Quantum synchronization and chimera states in a programmable quantum many-body system

Abstract

Synchronization is a hallmark of collective behavior in classical nonlinear systems, yet its realization as a robust many-body phenomenon in coherent quantum systems remains largely unexplored. Here we demonstrate symmetry-protected quantum synchronization and a quantum chimera state in coherent Floquet dynamics on programmable superconducting quantum processors. By implementing stroboscopic evolution of a two-dimensional Heisenberg model on IBM heavy-hex devices, we observe that initially phase-randomized spins spontaneously self-organize into coherent lattice-wide oscillations. On 28 qubits, synchronization persists even for strongly randomized initial states and is stabilized by SU(2) symmetry, as confirmed by explicit symmetry breaking. Scaling up to 156 qubits reveals a qualitatively distinct regime. For weak initial randomness, global synchronization extends across the device. For strong randomness, the system fails to synchronize globally, yet subsets of qubits exhibit robust local phase coherence under homogeneous unitary dynamics. This coexistence of globally desynchronized and locally synchronized regions constitutes a quantum analogue of a classical chimera state. Statevector and matrix-product-state simulations reproduce both the symmetry-protected synchronization and the chimera coexistence, demonstrating that these phenomena arise from the intrinsic Floquet many-body dynamics. Our results establish symmetry-protected synchronization and quantum chimera states as experimentally accessible nonequilibrium dynamical phases in programable many-body quantum systems.

Figures (6)

