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arXiv:quant-ph/0701240 · Physical Review A

Geometric phase gates based on stimulated Raman adiabatic passage in tripod systems

Ditte Møller, Lars Bojer Madsen, Klaus Mølmer

Published Jun 4, 2007• 82 citations
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Abstract

We consider stimulated Raman adiabatic passage (STIRAP) processes in tripod systems and show how to generate purely geometric phase changes of the quantum states involved. The geometric phases are controlled by three laser fields where pulse shapes, relative field strength, and phases can be controlled. We present a robust set of universal gates for quantum computing based on these geometric phases: a one-qubit phase gate, a Hadamard gate, and a two-qubit phase gate.

DOI
10.1103/physreva.75.062302

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We consider stimulated Raman adiabatic passage (STIRAP) processes in tripod systems and show how to generate purely geometric phase changes of the quantum states involved. The geometric phases are controlled by three laser fields where pulse shapes, relative field strength, and phases can be controlled. We present a robust set of universal gates for quantum computing based on these geometric phases: a one-qubit phase gate, a Hadamard gate, and a two-qubit phase gate.
Adiabatic geometric phase gates offer enhanced robustness against fluctuations compared to con- ventional Rydberg blockade-based phase gates that rely on dynamical phase accumulation. We theoretically demonstrate two- and multi-qubit phase gates in a neutral atom architecture, relying on a double stimulated Raman adiabatic passage (double-STIRAP) pulse sequence that imprints a controllable geometric phase on the qubit systems. The system is designed in such a way that every atom is individually addressable, and moreover, no extra laser is required to be applied on the target atom while scaling up the system from two- to multi-qubit quantum gates. The gate fidelity has been numerically analyzed by changing the gate operation time, and we find that 98% to 99% fidelity can be achieved for gate time ≃\simeq≃ 0.6 μμμs. We perform a systematic error analysis, which re- veals that our proposed gates can exhibit strong resilience against fluctuations in Rabi frequencies, finite blockade strength, and atomic position variations. These results establish our approach as a physically feasible and scalable pathway toward fault-tolerant quantum computation with neutral atoms. We simulate Grover's search algorithm for two-, three-, and four-qubit systems with high success probability and thereby demonstrate the utility and scalability of our proposed gates for quantum computation.
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.
We present schemes for geometric phase compensation in adiabatic passage which can be used for implementation of quantum logic gates with atomic ensembles consisting of an arbitrary number of strongly interacting atoms. Protocols using double sequences of stimulated Raman adiabatic passage (STIRAP) or adiabatic rapid passage (ARP) pulses are analyzed. Switching the sign of the detuning between two STIRAP sequences, or inverting the phase between two ARP pulses, provides state transfer with well defined amplitude and phase independent of atom number in the Rydberg blockade regime. Using these pulse sequences we present protocols for universal single-qubit and two-qubit operations in atomic ensembles containing an unknown number of atoms.
We present schemes for geometric phase compensation in an adiabatic passage which can be used for the implementation of quantum logic gates with atomic ensembles consisting of an arbitrary number of strongly interacting atoms. Protocols using double sequences of stimulated Raman adiabatic passage (STIRAP) or adiabatic rapid passage (ARP) pulses are analyzed. Switching the sign of the detuning between two STIRAP sequences, or inverting the phase between two ARP pulses, provides state transfer with well-defined amplitude and phase independent of atom number in the Rydberg blockade regime. Using these pulse sequences we present protocols for universal single-qubit and two-qubit operations in atomic ensembles containing an unknown number of atoms.