Adiabatic quantum trajectories in engineered reservoirs

Emma C. King; Luigi Giannelli; Raphaël Menu; Johannes N. Kriel; Giovanna Morigi

doi:10.22331/q-2024-07-30-1428

Adiabatic quantum trajectories in engineered reservoirs

Emma C. King¹, Luigi Giannelli^2,3,4, Raphaël Menu¹, Johannes N. Kriel⁵, and Giovanna Morigi¹

¹Theoretische Physik, Universität des Saarlandes, D-66123 Saarbrücken, Germany
²Dipartimento di Fisica e Astronomia ``Ettore Majorana'', Università di Catania, Via S. Sofia 64, 95123 Catania, Italy
³CNR-IMM, UoS Università, 95123 Catania, Italy
⁴INFN Sezione di Catania, 95123 Catania, Italy
⁵Institute of Theoretical Physics, Stellenbosch University, Stellenbosch 7600, South Africa

Published:	2024-07-30, volume 8, page 1428
Eprint:	arXiv:2311.11937v2
Doi:	https://doi.org/10.22331/q-2024-07-30-1428
Citation:	Quantum 8, 1428 (2024).

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Abstract

We analyze the efficiency of protocols for adiabatic quantum state transfer assisted by an engineered reservoir. The target dynamics is a quantum trajectory in the Hilbert space and is a fixed point of a time-dependent master equation in the limit of adiabatic dynamics. We specialize to quantum state transfer in a qubit and determine the optimal schedule for a class of time-dependent Lindblad equations. The speed limit on state transfer is extracted from a physical model of a qubit coupled to a reservoir, from which the Lindblad equation is derived in the Born-Markov limit. Our analysis shows that the resulting efficiency is comparable to the efficiency of the optimal unitary dynamics. Numerical studies indicate that reservoir-engineered protocols could outperform unitary protocols outside the regime of the Born-Markov master equation, namely, when correlations between the qubit and reservoir become relevant. Our study contributes to the theory of shortcuts to adiabaticity for open quantum systems and to the toolbox of protocols of the NISQ era.

Popular summary

Recent scientific breakthroughs and technological advancements have propelled us into the Noisy Intermediate-Scale Quantum (NISQ) era. While fault-tolerant quantum computers are now closer to reality, current NISQ devices struggle with noise mitigation and scalability.

Recent works suggest that protocols based on engineered reservoirs might improve the efficiency of adiabatic transfer, an important element of adiabatic quantum computing. This highlights the need to quantitatively assess the efficiency of these protocols with respect to their unitary counterparts.

In our work, we consider quantum state transfer in a qubit, the simplest element of a quantum computer. We determine the fastest time at which the transfer can be performed when the qubit undergoes an incoherent dynamics designed by the coupling with a reservoir, which tends to suppress unwanted excitations. By comparing the efficiency of this reservoir-engineered protocol to that of optimal unitary dynamics, we rigorously show that, when the reservoir is memoryless, the latter outperforms the reservoir-engineered protocol. Our insights contribute to the theory of shortcuts to adiabaticity for open quantum systems and to the toolbox of protocols of the NISQ era.

► BibTeX data

@article{King2024adiabaticquantum,
  doi = {10.22331/q-2024-07-30-1428},
  url = {https://doi.org/10.22331/q-2024-07-30-1428},
  title = {Adiabatic quantum trajectories in engineered reservoirs},
  author = {King, Emma C. and Giannelli, Luigi and Menu, Rapha{\"{e}}l and Kriel, Johannes N. and Morigi, Giovanna},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1428},
  month = jul,
  year = {2024}
}

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