Observing Quantum Correlation Dynamics in Tunable Superconducting Bose-Hubbard Simulators

Abstract

The dynamics of quantum correlations are central to understanding many physical properties of quantum systems. Here we experimentally study the correlation dynamics via two-particle quantum walks in superconducting Bose-Hubbard qutrit arrays, with tunable on-site interaction $U$ realized by Floquet engineering. Quantum walks show the characteristic change from bosonic bunching to fermionic antibunching with increasing $U$. The two-site entanglement and quantum correlation dynamics, as measured by negativity and quantum discord, are investigated. We find that depending on the initial state, the propagation of entanglement can be strongly suppressed with increasing $U$, while that of quantum discord exhibits considerably larger amplitude; or both of them appear insensitive to $U$. Furthermore, the forms of entanglement are found to persist throughout particle walks for $U =$ 0 and it is generally not the case when $U$ increases. Our work highlights the role of interaction in shaping quantum dynamics and extends the realm of simulating correlated quantum systems with superconducting circuits.

Figures (3)

• Figure 1: Experiment and energy spectrum measurement. (a) Schematic superconducting processor. Eight qutrits (crosses) are selected to form a chain by setting the couplers (rectangles) in different states. (b) Qutrit level shifts under longitudinal drive. (c) The measurement of partial energy spectrum. Two qutrits Q$_4$ and Q$_5$ are both initialized to the $|+\rangle$ state. All qutrits are brought to the resonant frequency to evolve with longitudinal drives applied to the even-labeled qutrits. At the end of evolution, each qutrit is measured in the Pauli-X or Pauli-Y basis. (d) Partial energy spectra reflected by Fourier transform magnitudes $S_{ij}(\omega)$ for five qutrit pairs. (e) Total energy spectrum of the system obtained by summing up the partial spectra in (d). (f) Spectrum by numerical simulation of experiment. (g) Spectrum by exact diagonalization.
• Figure 2: Quantum walks and density-density correlations with different initial states and $u$. (a)–(d) Experimental results for the initial state $\ket{\Phi_1}$, i.e., an 8-qutrit chain (Q$_1$ to Q$_8$) with two particles initially placed in the middle two qutrits Q$_4$ and Q$_5$. (e)–(h) Corresponding results with the initial state $\ket{\Phi_2}$. (i)-(l) Experimental results for the initial state $\ket{\Phi_3}$, i.e., a 7-qutrit chain (Q$_1$ to Q$_7$) with two particles initially placed in the middle qutrit Q$_4$. (a), (b), (e), (f), (i), (j) Quantum walks. (c), (d), (g), (h), (k), (l) Density-density correlations measured at $t$ = 68 ns for (c), (d), (g), (h) and 64 ns for (k), (l).
• Figure 3: Negativity ${\mathcal{N}}_{ij}$ and quantum discord ${\mathcal{D}}_{ij}$ with different initial states and $u$. (a)-(c) ${\mathcal{N}}_{45}$, ${\mathcal{N}}_{36}$, ${\mathcal{D}}_{45}$, and ${\mathcal{D}}_{36}$ with the initial state $\ket{\Phi_1}$ for the 8-qutrit chain. (d) Density matrix for Q$_4$Q$_5$ at the points shown as stars in (a). (e)-(h) Corresponding results with the initial state $\ket{\Phi_2}$. (i)-(k) ${\mathcal{N}}_{35}$, ${\mathcal{N}}_{26}$, ${\mathcal{D}}_{35}$, and ${\mathcal{D}}_{26}$ with the initial state $\ket{\Phi_3}$ for the 7-qutrit chain. (l) Density matrix for Q$_3$Q$_5$ at the points shown as stars in (i). Symbols and lines are the experimental results and theoretical results calculated using the experimental parameters, circles (solid lines) and triangles (dashed lines) correspond to the left and right scales, respectively.