Quantum computation using q-deformed coherent states

Raj, Aswathy (2018) Quantum computation using q-deformed coherent states. Masters thesis, Indian Institute of Science Education and Research Kolkata.

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Abstract

Continuous variables have played an important role in quantum information processing and communication (QIPC) with light, due to the highly efficient method of Homodyne detection. This provides a method to directly access the canonical variables of light. Here we have reviewed the paper "Quantum computation with optical coherent states" [T. C. Ralph, A. Gilchrist, and G. J. Milburn, Phys. Rev. A 68, 042319 (2003)], where coherent states |α> and |-α> is considered as logical qubits. Using these coherent states, they have implemented the universal logic gates by the techniques of linear optics. By following their method, we have now obtained the Bit-flip operator for more generalized q-deformed coherent states, where we have considered |α>q and |-α>q as logical qubits. Thus coherent state will be a limiting case of q-deformed coherent state and we can recover it in the limit when q tends to one. q-deformed phase rotation gate using the technique of q-deformed displacement operator is on progress because we need to understand the properties of the non-commutative quantum plane to proceed it further. We will be looking forward to finding the other q-deformed logic gates and we have to understand the advantage of q-deformed logic gates over the logic gates for coherent states.

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