Ahsan 10X Engineering Talk (Quantum Computing).pptx

Quantum Computing: fiction
becoming reality
Talk at 10X Engineering
by
Muhammad Ahsan
Department of Mechatronics and Control Engineering
University of Engineering and Technology Lahore

Quantum Computing in fiction??
Star Wars Teleporter Fiction based on Quantum Teleportation

Quantum Computing is Real
Experimental teleportation with diamond
spins at Henson Lab, TU Delft’s (2014)
https://qutech.nl/lab/hanson-lab/
research-highlights/hanson-lab-teleportation/
China experimental teleportation of photons with
Micius Satellite between Delingha and Nanshan
1120 Km apart (2020)
https://doi.org/10.1038/s41586-020-2401-y

Quantum Speedup
• D-Wave 1440-qubit Quantum Annealer solves instances of Monte Carlo
Path Integral Problem (https://www.nature.com/articles/s41467-021-20901-5)
• 1000 times faster than the NVIDIA Tesla V100 GPU
• 108 times faster than the i7-8650U CPU (single thread)
• Google 53-qubit Sycamore quantum processor generates a specific type of
quantum random number (https://www.nature.com/articles/s41586-019-1666-5)
• In less than 4 minutes, whereas the world most powerful supercomputer
Summit would take 10,000 years

Basic Philosophy of Quantum Computing
“What computers can or cannot do is determined by the
laws of physics alone, rather than pure mathematics”
David Deutsch
University of Oxford
(Pioneer of quantum
computing)
How powerful is our computer will depend on
our ability to manipulate physics for computation

Why Quantum Computing a Big Deal
Theoretically Secure
(Hack-Proof) Communication
Polynomial time O(n3) Integer factorization
Highly efficient solution of world’s most complicated problems
Speedup in hard optimization problem
Advancing Machine Learning Algorithms
Rapid Breakthroughs in Drug Design
Finding Killer strategies in War-fare
Cracking current encryption
Quantum
Cryptography

Who is interested in Quantum Computing?
P A K I S T A N ? ?

Agenda
• Basics of Quantum Computing
• Quantum Algorithms
• Experimental Progress
• Quantum Computing for Pakistan Defense

Quantum Bit (1)
+
-
Equation of classical LC oscillator
𝑑𝑄
𝑑𝑡2 = −
𝑄
𝐿𝐶
:
Charge (Q), Current
𝑑𝑄
𝑑𝑡
oscillates at single natural frequency 1
𝐿𝐶
Equation of quantum LC oscillator: 𝑖ℎ
𝑑
𝑑𝑡
|𝑄 = 𝐻|𝑄
Charge (Q), Current
𝑑𝑄
𝑑𝑡
can oscillate at SET of NATURAL FREQUENCIES
1
2 𝐿𝐶
, 3
2 𝐿𝐶
, 5
2 𝐿𝐶
, . . .
Discrete Energy Levels: E0
E1 E2 , . . .
𝛥𝐸 𝛥𝐸 𝛥𝐸
Schrodinger equation
Classical case: Single solution Q(t) VS Quantum case: Multiple solutions Q(t)

Quantum Bit (2)
+
-
1
2 𝐿𝐶
, 3
2 𝐿𝐶
, 5
2 𝐿𝐶
, . . .
Discrete
Energy Levels
E0
E1 E2 , . . .
𝛥𝐸 𝛥𝐸 𝛥𝐸
Oscillator
Initial energy
level
Pulse
energy: 𝛥𝐸
Oscillator
new energy
level
Pulse
energy:
1
2
𝛥𝐸
Oscillator is in the Quantum Superposition of Energy Levels E0 and E1
+
𝑖ℎ
𝑑
𝑑𝑡
|𝑄 = 𝐻|𝑄
Is satisfied by
|𝑄0 → |𝐸0
|𝑄1 → |𝐸1
as well as
𝛼|𝑄1 + 𝛽|𝑄2 →𝛼|𝐸0 + 𝛽|𝐸1
Complex
numbers
Oscillator new energy level
will be
1
2
𝐸0 , 𝑎𝑛𝑑
1
2
𝐸1
1
2
1
2

