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Quantum ComputingPaola CappellaroMassachusetts Institute of Technology
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?
• 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)
Feat
ure
size
(mm
)
Circuit components approach quantum size
Are computers already quantum?
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
Single photon source Beam splitter
Detector
Detector
50%
50%
Classical Probability
• Random coin flip: 50/50 probability
50%
50%
Quantum Interference
• A simple optic experiment:interferometer
?? %
Single photon source Beam splitter
Mirror
Mirror
Classical Probability
• Random coin flip: 50/50 probability50%
50%
Quantum Interference
• A simple optic experiment:interferometer
?? %
Single photon source Beam splitter
Mirror
Mirror
Quantum Interference
• A simple optic experiment:interferometer
Single photon source Beam splitter
Mirror
Mirror
Quantum Interference
• A simple optic experiment:interferometer
Single photon source Beam splitter
Mirror
Mirror
Quantum Interference
• A simple optic experiment:interferometer
Single photon source Beam splitter
Mirror
Mirror
Quantum Interference
• A simple optic experiment:interferometer
Single photon source Beam splitter
Mirror
Mirror
Quantum Interference
• A simple optic experiment:interferometer
0 %
100 %
Single photon source Beam splitter
Mirror
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 # classical bits
1 |0, |1 2 = 21
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 timeNeed 4 parameters to
describe the states
a|00+ b|01+ g|10+ d|11
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 # classical bits
1 |0, |1 2 = 21
2 |00, |01, |10, |11 4 = 22
3 |000, |001, |010, … ,|111 8 = 23
… … …
10 … |00…, |00…1, … ,|11…1 1k = 210
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
… … …
10 … |00…, |00…1, … ,|11…1 1k = 210
20 … |00…, |00…1, … ,|11…1 1M = 220
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
… … …
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 # classical bits
1 |0, |1 2 = 21
2 |00, |01, |10, |11 4 = 22
3 |000, |001, |010, … ,|111 8 = 23
… … …
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”
“oracle” tests all possible answers at once
N=2n states
n qubits a1 a2 a3
…
wave-functioncollapse
f(a1)f(a2)f(a3)
…
f(a)
but answers cannot be read out
The power of Quantum Computers• Qt. superposition ➙ parallel computation• Qt. interference ➙ oracle is always right
N=2n states
n qubits
wave-functioncollapse
f(a1)f(a2)f(a3)
…
Paths leading to incorrect answers interfere destructively Only the right answer is left upon measurement
interference
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:
2 inputs ⇓
1 output
0 , 0 ➞ 00 , 1 ➞ 01 , 0 ➞ 01 , 1 ➞ 1
Quantum Gates
Quantum computers
• NOT : 0⎟ 〉 ➞⎟ 1 〉 or 1⎟ 〉➞⎟ 0 〉
• CNOT: ⎟0 〉⎟0 〉
➞ ⎟0 〉⎟0 〉
⎟0 〉⎟1 〉
➞ ⎟0 〉⎟1 〉
⎟1 〉⎟0 〉
➞ ⎟1 〉⎟1 〉
⎟1 〉⎟1 〉
➞ ⎟1 〉⎟0 〉
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 sizeScalability
Decoherence
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