = Serial/Exact/Defined and precise
Quantum Computers:
QBit: = 1 and 0 simultaneously with uncertainty
QStates = ’n Qbits’ gives all 2n ‘instantly’
Process = Parallel/Superposition and imprecise
Just like
Schrodinger’s
Cat!

SOME COMPUTING BASICS
Digital Computers:
Binary States = ’n bits’ gives 2n possible states
Digital Process = Serial/Exact/Defined and precise
Quantum Computers:
QBit: = 1 and 0 simultaneously with uncertainty
QStates = ’n Qbits’ gives all 2n ‘instantly’
Process = Parallel/Superposition and imprecise
Just like
Schrodinger’s
Cat!
The sequential
propagation of
deterministic
states
A PROBABALISTIC
propagation of
energy waves
Coherent
solution states
are short lived
and noisy

B o o l e a n A l g e b r a R u l e s
A l l i s w e l l b e h a v e d , s t a b l e
d e t e r m i n i s t i c , r e p e a t a b l e ,
a c c u r a t e , r e l i a b l e , l o g i c a l
O n e m a t h e m a t i c a l
f r a m e w o r k a b l e t o
p o w e r a u t o m a t i o n ,
m e c h a n i c a l / l o g i c /
d i g i t a l c o m p u t i n g
t e l e p h o n e s w i t c h e s ,
m i c r o e l e c t r o n i c s
a n d s u p e r c o m p u t e r s
D I G I T A L C O M P U T I N G
C o n c a t e n a t e d g a t e s o f c e r t a i n t y

Q U A N T U M C O M P U T I N G ?
C o n c a t e n a t e d g a t e s o f n o i s y u n c e r t a i n t y
M a t h a l g o r i t h m s a n d l o g i c
s o l u t i o n s f o r c o m p l e x
p r o b l e m s e t s g r o w i n g
a h e a d o f t h e Q C h a r d w a r e
c a p a b i l i t y
C o m p l e x L o g i c F o r m s
S u i t e d t o t h e a n a l y s i s o f
n o n - l i n e a r s y s t e m s s u c h
a s d a t a b a s e s e a r c h e s ,
b i o l o g y , c h e m i s t r y , l i f e ,
f l u i d f l o w , w e a t h e r
s y s t e m s , p r e d i c t i o n s a l

BACK TO ANALOGUE
Q C i s a n e w p a r a d i g m
QCs are NOT:
-Digital
-Deterministic
-Conditionally stable
-Self reliant stand alone
QCs ARE:
-Analogue
-Subject to errors
-C o n d i t i o n a l l y u n s t a b l e
-Subject to all forms of noise
-R e l i a n t o n d i g i t a l c o m p u t e r s

Q C O P E R A T I O N S
N e e d s d i g i t a l c o n t r o l
Digital computers control programming, algorithms, error
correction, answer selection/testing and verification: and
this is very unlikely to change unless we make new and
fundamental discoveries in physics and/or materials
Digital computers also have a big ‘caretaker’ roll maintaining a
stable temperature controlled environment with cryogenics plant
down below 10mKelvin.

'Physics is to sex, as mathematics is to masturbation'
"I think I can safely say that nobody understands quantum mechanics."
Richard Feynman (1985)
P O S I T I O N I N G
What do we really know?
STILL
TRUE
Toda
y

“Probability and Statistics are a consequence of incomplete/sparse data”
S E G U A E
M o d e l l i n g
“Quantum Theory is a consequence of measurement and modelling
inadequacies”
“Both are victims of a
lack of dimensionality”
⤻
⤻

DEMO: DIMENSIONASLITY
A n ’ N ’ D i m e n s i o n a l w o r l d
A ‘one D’ world looks like this
…and all we can do to describe
the behaviour probabilistically !
Adding just one more dimension
tells the whole story !