Quantum Bit (3)
+
-
1
2 𝐿𝐶
, 3
2 𝐿𝐶
, 5
2 𝐿𝐶
, . . .
Discrete
Energy Levels
E0
E1 E2 , . . .
𝛥𝐸1 𝛥𝐸2
𝛥𝐸𝑛
|0 |1
|𝜑 = 𝛼|0 + 𝛽|1
Qubit Computational Basis
Non-Linear
Inductor
General Qubit State:
Physical realization of
a Superconductor
Qubit (Operating Temp ~ m K)
Discard Higher energy levels
for computation
(𝛥𝐸1 ≠ 𝛥𝐸2)

Introduction to Quantum Bit
+x =-|0>
-x
+y = |0>
-y = |1>
Quantum Bit
Unit Vector ANYWHERE on the Circle (actually Sphere)
|𝜑 = 𝛼|0 + 𝛽|1
=-|1>
→ α and β are complex
→ Three degrees of freedom a, b, θ ∈ ℜ
|𝛼|2 + |𝛽|2 = 1
or
|𝜑 = 𝑎|0 + eiθ b|1
Classical Bit Val: 0
|0>, |1> → classical binary states
|𝜑 =
𝛼
𝛽 ,
Quantum Bit (Qubit) has both magnitude (a, b) of |0> and |1> and phase (θ)
Phase of Qubit enables constructive and destructive interference
= |𝟎 = |𝟏

Introduction to Quantum Bit
+x =-|0>
-x
+y = |0>
-y = |1>
Quantum Bit
Unit Vector ANYWHERE on the Circle (actually Sphere)
|𝜑 = 𝛼|0 + 𝛽|1
=-|1>
Quantum Mechanics allows α and β to be complex
Three degrees of freedom a, b, θ ∈ ℜ
|𝛼|2 + |𝛽|2 = 1
or
|𝜑 = 𝑎|0 + eiθ b|1
Quantum Gate
𝑈𝑈† = 𝐼
Rotate |𝜑 on Bloch sphere using
Unitary transformation U = e-ihH
𝑈|𝜑 = 𝑈 𝛼|0 + 𝛽|1 = 𝑈
𝛼
𝛽
|0>, |1> → classical binary states
|𝜑 =
𝛼
𝛽 ,
𝑖ℎ
𝑑
𝑑𝑡
|𝜑(𝑡 = 𝐻|𝜑(𝑡
Solve for |𝜑(𝑡
|𝜑(𝑡 = 𝑒−𝑖ℎ𝐻𝑡
|𝜑(0
Quantum Bit (Qubit) has both magnitude (a, b) and phase (θ)
Simple
Matrix-Vector
Multiplication!

Introduction to Single-Qubit Quantum Gates
𝑋 =
0 1
1 0
𝐻 =
1
2
1 1
1 −1
Z =
1 0
0 −1
𝑋 𝛼|0 + 𝛽|1 = 𝛼|1 + 𝛽|0
𝑍 𝛼|0 + 𝛽|1 = 𝛼|0 − 𝛽|1
Bit-Flip (NOT) gate
Phase (flip) gate
Hadamard gate
𝐻|0 = 1 2 |0 + |1
𝐻|1 = 1 2 |0 − |1
X
Z
H
0 1
1 0
VS Classical NOT gate
No equivalent classical gate !
Superposition
Phase

Multi-Qubit Quantum System
|𝜑 1 =
𝛼1
𝛽1
|𝜑 2 =
𝛼2
𝛽2
|𝜑 12 = |𝜑 1 ⊗ |𝜑 2 =
𝛼1
𝛽1
⊗
𝛼2
𝛽2
=
𝛼1𝛼2
𝛼1𝛽2
𝛽1𝛼2
𝛽1𝛽2
|𝜑 123...𝑛 = |𝜑 1 ⊗ |𝜑 2 ⊗. . .⊗ |𝜑 𝑛 =
𝛼1𝛼2. . . 𝛼𝑛
𝛼1𝛼2. . . 𝛽𝑛
.
.
.
𝛽1𝛽2. . . 𝛽𝑛
2n dimensional vector
4 dimensional vector
2-dimensional vector(s)
Single-qubit
Two-qubits
.
.
.
.
.
n-qubits
Can represent 2n n-bits
long numbers
in superposition!
= 𝛼1|0 + 𝛽1|1 = 𝛼2|0 + 𝛽2|1
= 𝛼1𝛼2|00 + 𝛼1𝛽2|01 +
𝛽1𝛼2|10 + 𝛽1𝛽2|11
Tensor Product
= 𝛼1 𝛼2. . . 𝛼𝑛|00. . . 0 + 𝛼1𝛼2. . . 𝛽𝑛|00. . . 1 +
. . . +𝛽1𝛽2. . . 𝛽𝑛|11. . . 1
n-bits
2-bits
e.g. for n = 300 qubits
2300 > number of atoms
In the universe!
(= |𝜑 1|𝜑 2. . . |𝜑 𝑛)

