Simulating plasma wave propagation on a superconducting quantum chip

Abstract

Quantum computers may one day enable the efficient simulation of strongly coupled plasmas that lie beyond the reach of classical computation in regimes where quantum effects are important and the scale separation is large. In this article, we take a first step toward efficient simulation of quantum plasmas by demonstrating linear plasma wave propagation on a superconducting quantum chip. Using high-fidelity and highly expressive device-native gates, combined with an error-mitigation technique, we simulate the scattering of laser pulses from inhomogeneous plasmas. Our approach is made feasible by the identification of a suitable local spin model whose excitations mimic plasma waves, and whose circuit implementation requires a lower gate count than other proposed approaches that would require a future fault-tolerant quantum computer. This work opens avenues to study more complicated phenomena that cannot be simulated efficiently on classical computers, such as nonlinear quantum dynamics when strongly coupled plasmas are driven out of equilibrium.

Figures (22)

• Figure 1: We implement a one-dimensional spin model with nearest-neighbor interactions $J_{ij}$ and a staggered field $\vec{\Delta}_i$ [see Eq. \ref{['eq:H']}], which has the same energy spectrum as that of electromagnetic waves in a plasma, on a superconducting quantum computer. We use this model to simulate linear electromagnetic wave dynamics in a plasma.
• Figure 2: The dispersion relation of the spin Hamiltonian [Eq. \ref{['eq:H']}] is analogous to waves in plasmas. The spectrum is measured via a many-site Ramsey-type experiment, where the time evolution of the complex phase of local spin observables reveals the energies of the eigenmodes. We consider (a-b) a low density plasma ($\Delta\rightarrow0$) and (c-d) $\Delta=J/4$. Panels (a,c) show the error-mitigated observables versus time; panels (b,d) show the extracted excitation spectrum from noisy (yellow) and mitigated (blue) data, along with the exact spectrum (teal) and the expected spectrum from a noiseless simulation of the circuit (gray).
• Figure 3: Phase evolution of the eigenmodes of the system versus time for (a) $\Delta=0$, and (b) $\Delta=J/4$. Magenta, teal, and yellow points plot the complex phase of the eigenmodes obtained from error-mitigated data, the raw experimental data, and a noiseless simulation of the circuit. Black lines show linear fits to the error-mitigated data. Other colored lines are guides to the eye. Each panel corresponds to one eigenmode $q$. The eigenfrequency of each eigenmode is obtained by applying a linear fit to the error-mitigated data.
• Figure 4: An electromagnetic wave packet propagating (a) in vacuum ($\Delta = 0$), (b) from vacuum to a sharp jump in plasma density (which mimics the edge of a confined overdense plasma), and (c) through an inhomogeneous overdense plasma with a Gaussian density profile. In each case, the profiles of plasma frequency are shown on the bottom, and the intensity of the propagating wave packet is shown on the top. In (a), the wave packet propagates nearly ballistically until it approaches the edge, where the boundary condition is reflective. In (b) and (c), the wave packet propagates until it approaches the sharp jump or inhomogeneous profile and mostly reflects back. The black lines show the center of mass (CoM) of the wave packet obtained from the mitigated experimental data, and the red lines show the wave packet's CoM from a noiseless simulation of the experiment.
• Figure 5: Classical simulations of EM waves propagating in various mass profiles: (a) reflection from a sharp boundary and (b) propagation through a more complicated profile. The inset in (a) shows the intensity of the reflected wave, $|r|^2$, versus $k$. The solid line shows the analytically predicted reflection (see Appendix \ref{['app:reflection_coefficient']}) and the points show the numerically computed values.