This does not look like a deterministic world as there appears to be
no patterns visible. Therefore, all we can do is assume a probabalistic
model and apply statistical analysis as to the distribution, and duration,
of the ﬂashes and possibly discern their colour and brightness.
Just because we cannot see or imagine determinism here does not mean to
say that it does not exist. Let’s add just one more dimension and see what
gives…
ONE DIMENSIONAL WORLD

Now the full determinism of Newtonian Mechanics is revealed and the
mechanism at work is obvious and well known!
TWO DIMENSIONAL WORLD

STOP PRESS
This came as something
of a ‘big’ surprise - and
e x p l a i n s w h y s o m e
studies have hit a dead
end….they really do need
a Quantum Computer!

I G N O R A N C E
And incomplete/imperfect
model does not mean we
cannot exploit something

“Relax your grip on the solid, semi-solid, particle and wave models of the atomic,
sub-atomic and photonic - and start thinking in terms of:
‘clouds of energy’
M Y A D V I C E
A bit of a brain bender!
“And be prepared to ﬂip between time and frequency…and to extend that
understanding to spatial dimensions and forms”
“IFF you have studied Fourier and Laplace you will ﬁnd a lot of axioms here - but if not,
I will also try and explain graphically and with animations”

Cold Does Not Exist - but and absence of heat does
Darkness Does Not Exist - but and absence of photons does
SCIENTIFIC METHOD
A tried and tested framework
Observation
Hypothesis
Theory
Experiment
Agree Disagree
Corroboration
Teams all over the planet try to repeat the
results with some dedicated to disproving
the theory on a continual basis

Cold Does Not Exist - but and absence of heat does
Darkness Does Not Exist - but and absence of photons does
SCIENTIFIC METHOD
A tried and tested framework
Observation
Hypothesis
Theory
Experiment
Agree Disagree
Corroboration
Teams all over the planet try to repeat the
results with some dedicated to disproving
the theory on a continual basis
This methodology has
been tried and tested over
>400 years and is responsible
for the greatest advances our
species has ever enjoyed,
but it can never deliver
100% certainty!

S C I E N T I F I C D I S C I P L I N E
You can never be certain you are right
“The ﬁrst principle is that you must not fool
yourself — and you are the easiest person to
fool.”
“You have to be very careful. After you’ve not
fooled yourself, it’s easy not to fool other
scientists. You just have to be honest in a
conventional way after that.”
Richard P. Feynman

H I S T O R Y
A t o m i c M o d e l s
“These concepts all served us well and have been good enough for their time - but they are incomplete”
Heisenberg uncertainty principle: “As we learn more about the electron's
position, we know less about its energy, and vice versa - and as time and
experiments have progressed, the cloud analogy looks closer to the truth!

H I S T O R Y
A t o m i c M o d e l s
BUT WE MUST
START HERE
The increasing sophistication of these models went hand-in-hand with our ability
to make detailed observations based on laboratory experiments - and in turn gave
us a knowledge of chemistry and materials that has powered our modern world
“These concepts all served us well and have been good enough for their time - but they are incomplete”
Heisenberg uncertainty principle: “As we learn more about the electron's
position, we know less about its energy, and vice versa - and as time and
experiments have progressed, the cloud analogy looks closer to the truth!

A C T U A L I T Y 1
A s f a r a s we c a n o b s e r ve t o d a y
Erwin Schrödinger Wave Function Model 1926
“His conceptualisation and mathematical model turned out to be
a pretty good approximation to the truth given that he had no
way of making any realistic measurements or observations”
We h a v e t o t h i n k i n t e r m s o f p r o b a b i l i s t i c c l o u d s o f e n e r g y
t h a t a r e c o n s t a n t l y o n t h e m o v e a n d n e a r u n b o u n d e d f o r m
S c h r ö d i n g e r d i d n ot d e r i v e
t h i s e q u at i o n : it ‘ s o r t o f ’
p o p p e d i nto h i s h e a d !