Multi-Qubit Gates : Entanglement (1)
Two-Qubits Gate: Controlled NOT (CNOT)
|𝜑 𝑋𝑌 = 𝑎1|00 + 𝑎2|01 + 𝑎3|10 + 𝑎4|11
∀𝑎𝑖 ∈ ℂ2
𝐶𝑁𝑂𝑇 =
1 0 0 0
0 1 0 0
0 0 0 1
0 0 1 0
|𝑌 |𝑋 ⊕ 𝑌
|𝑋 |𝑋
CNOT |𝜑 𝑋𝑌 = 𝑎1|00 + 𝑎2|01 + 𝑎3|1𝟏 + 𝑎4|1𝟎
𝑎2, 𝑎4 = 0 ⇒ 𝐶𝑁𝑂𝑇|𝜑 𝑋𝑌 = 𝑎1|00 + 𝑎3|11
Cannot decompose |𝜑 𝑋𝑌 into |𝜑 𝑋 |𝜑 𝑌
Entanglement
|𝜑 𝑋 = 1
2
|0 + |1 |𝜑 𝑌 = 1
2
|0 − |1
|𝜑 𝑋𝑌 = |𝜑 𝑋 ⊗ |𝜑 𝑌 = 1
2 |00 − |01 + |10 − |11
CNOT |𝜑 𝑋𝑌 = 1
2 |00 − |01 − |10 + |11
= 1
2
|0 − |1 ⊗ 1
2
|0 − |1
Phase of Controlled-qubit X has flipped
Due to qubit Y !
Another Example:
Phase-Kick Back Effect

Multi-Qubit Gates : Entanglement (2)
Three-Qubits Gate: TOFFOLI
|𝜑 𝑋𝑌𝑍 = 𝑎1|000 + 𝑎2|001 + 𝑎3|010 + 𝑎4|011 +
𝑎5|100 + 𝑎6|101 + 𝑎7|110 + 𝑎8|111
∀𝑎𝑖 ∈ ℂ2
|𝑥
|𝑦
|𝑧
|𝑥
|𝑦
|(𝑥 and 𝑦 ⊕ 𝑧
TOFFOLI |𝜑 𝑋𝑌𝑍 = 𝑎1|000 + 𝑎2|001 + 𝑎3|010 + 𝑎4|011 +
𝑎5|100 + 𝑎6|101 + 𝑎7|11𝟏 + 𝑎8|11𝟎
|𝑥
|𝑦
|1
|𝑥
|𝑦
|𝑥 NAND 𝑦
Using Toffoli gates, we can simulate any
classical boolean logic circuit
Classical computation Subset
of Quantum Computation

Quick Introduction to Quantum Computing (2)
• Quantum Measurement
|0>
|1>
|𝜑 = 𝛼|0 + 𝛽|1 M
|𝜑 = |0 w.p. |𝛼|2
|𝜑 = |1 w.p. |𝛽|2
OR
• Quantum State Space: n-qubit system “simultaneously” spans all 2n bit-strings patterns
|𝜑 𝑛
=
𝑥=0
𝑥=2𝑛−1
𝑎x|𝑥 = 𝑎0|000. . . 0 + 𝑎1|000. . . 1 +. . . +𝑎2𝑛−1|111. . . 1
n-bit string
H
H
H
|0
|0
|0
Equal superposition state:
|𝜑 𝑛
with equal ai
𝑎0 = 𝑎1 =. . . = 𝑎2𝑛−1 =
2−𝑛 2
.
.
.
. .
.
.
|𝜑 𝑛 = 𝑎0|000. . . 0 + 𝑎1|000. . . 1 +. . . +𝑎𝑘|011. . . 1 +. . . +𝑎2𝑛−1|111. . . 1
n-qubit Measurement: |𝜑 𝑛
|𝜑 𝑛 = |000. . . 0 w.p. |𝑎0|2 |𝜑 𝑛
= |000 … 1 w.p. |𝑎1|2 |𝜑 𝑛 = |111 … 1 w.p. |𝑎2𝑛
−1|2
Designing Quantum Algorithm is all about clever manipulation of amplitudes: ai s
Quantum Algorithm should Measure |𝝋 𝒏
such that |ai|2 of correct solution string is close to 1
M or

