Quantum Computing

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