A C T U A L I T Y 2
A s f a r a s we c a n o b s e r ve t o d a y
M a n y d i f f e r e n t g r o u p s
g l o b a l l y h a v e i n d e p e n d e n t l y
o b s e r v e d t h e s t r u c t u r e ( o r
l a c k o f i t ) o f d i f f e re n t t y p e s
o f a t o m s u s i n g a v a r i e t y o f
t e c h n i q u e s , a n d a l l
p ro d u c e d re s u l t s t h a t s h o w
v i b r a t i n g a n d f u z z y c l o u d s
o f e n e r g y !

N o t i c e t h a t t h e ( c o h e r e n t )
m a t r i x s t r u c t u r e g i v e s w a y
t o ( d e c o h e r e n c e ) f a u l t
l i n e s f r o m t i m e - t o - t i m e
d u e t o d y n a m i c s t r e s s ,
s t r a i n , f i e l d s & e x t e r n a l
e n e r g y - a f e a t u r e e x p l o i t e d
i n s o m e s e n s o r s y s t e m s b u t a
r e a l ( n o i s y ) p r o b l e m i n Q C !
A C T U A L I T Y 3
A t o m i c c r y s t a l s o l i d i n m o t i o n

2.6km
5.3km
56m
30cm
The Sun & Gold Atom
Normalised to 30cm
radius
A C T U A L I T Y 4
‘ M o re N o t h i n g ’ t h a n t h e u n i ve r s e
A t o m s h a ve ~ 1 0 x
t h e ‘e m p t i n e s s ’ o f
o u r s o l a r s y s t e m

0
F U N D A M E N T A L S T A T E S
R e s o l v i n g t h e s e e m i n g l y i m p o s s i b l e
Digital Computers: two invariant stable states:
Binary States ’n bits’ gives 2n possible states
Quantum Computers: probabilistic semi- stable states:
QBit: = 1 and 0 simultaneously uncertain
QStates ’n Qbits’ gives all 2n ‘instantly’
1:0
1
superposition
?

BITS & QBITS
Some big differences
Binary
1
0
T h o u s a n d s
of Electrons
T e n s o f
Electrons 0
1
A t o m
o r
E l e c t r o n
o r
P h o t o n
1
0
Digital Computer Quantum Computer
Spin
Up
Spin
Down

B L O C H S P H E R E
A t o m s , E l e c t ro n s P h o t o n s , i n m a n y s t a t e s
C o n e o f p r o b a b i l i t y f o r a n e l e c t r o n ,
a t o m , o r p h o t o n e l e c t ro n i c a l l y f o rc e d
t o a s s u m e a g i v e n p o l a r i s a t i o n a s a
Q b i t … u n c e r t a i n t y i s m o s t l y d u e t o
e x t e r n a l i n f l u e n c e s u c h a s n o i s e , E M
r a d i a t i o n , t e m p e r a t u r e , v i b r a t i o n + + +
To o v e r c o m e t h e s e e f f e c t s o p e r a t i n g
t e m p e r a t u r e s g e n e r a l l y < 1 0 m K w i t h
e x t e n s i v e s h i e l d i n g a n d i n s u l a t i o n f r o m
t h e n a t u r a l w o r k i n g e n v i r o n m e n t …
i n c l u d i n g p e o p l e !

P O I N C A R E S P H E R E
A t o m s E l e c t ro n P h o t o n s & m a n y s t a t e s
A t o m s , E l e c t r o n s , a n d P h o t o n s o f f e r t h e
p o t e n t i a l f o r ’ n’ - l e v e l q u a n t u m s y s t e m s
w i t h s t a t e d i a g r a m s s i m i l a r t o d i g i t a l
r a d i o … h o we ve r, c o n t ro l a n d s t a b i l i t y a re
d e m a n d i n g i s s u e s
A l s o k n o w n a n d t h e B l o c h
o r R i e m a n n S p h e r e , & t h e
H i l b e r t S t a t e S p a c e
S i g n a lS t a t e
N o i s e