What we have learned so far
• Quantum Superposition:
• Allows qubit in state |0> and |1> simultaneously (e.g. |0> + |1>)
• Quantum Entanglement:
• State of one qubit depends on the state of the other ( e.g. |00> + |11>)
• Quantum Measurement:
• Reading qubit(s) state collapses superposition (or entanglement) (e.g.
Measuring (|0>+|1>) → 0 or 1 w.p. 0.5 each)

Quantum Algorithms(1)
A function fs(x) outputs inner product of n-bit input x and string s as 𝑠 • 𝑥 = 𝑠0𝑥0 ⊕ 𝑠1𝑥1 ⊕. . .⊕ 𝑠𝑛−1𝑥𝑛−1
s is unknown. The goal is to find s by calling fs(x)
Classical: Need upto n queries/calls to the function fs(x)
Quantum : Need only 1 query/call to the function fs(x)
H
H
H
|0
|0
|0
H
|1
|𝜑 4 = |000 |0
|𝜑 4 =
1
4
(|000 + |001 + |010 + |011 +
|100 + |101 + |110 + |111 |0 − |1
|𝜑 4
=
1
4
(|000 − |001 + |010 − |011 −
|100 + |101 − |110 + |111 |0 − |1
H
H
H
H
M
M
M
|𝜑 4
=
1
3
(|101 |0 − |1
fs(x)
|1
|1
|0
|1
Example:
Assume
fs(x)
with
s = (1,0,1)
s
Phase Kick-Back

Quantum Grover’s Search Algorithm(1)
Problem: Find solution to an unstructured search problem (e.g. NP-complete problems)
Quantum (Grover’s) Algorithm: O(√𝑁) Classical algorithms: O(𝑁)
Search space containing N candidate solutions
Worst Case
Complexity
|𝜑 = 1
8
|00 + |01 + |10 + |11 |0 − |1
Equal superposition of
4-candidate solutions |x>
Helping qubit
state
|𝜑 = 1
8
|00 + |01 − |10 + |11 |0 − |1
|𝜑 = 1
8
|10 |1
H
H
H
|0
|0
|1
f(x)
M
M
|1
1
2
−1 1 1 1
1 −1 1 1
1 1 −1 1
1 1 1 −1
𝑎1
𝑎2
𝑎3
𝑎4
𝑎 = 1 4 𝑎1 + 𝑎2 + 𝑎3 + 𝑎4
=
2 𝑎 − 𝑎1
2 𝑎 − 𝑎2
2 𝑎 − 𝑎3
2 𝑎 − 𝑎4
Example:
H
𝑓(𝑥 =
|𝑥 if |𝑥 ∉ Solution
−|𝑥 if |𝑥 ∈ Solution
Inversion about the mean
Solution obtained using only 1 Grover Iteration
Grover Iteration
Phase-kick back
in solution state

Grover Search ~ Quantum Tunneling
Landscape
Cost
Function
Classical: T ∝ exp(∆)
Quantum: T ∝ exp(∆1/2 w)
if w << ∆1/2 then T = O(2
√∆
)
Time (T) to reach global minima ∝ Energy to surmount the barrier
w
∆
∆: Height of Barrier
w: Width of Barrier
For hard optimization problems, let 2
∆
~ N (# possible solutions)
= O(√𝑵)
Example: Quadratic Unconstraint Binary Optimization problem
Maximize xT Q x s.t. x ∈ 𝟎, 𝟏 𝒏
QT = Q is defined by the problem
Machine Learning
Support Vector Machine Classifier
Computer aided Design
Jobs Scheduling
AI Labs at Google, NASA Intel

