The document discusses several key concepts in quantum computing including: - Qubits can represent 0, 1, and superpositions using complex numbers unlike classical bits. - Universal quantum gates like CNOT, Hadamard, and Phase gates along with measurement allow performing quantum algorithms. - Topological quantum computing uses topology to make quantum information resilient to errors. - Emerging technologies will see a mix of powerful classical and quantum computing capabilities working together.

1. “Deep in the human
unconscious is a pervasive need
for a logical universe that makes
sense. But the real universe is
always one step beyond logic.”
Frank Herbert, Dune

2. Image credit: https://www.howitworksdaily.com

3. Image credit: https://www.pcworld.com

7. We’re still helpless in
face of exponential
complexity problems

8. Nature computes using quantum
Niels Bohr Albert Einstein by Ehrenfest

11. The Bit The Qubit
0 / 1
𝛼
𝛽
𝛼, 𝛽 ∈ ℂ
𝛼 2 + 𝛽 2 = 1
WHY ?

12. The postulates of
Quantum Mechanics

13. |0 > =
1
0
|1 > =
0
1
| 𝜓 > = 𝛼 | 0 > + β | 1 >

15. 𝑋 ≡
0 1
1 0
𝑌 ≡
0 −𝑖
𝑖 0
𝑍 ≡
1 0
0 −1
𝐻 ≡
1
2
1 1
1 −1
𝑆 ≡
1 0
0 𝑖
𝑇 ≡
1 0
0 𝑒
𝑖𝜋
4

16. H|0> =
1
2
|0> +
1
2
|1>
Also referred as |+> (equal superposition)

17. | 𝜓 > = 𝛼0 | 0 > + 𝛼1| 1 >
| 𝜓 > = 𝛼00 | 00 > + 𝛼01| 01 > + 𝛼10 | 10 > + 𝛼11| 11 >
…
For n qubits, the state vector of the system has 2 𝑛 amplitudes!

18. The power of 2n

19. 𝐶𝑁𝑂𝑇 ≡
1 0 0 0
0 1 0 0
0 0 0 1
0 0 1 0
𝐶𝑁𝑂𝑇 𝑐 >, 𝑡 > = ቊ
𝑐 >, 𝑡 > 𝑖𝑓 𝑐 > = 0 >
𝑐 >, 𝑓𝑙𝑖𝑝 𝑡 > 𝑖𝑓 𝑐 > = 1 >

21. 00 > + 11 >
2
Bell state or EPR pair
a.k.a. “spooky action at a distance”

22. DEMO
The Building Blocks of
Quantum Algorithms

23. Any unitary operation can be approximated to arbitrary accuracy using
Hadamard (H), Phase (S), CNOT, and
𝜋
8
(T) gates.
H, S, CNOT, and T are universal gates

25. How does one design computing
algorithms without the capability of
performing measurements at will?

26. |0>,|0>,|0> = |000>
|0>,|0>,|1> = |001>
|0>,|1>,|0> = |010>
|0>,|1>,|1> = |011>
|1>,|0>,|0> = |100>
|1>,|0>,|1> = |101>
|1>,|1>,|0> = |110>
|1>,|1>,|1> = |111>

27. |000> |001> |010> |011> |100> |101> |110> |111>

28. |000> |001> |010> |011> |100> |101> |110> |111>
Amplitude amplification

29. The Microsoft Quantum Ecosystem
Azure Quantum Microsoft Quantum Network Quantum Development Kit

31. Topological Quantum Computing
Topology is a branch of mathematics describing
structures that experience physical changes such as
being bent, twisted, compacted, or stretched, yet still
maintain the properties of the original form.

32. The fundamental fabric of IT is morphing into a mix of
Ever more complex and powerful classical computing
Mind-bending quantum capabilities

33. THANK YOU!
Q & A
Ciprian Jichici
https://ciprianjichici.ai