Download Quantum Computing

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?
Are computers already quantum?
Circuit components
approach quantum
size
• 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)
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
Quantum Weirdness: Interference
• A simple optic experiment: beam splitter
50%
Detector
50%
Single photon source
Beam splitter
Detector
Classical Probability
• Random coin flip: 50/50 probability
50%
50%
Quantum Interference
• A simple optic experiment:
interferometer
Mirror
?? %
Single photon source
Beam splitter
Mirror
Classical Probability
• Random coin flip: 50/50 probability
50%
50%
Quantum Interference
• A simple optic experiment:
interferometer
Mirror
?? %
Single photon source
Beam splitter
Mirror
Quantum Interference
• A simple optic experiment:
interferometer
Quantum Interference
• A simple optic experiment:
interferometer
Quantum Interference
• A simple optic experiment:
interferometer
Quantum Interference
• A simple optic experiment:
interferometer
Quantum Interference
• A simple optic experiment:
interferometer
100 %
Mirror
0%
Single photon source
Beam splitter
Mirror
Quantum Weirdness: Interference
In quantum mechanics we can make sure that
the hiker (the photon) always reaches the cabin!
Quantum Weirdness: Superposition
# of Qubits
Quantum States
1
|0, |1
# classical bits
2 = 21
Quantum Superposition
# of Qubits
Quantum States
1
|0, |1
2 = 21
2
|00, |01, |10, |11
4 = 22
2 qubits can be in
4 states at the
SAME time
a|00+ b|01+ g|10+ d|11
# classical bits
Need 4 parameters to
describe the states
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
Quantum Superposition
# of Qubits
Quantum States
1
|0, |1
2 = 21
2
|00, |01, |10, |11
4 = 22
3
|000, |001, |010, … ,|111
8 = 23
…
…
…
10
…
# classical bits
|00…, |00…1, … ,|11…1
1k = 210
Quantum Superposition
# of Qubits
Quantum States
1
|0, |1
2 = 21
2
|00, |01, |10, |11
4 = 22
3
|000, |001, |010, … ,|111
8 = 23
…
…
…
# classical bits
10
…
|00…, |00…1, … ,|11…1
1k = 210
20
…
|00…, |00…1, … ,|11…1
1M = 220
Quantum Superposition
# of Qubits
Quantum States
1
|0, |1
2 = 21
2
|00, |01, |10, |11
4 = 22
3
|000, |001, |010, … ,|111
8 = 23
…
…
…
# classical bits
10
…
|00…, |00…1, … ,|11…1
1k = 210
20
…
|00…, |00…1, … ,|11…1
1M = 220
30
…
|00…, |00…1, … ,|11…1
1G = 230
Quantum Superposition
# of Qubits
Quantum States
1
|0, |1
2 = 21
2
|00, |01, |10, |11
4 = 22
3
|000, |001, |010, … ,|111
8 = 23
…
…
…
# classical bits
10
…
|00…, |00…1, … ,|11…1
1k = 210
20
…
|00…, |00…1, … ,|11…1
1M = 220
30
…
|00…, |00…1, … ,|11…1
1G = 230
40
…
|00…, |00…1, … ,|11…1
1T = 240
The Power of Quantum Computers
• Quantum superposition
➙ parallel computation
• Example: quantum “oracle”
n qubits
a1
a2
a3
f(a1)f(a2)f(a3)

N=2n states
wave-function
collapse

f(a)
“oracle” tests all possible answers at once
but answers cannot be read out
The power of Quantum Computers
• Qt. superposition ➙ parallel computation
• Qt. interference ➙ oracle is always right
interference
n qubits
wave-function
collapse
f(a1)f(a2)f(a3)

N=2n states
Paths leading to incorrect answers interfere destructively
Only the right answer is left upon measurement
Quantum speed-up
• Exponentially faster computations
– BUT: only for some algorithms
• Applications:
– Database search
– Factorization ( = code breaking)
…
– Simulations of (quantum) systems
– Precision measurement, secure communication, …
Implementations
• Need a physical qubit:
– Two level quantum system !
Trapped
ions
Implementations
• Need a physical qubit:
– Two level quantum system !
Trapped
atoms
Implementations
• Need a physical qubit:
– Two level quantum system !
Superconducting
circuit
Implementations
• Need a physical qubit:
– Two level quantum system !
Semiconductor
Quantum
dots
Implementations
• Need a physical qubit:
– Two level quantum system !
Nuclear &
Electronic
spins
Diamond Quantum Computer
• Electronic spin of the NV defect in diamond
– Optical initialization and readout
– Microwave control
Logical gates and circuits
Classical Gates
Classical computers
• NOT :
0 ➞ 1 or 1 ➞ 0
• AND:
0,0
0,1
1,0
1,1
➞
➞
➞
➞
0
0
0
1
2 inputs
⇓
1 output
Quantum Gates
Quantum computers
• NOT :
⎟0〉 ➞⎟1〉 or ⎟1〉➞⎟0〉
• CNOT:
⎟0〉
⎟0〉
⎟0〉
⎟1〉
⎟1〉
⎟0〉
➞
➞
➞
⎟0〉
⎟0〉
⎟0〉
⎟1〉
⎟1〉
⎟1〉
2 inputs
⇓
2 outputs
Quantum Gates
• Implementation by precise control of a
quantum system:
– New theoretical and technical tools required
Bz
Quantum Gates
• Implementation by precise control of a
quantum system:
– New theoretical and technical tools required
Bz
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
Conclusions
• Great promise but greater challenges
– When will we have the first quantum computer?
• In the meantime:
– Better knowledge of quantum mechanics
– Applications to
• Precision measurements
• Simulations
• Communications
Nuclear Science
& Engineering