Integer Factorization(Exponential Speedup)
Inverse
Quantum
Fourier
Transform
M
M
M
M
M
Solution: Choose a s.t.
For n-bit integer N
GCD (a, N) = 1, a < N
N = (ar/2-1) (ar/2+1)
Period r is hidden in
Eigenvalues of
U(x) = ax mod N
Quantum
Modular
Exponentiation
U(x) = ax mod N
|Input
qubits>
Period
(r)
Exponential Speedup over Best Known Classical Algorithm !
Classical: Finding eigenvalues of N x N matrix takes O(N3) → O(2n^3) Exponential in n
Quantum Integer Factorization Algorithm
Quantum Modular Exponentiation:
Complexity: O(log N)3 = O(n3)
Quantum Fourier Transform:
Complexity: O(log N)2 = O(n2)
Open threat to widely used RSA based public-key cryptosystems e.g. Internet!
Best-known Classical Algorithm for Integer Factorization: Sub-Exponential in n
Problem: Given N, a product of two very large unknown prime number x, y. Find x, y

Quantum Teleportation
Qubit state |𝜑 cannot be copied to another qubit (No-Cloning Theorem)
Problem: How to build ‘wires’ to transmit quantum state (signal) ??
Solution: Teleportation
H MA
MB
X Z
|B>
|C>
|𝐴𝐵𝐶 = 1
2
𝛼|0 + 𝛽|1 |00 + |11
|𝐴𝐵𝐶 = 1
2
𝛼|000 + 𝛽|110 + 𝛼|011 + 𝛽|101
|𝐴𝐵𝐶 = 1
2
|00 𝛼|0 + 𝛽|1 +
|01 𝛼|1 + 𝛽|0 +
|10 𝛼|0 − 𝛽|1 +
|11 𝛼|1 − 𝛽|0
|A>=𝛼|0 + 𝛽|1
|BC>= 1
2
|00 + |11 Einstein-Podolsky-Rosen
(EPR Pair)
X
Z
Both X, Z
Apply on |C>
If MA = 1: Apply Z on C
If MB = 1: Apply X on C
|AB> |C>
Teleportation: Re-creating Quantum State at the Destination
Destroying Quantum State at the Origin
𝛼|0 + 𝛽|1
= 𝛼|0 + 𝛽|1

Quantum Communication
Cannot make clones of qubit state Measuring qubit state changes the state of qubit
Theoretically Secure Key Distribution for cryptography
|0 H 1
2
|0 + |1 = | +
|1 H 1
2
|0 − |1 = | −
Two Types of Encoding basis States
|0 , |1 | + , | −
0 1 0 1
H H
Two ways to encode classical
bit into qubit |𝒙
If encoding basis is kept secret,
then Measuring |𝒙 Changes |𝒙
Measurement Basis
{|0 , |1 }
Measurement Basis
{| + or | − }
0: |𝑥 = |0 |𝑥 =|0 |𝑥 = | + or | −
prob. 0.5 each
1: |𝑥 = |1 |𝑥 = |1
0: |𝑥 = | + |𝑥 → |0 or |1 ,
prob. 0.5 each
|𝑥 = | +
1: |𝑥 = | + |𝑥 =| −

Quantum Key Distribution(1)
0 1 1 1 0 0 1 0 1 1
| + | − |1 | − |0 | + | − |0 | − |1
|0 ,
|1
| + ,
| −
|0 ,
|1
|0 ,
|1
| + ,
| −
|0 ,
|1
| + ,
| −
|0 ,
|1
| + ,
| −
|0 ,
|1
| + ,
| −
|0 ,
|1
|0 ,
|1
|0 ,
|1
| + ,
| −
| + ,
| −
|0 ,
|1
| + ,
| −
| + ,
| −
|0 ,
|1
0 0 1 0 0 0 1 0 1 1
Classical Channel
Classical Channel
Sender:
Alice
Receiver
Bob
Eve
Alice bit
Alice Basis
Eve Basis
Bob Basis
Bob’s bit 0 0
Secret Key: 0 1 0 1 1
Hacked bits