S U P E R P O S I T I O N
A n o u t c o m e o f t h e S c h rö d i n g e r ’s e q u a t i o n
P a r t i c l e s a re a c o n c e n t r a t i o n
o f e n e r g y i n t h e f o r m w a v e s
t h a t s e e a l l p o s s i b l e s t a t e s
a s s u m e d a t t h e s a m e t i m e … . .
… . n o t u n t i l w e i n s p e c t o r
o b s e r v e t h e p a r t i c l e d o e s i t
a s s u m e a s i n g u l a r s t a b l e s t a t e
O n a n a t o m i c
s c a l e a n e l e c t ro n
s p i n s ~ 1 0 1 1 f a s t e r
t h a n t h i s s i m p l e d e m o

A n o u t c o m e o f t h e S c h rö d i n g e r ’s e q u a t i o n
H e r e w e s l o w d o w n t o
o b s e r v e i n d i v i d u a l s t a t e s ,
b u t i n d o i n g s o we d e s t ro y
a l l s u p e r p o s i t i o n s

Charge
Atomic
Optical
Acoustic
Pressure
Economic
Electronic
Mechanical
Electromagnetic
ElectroMechanical
Electromagnetic
Pulse or
Particle Spectrum
of Waves
P A R A D O X - N O T !
Wa v e - Pa r t i c l e D u a l i t y i s N a t u r a l
Domain
Transformation
Fourier
Laplace
Hankel
Hilbert
Hermite
+++
Z- Transforms
Orthogonal Waves of
different frequencies
Frequency Spacing
= 1/Pulse Rep Rate
Width Deﬁnes the
Spectrum Spread

D U A L I T Y
Pa r t i c l e & Wa v e A n a l o g y
Pa r t i c l e s : A t o m s , E l e c t r o n , P h o t o n s
c a n i n f l u e n c e e a c h o t h e r b e c a u s e
t h r o u g h t h e i r w a v e n a t u r e

“We assign clouds of energy the descriptors of singular atoms with constituents defined by
combinations of singular orthogonal waves collectively interacting in the near and far field -
but we do so with gaps in our understanding of what fields, waves and energy actually are!
P u l s e , p a r t i c l e o r w a v e i n t e r f e r e n c e
The good news is: from the observed and mathematically predicted behaviours, we grasp
sufficient to build everything from MRI Scanners to Nuclear Power Stations+++

S O H E R E W E A R E
A s i n g l e Q b i t i n s u p e r p o s i t i o n
S p i n ‘ u p’
S p i n ‘d o w n ’
0 101

C o n c a t e n a t e dC o n c a
‘Stable’
Input Tensors
‘Noisy, Unstable
Probabalistic’
Output Tensors

C o n c a t e n a t e dC o n c a
‘Stable’
Input Tensors
‘Noisy, Unstable
Probabalistic’
Output Tensors
We have to create an
algorithm or problem
facsimile model and
feed in the input data
states to then inspect
the output DATA
the output has a short
coherence state that
is noisy and we have
to take many samples
to assess and rework
in reverse digitally

C O M P U T I N G
G a t e s / F u n c t i o n a l B l o c k s
A l l t h e m a t r i c e s u s e d a r e
i n t h e f o r m o f 1 : 0 p a t t e r n s
All the1:0 patterns are
made up of Qbits that
are short term stable…
…they occasionally hit a
coherent condition that
represents one possible
solution state

I M A G I N E
M a n y m a n y B l o c k s
E a c h e l e m e n t i s a m a t r i x o f
d i f f e r e n t s i z e & c o n f i g u r a t i o n s
In a quantum machine the qbit states ripple through in
the form of energy waves exhibiting emergent patterns
of coherence and decoherence that periodically reveal
the likely solutions to the problem at hand