• Figure 1: Emergence of global synchronization and quantum chimera in a 156-qubit Floquet system.a, Local in-plane magnetization vector field $(\langle \hat{X}_j\rangle,\langle \hat{Y}_j\rangle)$ from MPS simulations with bond dimension $\chi=600$ on a heavy-hex lattice with $L=156$. For weak phase randomness $(\phi^{\rm max}/\pi=1)$, an initially disordered configuration (left) evolves into a globally synchronized state at $t/T=30$ (right). For strong randomness $(\phi^{\rm max}/\pi=2)$, the system instead develops a quantum chimera at $t/T=30$ (right), where spatially separated regions retain internal phase coherence while remaining mutually incoherent. b, Synchronization order parameter $\kappa$ at $t/T=30$ as a function of initial-state randomness $\phi^{\rm max}$. $\kappa=1$ corresponds to perfect global phase alignment, whereas $\kappa=0$ indicates complete absence of coherence; intermediate values reflect partial synchronization. Black circles indicate the two values of $\phi^{\rm max}$ shown in a. Parameters are $(\theta_{XX},\theta_{ZZ},\theta_{Z})=(-0.25\pi,-0.25\pi,0.25\pi)$ (see Methods). Arrow lengths are rescaled independently in each panel for clarity.
• Figure 2: Symmetry-protected synchronization on a 28-qubit heavy-hex lattice. Data are obtained from experiments on the ibm_kobe quantum processor. a, Error-mitigated local transverse magnetizations $\langle \hat{X}_j(t)\rangle$ for all qubits (colored circles) on the $L=28$ heavy-hex subgraph. Black diamonds show the spatial average $\langle \hat{X}_{\rm avg}(t)\rangle$, with error bars indicating the spatial standard deviation $X_{\rm std}(t)$. The initial state has weak phase randomness, $\phi^{\rm max}/\pi=1$. b, Same quantities as in a for strong phase randomness, $\phi^{\rm max}/\pi=2$. c, Synchronization order parameter $\tilde{\kappa}(t)$ computed from the data in a (see Supplementary Information Sec. S1). d,$\tilde{\kappa}(t)$ computed from the data in b. Parameters are $(\theta_{XX},\theta_{ZZ},\theta_Z)=(-0.25\pi,-0.25\pi,0.25\pi)$.
• Figure 3: Quantum chimera dynamics on a $L=156$ heavy-hex lattice observed on the ibm_kobe quantum processor.a, Time evolution of the local magnetizations $\langle \hat{X}_{j}(t)\rangle$ for all qubits (colored circles). Black diamonds denote the spatial average $\langle \hat{X}_{\rm avg}(t)\rangle$ over all qubits $M=\{0,1,\ldots,L-1\}$, with error bars indicating the spatial standard deviation $X_{\rm std}(t)$. Two qubits ($j=64$ and 129) exhibit enhanced noise, but all qubits are retained in the analyses. b, Global synchronization order parameter $\tilde{\kappa}(t)$ computed from the full data in a. Inset: spatial map of the late-time-averaged local synchronization order parameter $\langle \tilde{\kappa}_j(t)\rangle_{\mathcal{T}}$ on the heavy-hex lattice, evaluated within a fixed-$K$ neighborhood ($K=4$ qubits) around each qubit $j$ and averaged over time interval $\mathcal{T}=[20,25]$ (see Methods). c,d, Time evolution of the local magnetizations $\langle \hat{X}_{j}(t)\rangle$ (colored circles) and the corresponding $\tilde{\kappa}(t)$ evaluated on qubits $M=\{0,1,\ldots,15\}$ highlighted in panel d, representing a synchronized subsystem. e,f, Same quantities as in c,d but for qubits $M=\{59,61,62,\ldots,75\}$ highlighted in panel f, representing a desynchronized region. All measured magnetizations are error-mitigated using the protocol described in Eq. (\ref{['eq:method-mitigation']}). Parameters are $(\theta_{XX},\theta_{ZZ},\theta_{Z})=(-0.25\pi,-0.25\pi,0.25\pi)$, and the initial state is prepared with strong randomness $\phi^{\rm max}=2\pi$.
• Figure 4: Quantum chimera dynamics reproduced by MPS simulations on the same $L=156$ heavy-hex system.a, Time evolution of the local magnetizations $\langle \hat{X}_{j}(t)\rangle$ for all qubits (colored circles). Black diamonds denote the spatial average $\langle \hat{X}_{\rm avg}(t)\rangle$ over all qubits $M=\{0,1,\ldots,L-1\}$, with error bars indicating the spatial standard deviation $X_{\rm std}(t)$. b, Global synchronization order parameter $\kappa(t)$ computed from the full data in a. Inset: spatial map of the late-time-averaged local synchronization order parameter $\langle \kappa_j(t)\rangle_{\mathcal{T}}$, evaluated within a fixed-$K$ neighborhood ($K=4$ qubits) around each qubit $j$ and averaged over time interval $\mathcal{T}=[20,25]$ (see Methods). c,d, Time evolution of the local magnetizations $\langle \hat{X}_{j}(t)\rangle$ (colored circles) and the corresponding $\kappa(t)$ evaluated on qubits $M=\{36,41,42,\ldots,55\}$ highlighted in panel d, representing a synchronized subsystem. e,f, Same quantities as in c,d but for qubits $M=\{76,81,82,\ldots,95\}$ highlighted in panel f, representing a desynchronized subsystem. MPS simulations are performed with bond dimension $\chi=600$. Parameters are $(\theta_{XX},\theta_{ZZ},\theta_{Z})=(-0.25\pi,-0.25\pi,0.25\pi)$, and the initial state is prepared with strong randomness $\phi^{\rm max}=2\pi$.
• Figure 5: Effect of SU(2) symmetry breaking on synchronization and entanglement. Statevector simulations of long-time dynamics on a $L=19$ heavy-hex lattice. Panels show the time evolution of the synchronization order parameter $\kappa(t)$, the mean oscillation radius $R_{\rm avg}(t)$, and the von Neumann entanglement entropy $S_{\rm vN}(t)$. a--c, SU(2)-symmetric (isotropic) case with $\theta_{XX}=\theta_{ZZ}=-0.25\pi$. d--f, SU(2)-broken (anisotropic) case with $(\theta_{XX},\theta_{ZZ})=(-0.25\pi,-0.02\pi)$. The magnetic-field parameter is fixed to $\theta_Z=0.25\pi$, and the initial state is prepared with weak randomness $\phi^{\rm max}=\pi$. The heavy-hex geometry used in the simulations is shown as an inset in panel c. The entanglement entropy $S_{\rm vN}(t)$ is evaluated for the subsystem $A=\{6,7,8,9,10,13,16\}$ highlighted in the inset of panel c; the red dashed line indicates the maximal value $S_{\rm vN}=|A|=7$.