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arXiv:2309.06031 · Physical Review Research

High-fidelity macroscopic superposition states via shortcut to adiabaticity

Mehdi Aslani, Vahid Salari, Mehdi Abdi

Published Sep 24, 2024• 2 citations
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Abstract

A shortcut to an adiabatic scheme is proposed for preparing a massive object in a macroscopic spatial superposition state. In this scheme we propose to employ counterdiabatic driving to maintain the system in the ground state of its instantaneous Hamiltonian while the trap potential is tuned from a parabola to a double well. This, in turn, is performed by properly ramping a control parameter. We show that a few counterdiabatic drives are enough for most practical cases. A hybrid electromechanical setup in superconducting circuits is proposed for the implementation. The efficiency of our scheme is benchmarked by numerically solving the system dynamics in the presence of noises and imperfections. The results show that a mechanical resonator with very-high-fidelity spatially distinguishable cat states can be prepared with our protocol. Furthermore, the protocol is robust against noises and imperfections. We also discuss a method for verifying the final state via spectroscopy of a coupled circuit electrodynamical cavity mode. Our work can serve as the ground work to feasibly realize and verify macroscopic superposition states in future experiments. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.033332

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A shortcut to an adiabatic scheme is proposed for preparing a massive object in a macroscopic spatial superposition state. In this scheme we propose to employ counterdiabatic driving to maintain the system in the ground state of its instantaneous Hamiltonian while the trap potential is tuned from a parabola to a double well. This, in turn, is performed by properly ramping a control parameter. We show that a few counterdiabatic drives are enough for most practical cases. A hybrid electromechanical setup in superconducting circuits is proposed for the implementation. The efficiency of our scheme is benchmarked by numerically solving the system dynamics in the presence of noises and imperfections. The results show that a mechanical resonator with very-high-fidelity spatially distinguishable cat states can be prepared with our protocol. Furthermore, the protocol is robust against noises and imperfections. We also discuss a method for verifying the final state via spectroscopy of a coupled circuit electrodynamical cavity mode. Our work can serve as the ground work to feasibly realize and verify macroscopic superposition states in future experiments. Published by the American Physical Society 2024
Since the establishment of the quantum mechanics, researchers in physics have been studying superposition states and especially proposing setups for generating macroscopic objects in a quantum superposition state. Such states are important and of interest both from a foundational perspective and for their applications in the emerging quantum technologies. Here, we propose a circuit quantum electrodynamical setup and an adiabatic scheme for preparing a macroscopic and massive object in a quantum superposition state. The scheme is based on establishing a spatial double-well potential for a macroscopic object and preparing it in the ground state of the potential via an adiabatic transition. The resulting state is a spatial superposition state where the object assumes a superposition of bulked to two opposite directions, e.g. right and left. By numerical solving of the quantum optical master equation and including the environmental effects, we show that the target cat state is achievable with a high fidelity provided the process satisfies the adiabaticity conditions.
We propose a scheme to fast prepare the three-qubit W state via superadiabatic-based shortcuts in a circuit quantum electrodynamics (circuit QED) system. We derive the effective Hamiltonian to suppress the unwanted transitions between different eigenstates by counterdiabatic driving, and obtain the W state with high-fidelity based on the superadiabatic passage. The numerical simulation results demonstrate that the proposed scheme can accelerate the evolution, and is more efficient than that with the adiabatic passage. In addition, the proposed scheme is robust to the decoherence caused by the resonator decay and qubit relaxation, and does not need additional parameters, which could be feasible in experiment.
Abstract We review a scheme for the systematic design of quantum control protocols based on shortcuts to adiabaticity in few-level quantum systems. The adiabatic dynamics is accelerated by introducing high-frequency modulations in the control Hamiltonian, which mimic a time-dependent counterdiabatic correction. We present a number of applications for the high-fidelity realization of quantum state transfers and quantum gates based on effective counterdiabatic driving, in platforms ranging from superconducting circuits to Rydberg atoms.
Shortcuts to adiabaticity provide fast protocols for quantum state preparation in which the use of auxiliary counterdiabatic controls circumvents the requirement of slow driving in adiabatic strategies. While their development is well established in simple systems, their engineering and implementation are challenging in many-body quantum systems with many degrees of freedom. We show that the equation for the counterdiabatic term—equivalently, the adiabatic gauge potential—is solved by introducing a Krylov basis. The Krylov basis spans the minimal operator subspace in which the dynamics unfolds and provides an efficient way to construct the counterdiabatic term. We apply our strategy to paradigmatic single- and many-particle models. The properties of the counterdiabatic term are reflected in the Lanczos coefficients obtained in the course of the construction of the Krylov basis by an algorithmic method. We examine how the expansion in the Krylov basis incorporates many-body interactions in the counterdiabatic term. Published by the American Physical Society 2024
Shortcuts to adiabaticity are powerful quantum control methods, allowing quick evolution into target states of otherwise slow adiabatic dynamics. Such methods have widespread applications in quantum technologies, and various shortcuts to adiabaticity protocols have been demonstrated in closed systems. However, realizing shortcuts to adiabaticity for open quantum systems has presented a challenge due to the complex controls in existing proposals. Here, we present the experimental demonstration of shortcuts to adiabaticity for open quantum systems, using a superconducting circuit quantum electrodynamics system. By applying a counterdiabatic driving pulse, we reduce the adiabatic evolution time of a single lossy mode from 800 ns to 100 ns. In addition, we propose and implement an optimal control protocol to achieve fast and qubit-unconditional equilibrium of multiple lossy modes. Our results pave the way for precise time-domain control of open quantum systems and have potential applications in designing fast open-system protocols of physical and interdisciplinary interest, such as accelerating bioengineering and chemical reaction dynamics.
Counterdiabatic driving (CD) offers a fast and robust strategy to manipulate and prepare the quantum state in multibody systems. However, the exact CD term involving the spectral properties of the system is difficult to calculate and generally takes a complicated form for higher-dimensional complex systems. Recently, Sels and Polkovnikov [Proc. Natl. Acad. Sci. U. S. A. 114, E3909 (2017)] proposed a variational method to optimally approximate the CD term with no need for the full spectral information of the original Hamiltonian. Using a nuclear-magnetic-resonance setup, here we report an experimental demonstration of this method to construct available shortcuts to adiabaticity in a nonintegrable spin-1/21/21/2 chain via only local controls. In this process, the ground state of such a system is rapidly prepared and the final state fidelity is significantly increased compared with the traditional adiabatic method. Our experiments prove the feasibility of this variational method to design CD in practice, and thus it is a promising strategy for fast, high-fidelity quantum-state manipulation in complex and noisy quantum systems.