1. Quantum Computing Paola Cappellaro
Massachusetts Institute of Technology
WHY QC?
Two reasons: A fundamental one and a practical one.

2. Physics and Information
Information is stored in a physical medium and manipulated by physical processes.
The laws of physics dictate the capabilities of any information processing device
Why not exploit quantum mechanics?

3. Are computers already quantum?
Circuit components approach quantum size
Feature size (mm)
Sources:
Ruth DeJule, Semiconductor International; Mark Bohr, Communications of the ACM.
Moore’s Law* sets limits to classical computation
* ”The number of transistors incorporated in a chip will approximately double every 24 months”, Gordon Moore, Intel Co-founder (1965)

4. Quantum Computation Information is stored in 2-level physical systems
Classical bits: 0 or 1
Quantum bits: |0 or |1
QUBITS can also be in a superposition state
a|0 + b |1
with |a|2 the probability of being in state |0
If you have an unsorted database with a million records in it, a classical computer would have to look at a substantial fraction of records, maybe half a million,"
The number of steps needed in Grover's algorithm is defined by the square root of the number items in the data base.
To solve the problem, Grover starts by setting a quantum register to a superposition of all possible items in the database. The quantum state contains the right answer, but if the register were observed at this point, the odds of picking the right answer would be as small as if one picked the item by random.
Grover's discovery involves a sequence of simple quantum operations on the register's state. He describes the process in terms of wave phenomena. "All the paths leading to the desired results interfere constructively, and the others ones interfere destructively and cancel each other out," Grover explains.

5. Quantum Weirdness: Interference
A simple optic experiment: beam splitter
50%
Detector
50%
Single photon source
Beam splitter
Detector

6. Classical Probability
Random coin flip: 50/50 probability
50%
50%

7. Quantum Interference A simple optic experiment: interferometer ?? %
Mirror
?? %
Single photon source
Beam splitter
Mirror

8. Classical Probability
Random coin flip: 50/50 probability
50%
50%

9. Quantum Interference A simple optic experiment: interferometer ?? %
Mirror
?? %
Single photon source
Beam splitter
Mirror

10. Quantum Interference A simple optic experiment: interferometer Mirror
Single photon source
Beam splitter
Mirror

11. Quantum Interference A simple optic experiment: interferometer Mirror
Single photon source
Beam splitter
Mirror

12. Quantum Interference A simple optic experiment: interferometer Mirror
Single photon source
Beam splitter
Mirror

13. Quantum Interference A simple optic experiment: interferometer Mirror
Single photon source
Beam splitter
Mirror

14. Quantum Interference A simple optic experiment: interferometer 100 %
Mirror
0 %
Single photon source
Beam splitter
Mirror

15. Quantum Weirdness: Interference
In quantum mechanics we can make sure that the hiker (the photon) always reaches the cabin!

16. Quantum Weirdness: Superposition
# of Qubits
Quantum States
# classical bits 1
|0, |1
2 = 21

17. Quantum Superposition
# of Qubits
Quantum States
# classical bits 1
|0, |1
2 = 21 2
|00, |01, |10, |11
4 = 22
2 qubits can be in 4 states at the SAME time
Need 4 parameters to describe the states
a|00+ b|01+ g|10+ d|11

18. Quantum Superposition
# of Qubits
Quantum States
# classical bits 1
|0, |1
2 = 21 2
|00, |01, |10, |11
4 = 22 3
|000, |001, |010, … ,|111
8 = 23

19. Quantum Superposition
# of Qubits
Quantum States
# classical bits 1
|0, |1
2 = 21 2
|00, |01, |10, |11
4 = 22 3
|000, |001, |010, … ,|111
8 = 23 … …
|00…, |00…1, … ,|11…1
1k = 210

20. Quantum Superposition
# of Qubits
Quantum States
# classical bits 1
|0, |1
2 = 21 2
|00, |01, |10, |11
4 = 22 3
|000, |001, |010, … ,|111
8 = 23 … …
|00…, |00…1, … ,|11…1
1k = 210 …
1M = 220

21. Quantum Superposition
# of Qubits
Quantum States
# classical bits 1
|0, |1
2 = 21 2
|00, |01, |10, |11
4 = 22 3
|000, |001, |010, … ,|111
8 = 23 … …
|00…, |00…1, … ,|11…1
1k = 210 …
1M = 220 …
1G = 230

