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International Journal of Optics and Photonics

Implementation of Single-Qutrit Quantum Gates via Tripod Adiabatic Passage

Rahim Naderali, Akbar Jafaridolama, M. Amniat-Talab

Published Jan 15, 2010• 0 citations
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•Jan 1, 2015•2 citations
Controlled and multi-controlled quantum gates, whose action on a target qubit depends on the state of multiple control qubits, represent a fundamental logical building block for complex quantum algorithms. We propose a scheme for realizing this class of gates based on non-Abelian holonomies in modulated photonic waveguide networks. Our approach relies on linear photonic cicuits formed by two star networks coupled via a two-path circuit. A star network with M peripheral waveguides coupled to a single central site, or M-pod, naturally generalizes the tripod structure used in non-Abelian Thouless pumping and stimulated Raman adiabatic passage (STIRAP). In the present work, we first analyze the minimal case of two connected tripods and design adiabatic driving loops that implement single-qubit, CNOT, and SWAP gates. We then show how extending the approach to larger M-pod structures enables the realization of multiply controlled operations, which we exemplify by designing Toffoli and the OR gate on two coupled pentapods. Finally, we demonstrate that networks of connected tripods can implement the Deutsch quantum query algorithm.
In this paper, we use stimulated Raman adiabatic passage technique to implement single-qutrit quantum gates in tripod systems. It is shown by using the Morris-Shore (MS) transformation, the six-state problem with 5 pulsed fields can be reduced to a basis that decouples two states from the others. This imposes three pulses not connected to the initial condition with have the same shape. Using this method, the six-state penta-pod system is reduced to a tripod system. We can design single-qutrit quantum gates by ignoring the fragile dynamical phase, and by suitable design of Rabi frequencies of the effective Hamiltonian
We discuss the quantum rotation gates in tripod system. We show that Stimulated Raman Adiabatic Passage (STIRAP) requires high Rabi frequencies to have a perfect rotation gate. Moreover, we improve this process by using superadiabatic approach. This approach requires additional Hamiltonian that can be implemented by driving the tripod with additional fields. Furthermore, we show that it is robust to the decay of the excited state, but not to the dephasing caused by collisions or phase fluctuations of the driving fields.