Q B I T S T A T E W A V E S
M a t r i c e s o f Q b i t s s e e e n e r g y f l o w s
In a digital machine
we might envisage bits
on the march: a bit and
a gate at a time moving
in synchrony a clock tick
at a time from input to output…
In a quantum machine the qbit states
ripple through in the form of energy waves
with emergent patterns of coherence and
decoherence that periodically reveal the
likely solutions to the problem at hand
NOTE: This illustration is
a model and not actuality

EXAMPLE
Prime factors
Biggest QC Prime Factorisation to date: 1,099,551,473,989 = 1,048,589 x1,048,601
=>> O(1012)
RSA 1024 is =>> O(10309) : RSA 2048 is =>> O(10617)

A R C H I T E C T U R E R S
There are many - experimental
Nowhere near a
production line!

ANALOGUE OUTPUT
O u t p u t f o r m a t !
E r r o r r a t e s o f Q B i t s a n d
c o h e r e n c e u n c e r t a i n t y
l e a d t o a s o l u t i o n s p r e a d
d e m a n d i n g s e v e r a l ‘ r u n s
o r t r i a l s ’ t o h e l p i d e n t i f y
t h e c o r r e c t a n s w e r ( s )
Region of Likely
Answers
Answers Checked
by Digital Computer

S e l e c t N u m b e r
P a i r s f o r Te s t i n g
C h e c k
V a l i d i t y
PAR AD IG M
N o t U n i q u e
C o m p l e x i t y b e y o n d
d i g i t a l c o m p u t e r
F a c t o r i s e : 2 3 7 8 9 . . 0 7
C o m p l e x
Q u a n t u m
A n a l y s i s
M u l t i p l e p o s s i b l e
a n s w e r s t e s t e d b y
d i g i t a l c o m p u t e r
P o s s i b l e s :
7 0 0 4 … 0 1 7
3 1 2 3 … 4 1 9
+ + + +
+ + + +
1 3 6 4 … 0 0 3
Q C
D i g i t a l
C o m p u t e r
M u l t i p l i e s l a r g e p r i m e s
i n c o m b i n a t i o n p a i r s
Ve r i f i e d
R e s u l t

Q B I T P R O G R E S S
N o i s e / S t a b i l i t y C h a l l e n g e
2 Qbits
IBM, MIT
Oxford
Berkley
Stanford
7 Qbits
LosAlamos
5 Qbits
TU Munich 12 Qbits
MIT
50 Qbits
IBM
72 Qbits
Google
128 Qbits
Rigetti
Honeywell
1998 2000 2006
2018
20202017
68 Qbits
IBM

P R O G R E S S
O n a l l f r o n t s

S A N I T Y C H E C K
We h a ve b e e n h e re b e f o re
1 9 5 0 s t a s k s p e c i f i c c o m p u t i n g
& t h e 2 4 x 7 m a i n t e n a n c e c re w
E l e c t r i c M o t o r
f o r t h e 2 M b y t e
H a rd D r i ve

Universal Quantum
Computing Engines
（100k- 1M QBits）
“Probably be the ultimate brain
in the making”
BUT we have NO:
- QBit tech small/reliable enough
- Machine architectures
- Software frameworks
Quantum
Simulation
（Combinatorial
Complexity）
“ T h e c u r r e n t
industry focus”
THE SPECTRUM?
Beyond the BS we have
ProcessingPower&Apps
Time to Commercialisation
Quantum
Annealing
（Optimisation）
Shor’s algorithm: factoring numbers for code breaking >2k Qbits RSA1024
Grover’s algorithm: searching massive unstructured data sets
>50 other unique algorithms have been developed
BUT there are no machines to test them on yet!
Commercialised
‘D’ Wave
QCAAS
Available
2025/30 2035/40

F I N - Q & A ?
www.petercochrane.com
“A digital computer is to a piano as a quantum computer
is to an orchestra”

Quantum Computing Reality Check

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