22. Quantum Superposition
# of Qubits
Quantum States
# classical bits 1
|0, |1
2 = 21 2
|00, |01, |10, |11
4 = 22 3
|000, |001, |010, … ,|111
8 = 23 … …
|00…, |00…1, … ,|11…1
1k = 210 …
1M = 220 …
1G = 230 …
1T = 240

23. The Power of Quantum Computers
Quantum superposition
➙ parallel computation
Example: quantum “oracle”
wave-function
collapse
n qubits a1 a2 a3 …
f(a1)
f(a2)
f(a3) …
If you have an unsorted database with a million records in it, a classical computer would have to look at a substantial fraction of records, maybe half a million,"
The number of steps needed in Grover's algorithm is defined by the square root of the number items in the data base.
To solve the problem, Grover starts by setting a quantum register to a superposition of all possible items in the database. The quantum state contains the right answer, but if the register were observed at this point, the odds of picking the right answer would be as small as if one picked the item by random.
Grover's discovery involves a sequence of simple quantum operations on the register's state. He describes the process in terms of wave phenomena. "All the paths leading to the desired results interfere constructively, and the others ones interfere destructively and cancel each other out," Grover explains.
f(a)
N=2n states
“oracle” tests all possible answers at once
but answers cannot be read out

24. The power of Quantum Computers
Qt. superposition ➙ parallel computation
Qt. interference ➙ oracle is always right
interference
wave-function
collapse
n qubits
f(a1)
f(a2)
f(a3) …
If you have an unsorted database with a million records in it, a classical computer would have to look at a substantial fraction of records, maybe half a million,"
The number of steps needed in Grover's algorithm is defined by the square root of the number items in the data base.
To solve the problem, Grover starts by setting a quantum register to a superposition of all possible items in the database. The quantum state contains the right answer, but if the register were observed at this point, the odds of picking the right answer would be as small as if one picked the item by random.
Grover's discovery involves a sequence of simple quantum operations on the register's state. He describes the process in terms of wave phenomena. "All the paths leading to the desired results interfere constructively, and the others ones interfere destructively and cancel each other out," Grover explains.
N=2n states
Paths leading to incorrect answers interfere destructively Only the right answer is left upon measurement

25. Quantum speed-up Exponentially faster computations Applications:
BUT: only for some algorithms
Applications:
Database search
Factorization ( = code breaking) …
Simulations of (quantum) systems
Precision measurement, secure communication, …

26. Implementations Need a physical qubit: Trapped ions
Two level quantum system !
Trapped
ions

27. Implementations Need a physical qubit: Trapped atoms
Two level quantum system !
Trapped
atoms

28. Implementations Need a physical qubit: Superconducting circuit
Two level quantum system !
Superconducting
circuit

29. Implementations Need a physical qubit: Semiconductor Quantum dots
Two level quantum system !
Semiconductor Quantum dots

30. Implementations Need a physical qubit: Nuclear & Electronic spins
Two level quantum system !
Nuclear &
Electronic
spins

31. Diamond Quantum Computer
Electronic spin of the NV defect in diamond
Optical initialization and readout
Microwave control

32. Logical gates and circuits

33. Classical Gates Classical computers NOT : 0 ➞ 1 or 1 ➞ 0 AND: 0 , 0 ➞
0 , 1
1 , 0
1 , 1 1
2 inputs ⇓
1 output

34. Quantum Gates Quantum computers NOT : ⎟0〉 ➞⎟1〉 or ⎟1〉➞⎟0〉 CNOT: ⎟0〉⎟0〉
⎟0〉⎟1〉
⎟1〉⎟0〉
⎟1〉⎟1〉
2 inputs ⇓
2 outputs

35. Quantum Gates
Implementation by precise control of a quantum system:
New theoretical and technical tools required Bz
Maybe just little movie of rf rotating a spin.

36. Quantum Gates
Implementation by precise control of a quantum system:
New theoretical and technical tools required Bz
Maybe just little movie of rf rotating a spin.

37. Challenges Quantum systems are fragile
No quantum weirdness in everyday life
Interaction with environment destroys the quantum superposition
Loss of quantum speedup
Challenges worsen with system size
Scalability
Decoherence

38. Conclusions Great promise but greater challenges In the meantime:
When will we have the first quantum computer?
In the meantime:
Better knowledge of quantum mechanics
Applications to
Precision measurements
Simulations
Communications

39. Nuclear Science
& Engineering