Transcript Slides - IICQI

Suggestion for Optical
Implementation of Hadamard
Gate
Amir Feizpour
Physics Department
Sharif University of Technology
•Contents
•Motivation
•Implementation Methods
Contents of my talk
•Optical Implementations
•The Main Problem
•Solution
•Model Proposed
•Results
Motivation
Implementation Methods
Optical Implementations
The main Problem
Solution
Model Proposed
Results
•Contents
•Motivation
•Implementation Methods
Why QI & QC?
•Optical Implementations
•The Main Problem
•Solution
•Model Proposed
•Results
Quantum Computation
Reduces the needed steps to accomplish a
certain job
Quantum Information
Reduces the amount of data needed to
transmit a certain amount of Information
•Contents
•Motivation
•Implementation Methods
Quantum Computer
•Optical Implementations
•The Main Problem
•Solution
•Model Proposed
•Results
DiVincenzo’s Criteria
A scalable physical system with well
characterized qubits.
The ability to initialize the state of the qubits to a
simple fiducial state.
A universal set of quantum gates such as
generic one-qubit gates and a two-qubit gate.
A qubit-specific measurement capability.
Long relevant decoherence times, much longer
than the gate operation time.
•Contents
•Motivation
•Implementation Methods
Implementation Candidates
•Optical Implementations
•The Main Problem
•Solution
•Model Proposed
•Results
NMR
Ion trap and neutral atom trap
Schemes based on solid state physics
Quantum dot qubits
Superconducting qubits
Schemes based on quantum optics
•Contents
•Motivation
•Implementation Methods
Why Photons?
•Optical Implementations
•The Main Problem
•Solution
•Model Proposed
•Results
Advantages of using photons as qubit
Quantum optics is a well developed field.
Photons decohere slowly.
Photons travel well.
Photons can be experimented with at room
temperature.
•Contents
•Motivation
•Implementation Methods
How to use optics?
•Optical Implementations
•The Main Problem
•Solution
•Model Proposed
•Results
From the view point of qubit
Single photon,
Coherent states.
From the view point of gates
Linear optics,
Non-linear optics.
•Contents
•Motivation
•Implementation Methods
Optical Schemes
•Optical Implementations
•The Main Problem
•Solution
•Model Proposed
•Results
Early optical quantum computer based on
non-linearities
Qantum optical Fredkin gate (Milburn 1989)
N- port interferometers and optical circuits
Decomposition of unitary (Zielinger et. al,
1998)
Optical Simulation of Quantum Logic (Cerf et. al,
1998)
•Contents
•Motivation
•Implementation Methods
Optical Schemes (Continued)
•Optical Implementations
•The Main Problem
•Solution
•Model Proposed
•Results
KLM theory (Knill et al, 2001)
Linear optics (beam splitter and phase shifter)
Probabilistic gates
Teleported gates
Schemes based on coherent state
Non-linear optics
Linear optics
•Contents
•Motivation
What’s the problem?
•Implementation Methods
•Optical Implementations
•The Main Problem
•Solution
•Model Proposed
•Results
Single photon
Photons do not interact directly, making two
qubit gates very difficult
Coherent State
Producing superposition states is a hard to
accomplish
•Contents
•Motivation
What’s the way out?
•Implementation Methods
•Optical Implementations
•The Main Problem
•Solution
•Model Proposed
•Results
Pay more to get what you want
KLM theory: ancila bits and postmeasurement
Using a intermediate medium: optical nonlinearities
But optical non-linearities are usually weak
•Contents
•Motivation
There’s yet another way
•Implementation Methods
•Optical Implementations
•The Main Problem
•Solution
•Model Proposed
•Results
Enhance the effective non-linearity of the
medium
Trapping the photons in the medium
Thus: Increasing the interaction time
How to do that?
Micro-resonator
Photonic crystal
•Contents
•Motivation
•Implementation Methods
Qubit
•Optical Implementations
•The Main Problem
•Solution
•Model Proposed
•Results
 Coherent state with a  phase difference and the
same average number of
photons
 Larger values of  make
the chosen basis more
nearly orthogonal
 , 
0 L, 1
L
•Contents
•Motivation
•Implementation Methods
Semi-Hadamard Gate
•Optical Implementations
•The Main Problem
•Solution
•Model Proposed
•Results
 Consider this example:

exp  i  Z
2



 Z
exp

The fidelity can be used2as a proper criteria
1
This transformation
  isi possible
f 
  U  using a Kerr
media which produces
a  2phase change.
2
•Contents
•Motivation
•Implementation Methods
Gate: CROW
•Optical Implementations
•The Main Problem
•Solution
•Model Proposed
•Results
A coupled resonator optical waveguide
made up of micro-rings with large Kerr
coefficient
•Contents
•Motivation
•Implementation Methods
Dispersion Relation
•Optical Implementations
•The Main Problem
•Solution
•Model Proposed
•Results
 Transfer Matrix
Method
n0  1.5,
  -0.8i,
m  100,
N  5.
•Contents
•Motivation
•Implementation Methods
Unitary Evolution
•Optical Implementations
•The Main Problem
•Solution
•Model Proposed
•Results
 Effective unitary evolution

exp iN (a  a) 2

 where
 s 
Fs
3 c
m


2
4 
2 0 RV0 (vg (s ) c)ne  res 
( 3)
2
•Contents
•Motivation
•Implementation Methods
Fidelity
•Optical Implementations
•The Main Problem
•Solution
•Model Proposed
•Results
 Fidelity of obtained output to the desired output
for
α  2,
2
m  100 ,
ωs
 1.003,
ωres
n0  1.5,
vg
 0.1,
c
R  16.4 μm,
d  1μm,
χ ( 3 )  1 10 - 23
•Contents
•Motivation
•Implementation Methods
Size Sensitivity
•Optical Implementations
•The Main Problem
•Solution
•Model Proposed
•Results
αα 22, ,
100, ,
mm100
22
ωωs s
.003, ,
11.003
ωωresres
nn0 011.5.5, ,
vvg g
00.1.,1,
c
c
dR116
μm.4, μm,
(3)
10- 23- 23
χχ( 3 ) 1110
Acknowledgement
At the end, I must thank my advisors
Prof. A. R. Bahrampour and Prof. V.
Karimipour, and all members of
Quantum Information Group and Optics
Group
at
Sharif
University
of
Technology.