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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 iN (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 ωres 1.003, 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, , mm100 22 ωωs s .003, , 11.003 ωωresres nn0 011.5.5, , vvg g 00.1.,1, c c 16.4, μm, dR1μm (3) 10- 23- 23 χχ( 3 ) 1110 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.