Experimental Realization of Shortcuts to Adiabaticity in a Nonintegrable Spin Chain by Local Counterdiabatic Driving

Hui Zhou, Yunlan Ji, Xinfang Nie, Xiaodong Yang, Xi Chen, Ji Bian, and Xinhua Peng

Phys. Rev. Applied 13, 044059 – Published 23 April 2020

Abstract

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- $1 / 2$ 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.

Received 28 October 2019
Revised 16 February 2020
Accepted 23 March 2020

DOI:https://doi.org/10.1103/PhysRevApplied.13.044059

Physics Subject Headings (PhySH)

Adiabatic quantum optimization Entanglement production Quantum control Quantum information processing Quantum simulation

Molecules

Nuclear magnetic resonance Quantum spin chains

Quantum Information, Science & Technology

Authors & Affiliations

Hui Zhou ¹, Yunlan Ji^2,3, Xinfang Nie⁴, Xiaodong Yang ^2,3, Xi Chen^2,3, Ji Bian^2,3, and Xinhua Peng^2,3,5,*

¹Department of Physics and Institute of Theoretical Physics, Shaanxi University of Science and Technology, Xi’an, 710021 Shaanxi, China
²Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, 230026 Anhui, China
³CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei, 230026 Anhui, China
⁴Department of Physics and Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055 Guangdong, China
⁵Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026 Anhui, China

^*xhpeng@ustc.edu.cn

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Vol. 13, Iss. 4 — April 2020

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Images

Figure 1
(a) Molecular structure and relevant parameters of iodotrifluoroethylene at 303 K. The chemical shifts and $J$ -coupling constants are on and below the diagonal in the table, respectively. This molecular structure is shown in the inset with $^{13} C$ in natural abundance of 1%. To distinguish those molecules against the large background, we read out all three $^{19} F$ qubits via the $^{13} C$ channel. (b) Experimental reconstructed density matrix of the initial state. (c) Pulse sequence for simulating the dynamic evolution operator (12). Here time durations $τ_{i j} = (2 Δ t | J [t_{m}] |) / π | J_{i j} |$ represent the free evolutions under the natural Hamiltonian (7); the colored rectangles denote the local pulses applied to the individual qubit and pulse phases are indicated inside them. Note that $z$ -direction pulses can be realized with the combined pulses in the $x$ direction and the $y$ direction.
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Figure 2
Experimental reconstructed density matrix of the final state. The left panel represents the theoretical expectation, and the right panel corresponds to the real part of the experimental result. Here $Im ρ_{expt} (T)$ is not shown since the imaginary part is quite small. The rows and columns denote the standard computational basis in binary order from $| 0000 ⟩$ to $| 1111 ⟩$ .
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Figure 3
Instantaneous fidelities and $^{13} C$ spectra in the experiment. (a) Experimental instantaneous fidelities with three different driving strategies: (i) the native Hamiltonian $H_{0} (t)$ (green squares), (ii) the image driving ${\tilde{H}}_{CD} (t)$ (purple circles), and (iii) the real driving ${\bar{H}}_{CD} (t)$ (blue diamonds). The times are nonuniformly sampled to highlight the different experimental results with the three driving protocols, and the solid lines correspond to the theoretical expectations. (b),(c) $^{13} C$ spectra of the evolved states (taking the pseudopure state as the reference spectrum) after the $π / 2$ readout pulse applied to the third qubit with (b) the image driving ${\tilde{H}}_{CD}$ and (c) real driving ${\bar{H}}_{CD}$ . The red and blue spectra, respectively, denote the theoretically simulated and experimental results. A detailed explanation is given in the main text.
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Figure 4
Ground-state fidelity $F$ ( $◻$ ) versus the system size $N$ , and its increasing ratio $Γ$ ( $⊲$ ) compared with the native protocol. The $y$ axes on the left and right represent $F$ and $Γ$ , respectively. Note that the parameters are set the same as in the main text.
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Figure 5
Ground-state fidelity $F$ versus the imperfection of amplitude $η$ (arb. units) and phase $δ$ (radians) in the sweep functions $λ (t)$ .
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