1. Suggestion for Optical Implementation of Hadamard Gate Amir Feizpour Physics Department Sharif University of Technology

2. Contents of my talk  Motivation  Implementation Methods  Optical Implementations  The main Problem  Solution  Model Proposed  Results Contents Motivation Implementation Methods Optical Implementations The Main Problem Solution Model Proposed Results

3. Why QI & QC?  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 Optical Implementations The Main Problem Solution Model Proposed Results

4. Quantum Computer  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 Optical Implementations The Main Problem Solution Model Proposed Results

5. Implementation Candidates  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 Optical Implementations The Main Problem Solution Model Proposed Results

6. Why Photons?  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 Optical Implementations The Main Problem Solution Model Proposed Results

7. How to use optics?  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 Implementations The Main Problem Solution Model Proposed Results

8. Optical Schemes  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 Implementations The Main Problem Solution Model Proposed Results

9. Optical Schemes (Continued)  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 Implementation Methods Optical Implementations The Main Problem Solution Model Proposed Results

10. What’s the problem?  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 Implementation Methods Optical Implementations The Main Problem Solution Model Proposed Results

11. What’s the way out?  Pay more to get what you want  KLM theory: ancila bits and post- measurement  Using a intermediate medium: optical non- linearities  But optical non-linearities are usually weak Contents Motivation Implementation Methods Optical Implementations The Main Problem Solution Model Proposed Results

12. There’s yet another way  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 Optical Implementations The Main Problem Solution Model Proposed Results

13. Qubit  Coherent state with a - phase difference and the same average number of photons  Larger values of make the chosen basis more nearly orthogonal Contents Motivation Implementation Methods Optical Implementations The Main Problem Solution Model Proposed Results

14. Semi-Hadamard Gate  Consider this example: Contents Motivation Implementation Methods Optical Implementations The Main Problem Solution Model Proposed Results This transformation is possible using a Kerr media which produces a phase change. The fidelity can be used as a proper criteria

15. Gate: CROW  A coupled resonator optical waveguide made up of micro-rings with large Kerr coefficient Contents Motivation Implementation Methods Optical Implementations The Main Problem Solution Model Proposed Results

16. Dispersion Relation Contents Motivation Implementation Methods Optical Implementations The Main Problem Solution Model Proposed Results  Transfer Matrix Method

17. Unitary Evolution  Effective unitary evolution  where Contents Motivation Implementation Methods Optical Implementations The Main Problem Solution Model Proposed Results

18. Fidelity  Fidelity of obtained output to the desired output for Contents Motivation Implementation Methods Optical Implementations The Main Problem Solution Model Proposed Results

19. Size Sensitivity Contents Motivation Implementation Methods Optical Implementations The Main Problem Solution Model Proposed Results

20. 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.