Flashcards in QIC Deck (46):

1

## Limits of Classical Computing (2)

###
1) Moore's law - double no. transistors on chip in 18 months, will reach size of atom by 2020

2) Thermodynamics - logic gates have 2ips and 1op - loss of information, change of entropy, gives off heat which must be dissipated

2

##
General Qubit State

N Qubit state

###
|phi> = a|0>+b|1>

Isomorphic to spin 1/2 system

|phi> = a1|00..0> + a2|00..1>.. 2^N coefficients - exponential scaling gives quantum power

3

## How do you achieve single-qubit rotation?

### Resonant EM field

4

## What happens to 2 level system subject subject to resonant excitation?

### Rabi oscillations

5

## Physical explanation of origin of population oscillations

### Populations oscillate with Rabi oscillations, cycles of absorption and stimulated emission

6

## 2 Kinds of rotation of state on Bloch Sphere

###
1) Free evolution - precesion around z axis

2) Interatction with an external field - takes qubits from |0> or |1> to equitorial plane

7

## Bloch Sphere positions

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+z : |0>

-z : |1>

(p = 1/root2)

+x : p(|0>+|1>)

-x : p(|0>-|1>)

+y : p(|0>+i|1>)

-y : p(|0>-i|1>)

8

## theta and phi L

###
thetaL = extent of rotation, determined by strength and duration of pulse

PhiL gives axis about which rotation occurs, determined by phase of external field

9

## pi/2 pulse, pi pulse, 2pi pulse, 4pi pulse

###
pi/2 - takes you from |0> to -x or +x

pi - change from 0 to 1 and vice versa

2pi - 0 back to top of sphere, global sign not represented

4pi - recovers original state of spin 1/2 system

10

## 2 Applications of Ramsey interferometry

###
1)Atomic clocks

2) Measurement of fundamental constants

11

## Qubit A has state vector |phi>a in vector space Ha and Qubit B has same in B, 2 qubit state |phi>ab lives in?

### Ha tensor product Hb

12

## What is density operator rho?

###
outer product

rho = |psi>

13

## Difference between product and entangled state, example of each

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Product state |psi>ABC has 6 = 2N coefficients, but general state has 8 = 2^N - can't make all states, others are entangled, can't be written as prouct of 6-qubit state

eg 1/root2(|00>+|11>)

14

## How do you use density matrix formulism to calculate expectation value of operator M

### = Tr(rho M) = Tr(M rho)

15

## Classical correlations

### Socks - measuring string of L and R, measurements are correlated

16

## EPR Paradox

### It is tempting to think that qubits A and B have well defined states after they interact but this does not produce the same correlations as QM result

17

## Bell states

###
p = 1/root2

|phi+-> = p(|01>+-|10>)

|psi+-> = p(|00>+-|11>)

18

## How to engineer entangled state from product state with controlled collision

### Start with qubits in neighbouring boxes, both state 0, apply pi/2 pulse to both - positive x direction. Displace 0 component of A towards 1 component of B - state evolves and gives entangled state.

19

## CNOT gate

###
conditional Ramsey interferometer, qubits labelled target and control

2 i/p 2 o/p not fighting thermo, reversible - know what went in

20

## Truth table for CNOT

###
IN OUT

00 00

01 01

10 11

11 10

If control is 1, target changes, pi phase change

21

## CNOT universal

### Network of CNOT gates and single qubit rotation is sufficient for performing arbitrary computation

22

## 5 DiVincenzo criteria

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1)Scalable system with well characterized qubits

2) Initialization into well defined state

3) Long decoherance times

4) Universal set of quantum gates

5) Efficient procedure for measuring state of qubits at end of calculation

23

## What might archtecture of QC look like?

###
Input -> quantum logic gates -> output

000, 001 --> Function of 0's and ones

24

## Choices of qubits

###
Photons - good for conveying info but not storing (travel at c)

NMR - no scalability

Quantum Dots - CM

Superconductiong Josephson Junction - CM

Laser cooled atoms

25

## Laser cooling hinges on 3 effects

###
1) Radiation Pressure

2) Doppler effect

3) Resonance

26

## Momentum photon in plane wave

###
p = hbar k

Atom that absorbs photon recoils to conserve momentum

27

## How is it possible to use lasers to cool atoms?

###
Atoms absorb photons and recoil, typical change of speed 3cms-1, absorb photons to slow atoms, need closed system

Detuning

Resonance, atom going away from beam shifts left, right shifts closer to resonance, net force opposes motion - friction

28

## If detuning of laser from resonance for stationary atom is delta, for atom with vel v?

### delta - k.v

29

## Atomic absorption line

### Power broadened lorentzian with scattering rate R (in notes)

30

## How do you use optical molasses in 3D

### 3 pairs of counterpropagating beams which are mutually orthogonal

31

## What happens in optical molasses?

### The atoms get into equilibrium when laser cooling balances momentum diffusion

32

## Lowest achievable temperature

### kbTdoppler = 1/2 hbar gamma

33

## Trapping atoms

### Neutral atoms can be trapped with dipole potentials

34

## Stark shift - lightshift

###
Look at graphs

Light shift interpreted as ac stark shift

35

## Origin of Dipole Force

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E induces dipole d in atom

If wL>w0 - d.E out of phase by pi -d.E is positive

36

## Geometries for strong dipole force

###
1) counterpropagating beams - can extend to 3D with more beams, optical lattice.

2)Focussed laser beam - steep gradient: large force

37

## Trapping atoms delta

###
Trap atoms at intensity maxima if delta is negative

Trap at minima if delta is positive

38

## Principles of laser cooling and importance of each

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i) Radiation pressure - provides momentum transfer

ii) Doppler effect - ensures force opposes motion

iii) resonance - detuning laser frequency in vicinity of resonance provides strong frictional force

39

## KE group of atoms

###
ke = 3/2 N k_b T

approx 100 micro K so turns out to be change of ke of 3/2 N kb T

40

## Where does energy go Doppler?

### Radiated light carries away energy as average energy of emitted photon larger than energy used for laser cooling

41

## CNOT, inverse CNOT, swap

###
1000

0100

0001

0010

1000

0001

0010

0100

1000

0010

0100

0001

42

## R(pi/2, pi/2)

###
1 -1

1 1

43

## Eigenenergies

###
+- hbar/2 (omega^2 + delta^2)^1/2

E1,2 = +- hbar/2 (Delta/2 + omega^2/4delta)

first term E difference between atom and light, second term is light shift or ac stark shift

44

## Scattering rate

###
As more atoms are scattered, atom accelerates and is doppler shifted off resonance, rate decreases

Force is R x energy (hbar k)

45

## How to check eigenvalue

###
Want to know if k is eigenvalue of A

Ak = lamda k

46