Quantum Key Distribution(2)
Prob. (Alice key bit = Bob’s key bit) = Prob. (Eve chose correct basis) +
Prob. (Eve chose incorrect basis) × Prob. (Bob’s still gets correct key bit)
= ½ + ½ × ½ = ¾
How can Alice and bob detect the presence of Eve (Eavesdropper)??
Insight: Eve introduces error into Bob’s measurement
Prob. (Perfect match between Alice and Bob’s 1 key bit) = ¾
Prob. (Perfect match between Alice and Bob’s n key bits) = 𝟑
𝟒
𝑛
Prob. (eavesdropper is detected) = Prob. (bit hacked) = Prob. (one or more mismatch in Alice and Bob’s n key bits) = 1 - 𝟑
𝟒
𝑛
To detect eavesdropper with Prob. > 0.95, 1 - 𝟑
𝟒
𝑛 > 0.95 → 𝑛 = 20
Advantage: By increasing the length of Key, eavesdropper can be detected with arbitrarily high probability
Theoretically Secure Communication
Experimentally QKD has been achieved over a distance of 20,000 Km

Experimental Progress in
Quantum Key Distribution
Year
Description of advances in
quantum communication
technology
Distance between
entangled qubits
Distance of secure
communication
Circuit
circuit error-rate
(E) /Quantum bit
error- rate (QBER)
2015
Entanglement demonstration on
board a nano-satellite
Less than Km N/A 4% (QBER)
2016
Quantum key distribution (QKD) in
free space
53 Km N/A 3.3-9.5% (QBER)
2016 Entanglement with satellite > 1200 Km N/A 10% (E)
2017
Ground to satellite QKD and satellite
to ground quantum teleportation
> 1200 Km N/A
20% and 1.1% (E)
2018
Satellite relayed Intercontinental
quantum network
N/A >7,600 Km
1-2.4% (QBER)
2018
Quantum communication from
global navigation satellite system
N/A > 20,000Km
44% (E)
2020 Entanglement based QKD 1,120 Km 1,120 Km Unknown
2021 Integrated satellite and ground QKD N/A 4,600 Km Unknown

Quantum Hardware (Trapped-Ion, Photons)
Laser (gate)
Ions (qubits)
Electrodes
Optical
Switch
Photon
Detectors
Photons
Ballistic
Shuttling
Channel
U
|𝑥
|𝑦
|𝑧
|𝑥
|𝑦
|𝑥 ⊕ 𝑦 ⊕ 𝑧
|𝑥
|𝑦
|𝑥
|𝑥 ⊕ 𝑦
|𝑥 𝑈|𝑥
M
|𝑥 {|0>,
|1>}
Entangled
Pair
(EPR pair)
Quantum
Gates
(Qubits) Video credit: Jason Amini
Beam
Splitter
|0
|1
Stable Energy
Levels

Quantum Computer Control Hardware
Microelectromechanical
(MEMS) Mirror
V1
V2
V3
V4
V6
V5
Individual addressing of ion
Quantum Gates
Ballistic Shuttling of ions
Laser Pulses
Laser Control
System
Digital to
Analogue
Converter
FPGA

Experimental Progress in Quantum Computing
Size of
quantum
processor
# qubits
Company
127 IBM
80 Rigetti
53 Google
20 IonQ
12 Honeywell
11 Baidu
D-Wave Quantum
Computer
2007 28-qubits
2011 128-qubits
2013 512-qubits
2015 >1000-qubits
VS
Quantum Superposition, Entanglement Only Quantum Tunneling
Superposition??
Entanglement??
General Purpose
Quantum
Computing??
Fully Quantum
D-Wave Customers:

Experimental Challenges in Quantum Computing
• Practically, quantum device component (qubits, gates) are very noisy
and unreliable than classical computers (Both Bit-flip and Phase-flip errors)
Need Error-Correction (Redundancy) to protect quantum Information
Mean Time to Failure:
Classical:
~ 107 – 108 hours
Quantum:
~Seconds – Minutes
Failure Prob.
p = 10-3
1 in 1,000 Quantum
Gate fails

