Optimal control for the quantum simulation of nuclear dynamics

We propose a method for enacting the unitary time propagation of two interacting neutrons at leading order of chiral effective-field theory by efficiently encoding the nuclear dynamics into a single multilevel quantum device. The emulated output of the quantum simulation shows that, by applying a single gate that draws on the underlying characteristics of the device, it is possible to observe multiple cycles of the nuclear dynamics before the onset of decoherence. Owing to the signal's longevity, we can then extract spectroscopic properties of the simulated nuclear system. This allows us to validate the encoding of the nuclear Hamiltonian and the robustness of the simulation in the presence of quantum-hardware noise by comparing the extracted spectroscopic information to exact calculations. This work paves the way for transformative calculations of the dynamical properties of nuclei on near-term quantum devices.

Figure 1

Schematic description of the leading-order nucleon-nucleon interaction. The left diagram depicts a single pion exchange while the middle and right diagrams depict a spin-independent and a spin-dependent contact term, respectively.

Figure 2

Schematic potential-energy diagram of a transmon superconducting quantum device as a function of the change of the magnetic flux ($\varphi$) of the Josephson junction. The first four energy levels are labeled in terms of their Fock number on the left side of the potential-energy well while the right side shows the correspondence to two-neutron spin states in the independent spin basis.

Figure 3

(a) Numerically optimized time-dependent drive in the rotating frame of the ground-state energy transition of the transmon device that at its completion enacts the short time propagator of the nuclear Hamiltonian. (b) Discrete Fourier transform of panel (a) showing the spectral components correspond to the underlying energy transitions of the quantum device.

Figure 4

Occupation probabilities as a function of time. Colored circles depict the output probability as a function of simulation time step. Each point is obtained by solving the Lindblad master equation and determining the overlap with the particular nuclear spin (Fock state) of interest. The simulation includes dissipation and dephasing terms common in 3D transmon systems. Solid lines result from direct integration of the interaction Hamiltonian and use dissipation and dephasing quantum device terms appropriately scaled to nuclear interaction strengths. The collapse of the four probabilities at later times is a result of device decoherence.

Figure 5

Energy spectra. The solid line is the Fourier transform of the $\left|\downarrow \uparrow \right.〉$ state (first Fock state) time-dependent probability distribution for the exact neutron-neutron interaction propagator (without noise). The spectral lines correspond to all possible eigenenergy differences. The circles correspond to the discrete Fourier transform of the $\left|\downarrow \uparrow \right.〉$ state (first Fock state) time-dependent probability distribution for repeated application of the n-n interaction digital time propagator (including realistic 3D transmon decoherence). Even with decoherence, the pairwise eigenenergies differences are discernible in the spectra.