Quantum state preparation via engineered ancilla resetting

Daniel Alcalde Puente1,2, Felix Motzoi1, Tommaso Calarco1,2,3, Giovanna Morigi4, and Matteo Rizzi1,2

1Forschungszentrum Jülich, Institute of Quantum Control, Peter Grünberg Institut (PGI-8), 52425 Jülich, Germany
2Institute for Theoretical Physics, University of Cologne, 50937 Köln, Germany
3Dipartimento di Fisica e Astronomia, Universitá di Bologna, 40127 Bologna, Italy
4Theoretical Physics, Department of Physics, Saarland University, 66123 Saarbrücken, Germany

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Abstract

In this theoretical investigation, we examine the effectiveness of a protocol incorporating periodic quantum resetting for preparing ground states of frustration-free parent Hamiltonians. This protocol uses a steering Hamiltonian that enables local coupling between the system and ancillary degrees of freedom. At periodic intervals, the ancillary system is reset to its initial state. For infinitesimally short reset times, the dynamics can be approximated by a Lindbladian whose steady state is the target state. For finite reset times, however, the spin chain and the ancilla become entangled between reset operations. To evaluate the protocol, we employ Matrix Product State simulations and quantum trajectory techniques, focusing on the preparation of the spin-1 Affleck-Kennedy-Lieb-Tasaki state. Our analysis considers convergence time, fidelity, and energy evolution under different reset intervals. Our numerical results show that ancilla system entanglement is essential for faster convergence. In particular, there exists an optimal reset time at which the protocol performs best. Using a simple approximation, we provide insights into how to optimally choose the mapping operators applied to the system during the reset procedure. Furthermore, the protocol shows remarkable resilience to small deviations in reset time and dephasing noise. Our study suggests that stroboscopic maps using quantum resetting may offer advantages over alternative methods, such as quantum reservoir engineering and quantum state steering protocols, which rely on Markovian dynamics.

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[2] Samuel Morales, Yuval Gefen, Igor Gornyi, Alex Zazunov, and Reinhold Egger, "Engineering unsteerable quantum states with active feedback", Physical Review Research 6 1, 013244 (2024).

[3] Ruoyu Yin, Qingyuan Wang, Sabine Tornow, and Eli Barkai, "Restart uncertainty relation for monitored quantum dynamics", arXiv:2401.01307, (2024).

[4] Anish Acharya and Shamik Gupta, "Tight-binding model subject to conditional resets at random times", Physical Review E 108 6, 064125 (2023).

[5] Sayan Roy, Christian Otto, Raphaël Menu, and Giovanna Morigi, "Rise and fall of entanglement between two qubits in a non-Markovian bath", Physical Review A 108 3, 032205 (2023).

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