Cloud Quantum Computing of an Atomic Nucleus

We report a quantum simulation of the deuteron binding energy on quantum processors accessed via cloud servers. We use a Hamiltonian from pionless effective field theory at leading order. We design a low-depth version of the unitary coupled-cluster ansatz, use the variational quantum eigensolver algorithm, and compute the binding energy to within a few percent. Our work is the first step towards scalable nuclear structure computations on a quantum processor via the cloud, and it sheds light on how to map scientific computing applications onto nascent quantum devices.

Figure 1

Low-depth circuits that generate unitary rotations in Eq. (7) (a) and Eq. (8) (b). Also shown are the single-qubit gates of the Pauli $X$ matrix, the rotation $Y(\theta )$ with angle $\theta$ around the $Y$ axis, and the two-qubit cnot gates.

Figure 2

Experimentally determined energies for $H_2$ (top) and expectation values of the Pauli terms that enter the two-qubit Hamiltonian $H_2$ as determined on the QX5 (center) and 19Q (bottom) chips. Experimental (theoretical) results are denoted by symbols (lines).

Figure 3

Noise extrapolation of the $N=3$ qubit problem run on the QX5. The $H_3$ energy (left axis, black line) and individual Pauli expectation values (right axis) are given as a function of the number cnot gate scaling factor $r$.