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Implementation of one-qubit holonomic rotation gate by adiabatic passage

Rahim Naderali, M. Amniat-Talab, M. Saadati-Niari, M Mir-Mehdi

Published Jun 1, 2010• 0 citations
OpenAlex

Abstract

We propose a robust scheme, using tripod stimulated Raman adiabatic passage, to generate one-qubit rotation gate. In this scheme, a four-level atom interacts with three resonant laser pulses and time evolution of the corresponding coherent system is designed such that the rotation gate is implemented at the end of process. Rotation angle in this gate is holonomic and has a geometrical basis in the parameter space. We also explore the effect of spontaneous emission on the population transfer with numerical solution of Schrödinger and Liouville equations.

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We propose a robust scheme, using tripod stimulated Raman adiabatic passage, to generate one-qubit rotation gate. In this scheme, a four-level atom interacts with three resonant laser pulses and time evolution of the corresponding coherent system is designed such that the rotation gate is implemented at the end of process. Rotation angle in this gate is holonomic and has a geometrical basis in the parameter space. We also explore the effect of spontaneous emission on the population transfer with numerical solution of Schrödinger and Liouville equations.
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.
The Toffoli gate is an essential logic element, which permits implementation of a reversible processor. It is of relevance both for classical as well as quantum logics. We propose and theoretically study all-optical implementations of three-bit and four-bit Toffoli gates by application of adiabatic population transfer techniques. For a three-bit Toffoli gate we use variants of stimulated Raman adiabatic passage (STIRAP) processes in a ΛΛΛ-type level scheme, driven by two laser pulses at sufficiently large detunings. For the implementation of a four-bit Toffoli gate, we apply reversible adiabatic population transfer in five-level quantum systems, interacting with three laser pulses. We demonstrate correct all-optical implementation of the truth table of three-bit and four-bit Toffoli gates. Moreover, we derive conditions for adiabatic evolution of the population dynamics and robust operation of the gates.
We introduce a procedure for qubit rotation, alternative to the commonly used method of Rabi oscillations of controlled pulse area. It is based on the technique of stimulated Raman adiabatic passage and, therefore, it is robust against fluctuations of experimental parameters. Furthermore, our work shows that it is, in principle, possible to perform quantum logic operations via stimulated Raman adiabatic passage. This opens up the search for a completely new class of schemes to implement logic gates.
In the context of Rydberg anti-blockade, this paper proposes a new scheme for a high-fidelity controlled-unitary gate based on non-adiabatic holonomic quantum computation. Under specific detuning and interaction conditions, the scheme achieves a suitable evolution path for non-adiabatic holonomic quantum computation through reverse engineering of pulse parameters. This scheme can implement arbitrary two-qubit controlled gates with favorable robustness. We also evaluate the effects of spontaneous emission and laser intensity errors on the fidelity; numerical simulations show that the geometric gate scheme still exhibits excellent performance under these errors. Furthermore, we extend the scheme to non-local gates via entanglement transfer and quantum teleportation techniques, and demonstrate its application in the mutual conversion among four-qubit entangled states (GHZ, cluster, and W states). This finding indicates the potential applicability of our scheme to complex quantum information processing tasks.