Example: Fault Tolerant 3-qubit (Toffoli) Gate
Error Correction
Encoding
Encoding
Encoding
Error Correction
Error Correction
|𝑥
|𝑦
|𝑧
|𝑥
|𝑦
|(𝑥. 𝑦 ⊕ 𝑧
|𝑥 𝐿
|𝑦 𝐿
|𝑧 𝐿
4-cat
4-cat
dec.
4-cat
4-cat
dec.
4-cat
4-cat
dec.
4-cat
4-cat
dec.
4-cat
4-cat
dec.
4-cat
4-cat
dec
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
Recovery
Unprotected Quantum Gate Fault Tolerant Quantum Gate
Parity
Checks
Special
Entangled
Qubit
State
Large Number of Additional Qubits, Gates to reduce effective Noise Level from O(p) -> O(p2)
|𝑥
e.g. Steane [[7,1,3]] code
- -
- -
- -
- -
- -
- -
- -
Special
Entangled
Qubit
State

Quantum practically superior than Classical
How many physical qubits?
Practically we need
3 million qubits quantum computer to factorize
2,048-bits number in 5 months
-Ahsan et al., 2015
Current world record of Integer factorization: 768-bit integer factorized in 2005
Classical Computers: 2048-bit number impossible to be factorized in realistic time scale

Worldwide attention to my PhD research
• Designing a Million-Qubit Quantum Computer Using a Resource
Performance Simulator
• Cited in IBM patent US11314908B2
• Cited (X-category) in Google patent WO2022/051030 A3
• Cited in the book ‘Quantum Computing Progress and Prospects’ published by
National Academies of Sciences, Engineering and Medicine USA. ISBN 978-0-309-
47969-1
• Open source SQrIpT toolbox
• Submitted to IARPA, USA (Quantum Computer Science project 2013-2015)
• PhD students Iran universities (Research)
• Reported as fasted qubit partitioning tool in the comparison
(https://iopscience.iop.org/article/10.1088/1402-4896/abd57c)
• Photonic Inc. Burnaby, BC Canada (Research and Development)

Military Application of Quantum Computing
Breaking RSA based encryption
(Hacking the enemy)
Secure Communication
(Hack-Proof Networking)
Quantum Sensing, Imaging
(Gravity Sensors to detect
Underground Bunkers)
Quantum Navigation
(Navigation in the GPS
Denied Environment)
Quantum Physics
Optimization of military
travel path
Warfare-Planning and
Sequence of operations
Quantum Communication
Quantum Search Algorithms U.S and China spending millions of
dollars on Quantum Computing

Pakistan Defense
Battle-field is like a chess-board (to some degree)
military resources → chess pieces (rook, knight, queen etc.)
To win the game of Chess, you need to move pieces
1. Outsmart
2. Outpace
the opponent
Historically, Pakistan has fewer pieces than its opponent
Compensate by finding killer moves faster than the opponent
Quantum Search: O(√𝑵) time-steps to find killer move
(vs O(N) for classical search)
Quantum Speed-up can be crucial to win the battle

A little bit of quantum mechanics
In Quantum Mechanics, the measurable physical state (e.g. position, momentum) of a system
1. are discrete and quantized (Eigenvalues/vectors of Hermitian matrix H)
2. are described by a wave function |𝜑(𝑡 which tells:
“What is the probability that system state in a given eigenvalue of H?”
|𝜑 = 𝑝1 𝑝2 . . . 𝑝𝑛
e1 e2 . . . en
Prop. to Probability Distribution (p2
1 + p2
2 + … + p2
n = 1)
Eigenvalues of H
𝑖ℎ
𝑑
𝑑𝑡
|𝜑(𝑡 = 𝐻|𝜑(𝑡 |𝜑 1 = 𝑝1
1
𝑝2
1
. . . 𝑝𝑛
1
Satisfies Schrodinger equation
|𝜑 2
= 𝑝1
2
𝑝2
2
. . . 𝑝𝑛
2
Also satisfies Schrodinger equation
𝛼|𝜑 1 + 𝛽|𝜑 2
Schrodinger’s equation
Linear Superposition:
Superposition allows quantum system states in two different states simultaneously!

Ahsan 10X Engineering Talk (Quantum Computing).pptx

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