Topological Quantum Computation II VATSHAL SRIVASTAV 14790 INSTRUCTOR

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Topological Quantum Computation- II -VATSHAL SRIVASTAV (14790) -INSTRUCTOR (PROF DR. RAJAT MITTAL) – QUANTUM

Topological Quantum Computation- II -VATSHAL SRIVASTAV (14790) -INSTRUCTOR (PROF DR. RAJAT MITTAL) – QUANTUM COMPUTING VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

Revision q. Obstacles while building a quantum computer q. Quantum Statistics q. Anyons q.

Revision q. Obstacles while building a quantum computer q. Quantum Statistics q. Anyons q. Braid statistics VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

https: //www. youtube. com/watch? v=GJHhnr 9 R_ZM&t=190 s VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

https: //www. youtube. com/watch? v=GJHhnr 9 R_ZM&t=190 s VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

https: //www. youtube. com/watch? v=GJHhnr 9 R_ZM&t=190 s VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

https: //www. youtube. com/watch? v=GJHhnr 9 R_ZM&t=190 s VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

Overview • Fusion Rules • Phase exchange for fused anyons • Fibonacci Anyons •

Overview • Fusion Rules • Phase exchange for fused anyons • Fibonacci Anyons • Structure of Hilbert Space • Braiding Fibonacci Anyons • Computing With Fibonacci Anyons • Conclusion VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

Fusion Rules VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

Fusion Rules VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

Phase exchange for fused anyons VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

Phase exchange for fused anyons VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

Fibonacci Anyons VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

Fibonacci Anyons VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

Structure of Hilbert space VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

Structure of Hilbert space VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

Braiding Fibonacci Anyons VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

Braiding Fibonacci Anyons VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

Computing with Fibonacci Anyons VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

Computing with Fibonacci Anyons VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

Conclusion • We can make C-NOT gates, NOT Gates etc. • Makes it universal

Conclusion • We can make C-NOT gates, NOT Gates etc. • Makes it universal set of quantum computation • Extension of similar non-Abelian theories VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

Acknowledgement • Prof Dr. Rajat Mittal (Departmant of Computer Science and Engineering) • Srujan

Acknowledgement • Prof Dr. Rajat Mittal (Departmant of Computer Science and Engineering) • Srujan Sapkal, Abu, Aditya Sinha, Ayush Mukherjee References • Sumathi Rao, Introduction to abelian and non-abelian anyons • Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, Sankar Das Sarma, Non-Abelian Anyons and Topological Quantum Computations VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

Thank you! Questions? ? VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

Thank you! Questions? ? VATSHAL SRIVASTAV | TOPOLOGICAL QUANTUM COMPUTATION

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