Adiabatic speedup in cutting a spin chain by pulse control in a laboratory frame
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Adiabatic speedup in cutting a spin chain by pulse control in a laboratory frame Rui Wang1 · Feng-Hua Ren2 · Yong-Jian Gu1 · Zhao-Ming Wang1 Received: 14 January 2020 / Accepted: 17 July 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Techniques for the speedup of the adiabatic evolution by adding a leakage elimination operation (LEO) Hamiltonian to the system in an adiabatic frame have been developed recently. The LEO Hamiltonian can be implemented by a sequence of pulses, and the required pulse conditions for obtaining the effective adiabatic speedup have been analyzed. However, the required pulses obtained in an adiabatic frame have to be transformed into the forms in a laboratory frame since the pulses need to be added in a laboratory frame in an experiment. In this paper, we add an LEO Hamiltonian directly in a laboratory frame and find that the required pulse conditions obtained in the adiabatic frame are no longer valid. By exact numerical calculation, we obtain the new pulse conditions in the laboratory frame. We discuss the adiabatic speedup for different types of pulses using the process of cutting a ring spin chain as an example. The fidelity which measures the adiabaticity is found to be nearly one by carefully designing the pulse period and strength for a predefined time. Our scheme is more feasible to be realized in a practical experiment, since the physical implementation of the pulses is a challenging task after a transformation from an adiabatic frame to a laboratory frame. Keywords Adiabatic speedup · Spin chain · Pulse control
1 Introduction The adiabatic theorem [1] asserts that a system prepared in a nondegenerate eigenstate will remain in that instantaneous eigenstate if the system’s Hamiltonian changes sufficiently slow, even though the eigenvalue could change. The performance of the
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Zhao-Ming Wang [email protected]
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Department of Physics, Ocean University of China, Qingdao 266100, China
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College of Information and Control Engineering, Qingdao Technology University, Qingdao 266520, China 0123456789().: V,-vol
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adiabatic evolution is dictated by a long evolution time compared to the inverse of a power of the energy gap the system. It proves to be very useful in a variety of quantum information processing tasks, such as adiabatic quantum computation [2–7], quantum state transmission [8,9], adiabatic algorithm [10–13], and adiabatic quantum annealing [14]. However, during the evolution, the noise from the environment can destroy the quantum nature of the system and the accumulative effect of the environment will be greater for a longer evolution time [15]. Decoherence is a typical example of the deterioration of quantum information in a system due to interactions with the environment[16,17]. As a result, the adiabaticity will be destroyed. However, the adiabatic evolution requires a sufficiently long time. It is difficult to determine the optimal anneal time because while the adiabatic theorem requires a suf
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