Quantum simulation of nuclear inelastic scattering

We present a time-dependent quantum algorithm for nuclear inelastic scattering in the time-dependent basis function on qubits approach. This algorithm aims to quantum simulate a subset of the nuclear inelastic scattering problems that are of physical interest in which the internal degrees of freedom of the reaction system are excited by time-dependent external interactions. We expect that our algorithm will enable an exponential speedup in simulating the dynamics of the subset of the inelastic scattering problems, which would also be advantageous for the applications to more complicated scattering problems. For a demonstration problem, we solve for the Coulomb excitation of the deuteron, where the quantum simulations are performed with IBM Qiskit.

Figure 1

Schematic quantum circuit design of $\tilde{U}(t_f;t_0)$ for the complete time evolution according to Eq. (24) on an $N_q$-qubit quantum register. The circuit operates from left to right. The gate $\tilde{U}\left(t_k\right)$, with $t_k=t_1,t_2,\cdots ,t_n$ and $t_n=t_f$, corresponds to the time-evolution operator of a single time step at scattering time $t_k$. Though varying with $t_k$, the $\tilde{U}\left(t_k\right)$ is considered to be time invariant during each short time step $[t_{k-1},t_k]$. ${|q\rangle }^{\otimes N_q}$ denotes the $N_q$-qubit register.

Figure 2

Schematic circuit design for the time-evolution operator of a single time step, $\widehat{U}\left(t_k\right)$, for the case with $m=2$ on a $N_q$-qubit quantum register. ${|q\rangle }^{\otimes N_q}$ denotes the $N_q$-qubit register. The circuit operates from the left to right. The circuit illustrates the idea to design the gate $\tilde{U}\left(t_k\right)$ [see in Fig. 1] according to the decomposition principle Eq. (23). More complicated cases (with larger $m$) can be generalized based on this design. See details in the text.

Figure 3

Setup for the Coulomb excitation of the deuteron in the peripheral collision with a heavy ion (adopted from Refs. [35, 36]). See the text for more details.

Figure 4

Transition probabilities and scattering observables calculated by the tBF method and the tBFQ method. Panels (a)–(g) [panel (a) presenting the initial state] are the transition probabilities of the selected basis states in Table 1. Panels (h) and (i) show the excitation of intrinsic energy and the expansion of the state-average rms point-charge radius of the deuteron system arising from the Coulomb excitation, where the results are obtained by both the classical tBF method (smooth red lines in each panel) and the tBFQ method via quantum simulations on IBM Qiskit (discrete blue points in each panel).