Observing quantum many-body dynamics in emergent curved spacetime using programmable quantum processors

Abstract

We digitally simulate quantum many-body dynamics in emergent curved backgrounds using 80 superconducting qubits on IBM Heron processors. By engineering spatially varying couplings in the spin-$\frac12$ XXZ chain, consistent with the low-energy description of the model in terms of an inhomogeneous Tomonaga-Luttinger liquid, we realize excitations that follow geodesics of an effective metric inherited from the underlying spatial deformation. Following quenches from Néel and few-spin-flip states, we observe curved light-cone propagation, horizon-induced freezing in the local magnetization, and position-dependent oscillation frequencies set by the engineered spatial deformation. Despite strong spatial inhomogeneity, unequal-time correlators reveal ballistic quasiparticle propagation in the spin chain. These results establish large-scale digital quantum processors as a flexible platform for detailed and controlled exploration of many-body dynamics in tunable and synthetic curved spacetimes.

Figures (11)

• Figure 1: Simulating spatially inhomogeneous dynamics with quantum processors. (a) In our inhomogeneous quench protocol, the initial state acts as a source of pairs of quasiparticles (illustrated as white dots), which propagate along geodesics on a curved background. (b) Quantum circuit implementation of the time evolution operator $\exp(-i \delta t {H})$ for the deformed XXZ spin chain, \ref{['eq:deformedXXZ']}, using a first-order Suzuki-Trotter decomposition with a time step of duration $\delta t$. Each Trotter layer consists of an "odd" and "even" sublayer composed of unitaries that couple nearest-neighbour qubits. (c) The corresponding two qubit quantum circuit; here the rotation gate angles are $\theta = 2 \delta t v_j \Delta + \pi / 2$ and $\phi = - 2 \delta t v_j - \pi / 2$ encoding both local interactions through the anisotropy $\Delta$ and emergent spacetime curvature through the deformation profile $v_j$.
• Figure 2: Curved light-cone propagation. Light-cone propagation in the two-point correlation function $|C_{ij}^{zz}(t)|$ following a quench with \ref{['eq:deformedXXZ']} from an initial Néel state in an interacting chain of $N=80$ qubits. (a) Uniform XXZ chain simulated on ibm_fez with $\Delta=1/2$. (b) Deformed XXZ chain simulated on ibm_marrakesh with the same anisotropy ($\Delta=1/2$) and a deformation given by \ref{['eq:deformationprofileXXZ']}, with Rindler horizons located at $j_*+1$ and $N+1-j_*$ with $j_*=N/7$ (indicated with black dash-dot vertical lines). The observed light cones are compared to the geodesics of the metric, \ref{['eq:curvedspacetimemetric']} (black dashed curves) for various initial positions $i$, computed using $\frac{1}{8} \int_{i}^{j} \text{d}x \, v(x)^{-1}$. Color maps share a common logarithmic scale, with the lower bound set by the order of magnitude associated with the standard error in each observable.
• Figure 3: Tuning interactions. (a) Spatially averaged two-point correlator $|C^{zz}(x,t)| = |\frac{1}{N_x}\sum_i C_{i,i+x}^{zz}(t)|$, where $N_x$ is the number of pairs of sites separated by distance $|x|$Keesling2019, following a quench with the uniform XXZ chain initialized in a Néel state using several interaction strengths, $\Delta = 0, 1/2, 1,$ and $2$. (b) Correlation function $|C_{ij}^{zz}(t)|$ following a quench with the inhomogeneous XXZ chain (same deformation as in \ref{['fig:curvedlight-cone_propagation']}(b)) for different positions, $i=37,59,63$, using the same initial state and $\Delta$ values as in (a). All quantum simulations here were performed on ibm_fez.
• Figure 4: Magnetization dynamics. (a) Time evolution of the local magnetization $M^z_j(t)$ from an initial Néel state, for the same parameters as \ref{['fig:different_Delta']}(b). The effective velocity profile in the metric, \ref{['eq:curvedspacetimemetric']}, manifests as inhomogeneous oscillation periods that freeze at the horizons (denoted by black dash-dot vertical lines). (b) Damped oscillations at different initial positions reveal a strong position dependence of the frequency. (c) Collapse of the magnetization curves after rescaling the time axis by the spatial deformation. Standard errors in each measurement have been included. (d-f) Corresponding results in the gapped phase ($\Delta=2$), where oscillations are suppressed.
• Figure 5: Ballistic spreading of correlations. Panels (a) and (c) show $N=80$ qubit simulation results of the unequal-time correlation function for a uniform chain and a deformed chain ($\Delta=1/2$), respectively, when the initial state contains two spin flips located at sites 20 and 30. Panels (b) and (d) instead compare the dynamics starting from a single spin flip: we prepare one state with the flip at site 20 and another at site 30, compute the corresponding correlation functions, and overlay the results for direct comparison with the two-spin flip state. In all cases we have subtracted off the background magnetization by performing simulations with an initial all-up spin state.