B. P. Das

The quantum-classical hybrid variational quantum eigensolver (VQE) algorithm is among the most actively studied topics in atomic and molecular calculations on quantum computers, yet few studies address properties other than energies or account for relativistic effects. This work presents high-precision 18-qubit relativistic VQE simulations for calculating the permanent electric dipole moments (PDMs) of BeH to RaH molecules on traditional computers, and 6- and 12-qubit PDM computations for SrH on IonQ quantum devices. To achieve high precision on current noisy intermediate scale era quantum hardware, we apply various resource reduction methods, including Reinforcement Learning and causal flow preserving ZX-Calculus routines, along with error mitigation and post-selection techniques. Our approach reduces the two-qubit gate count in our 12-qubit circuit by 99.71%, with only a 2.35% trade-off in precision for PDM when evaluated classically within a suitably chosen active space. On the current generation IonQ Forte-I hardware, the error in PDM is -1.17% relative to classical calculations and only 1.21% compared to the unoptimized circuit.

We propose a method for measuring parity violation in neutral atoms. It is an adaptation of a seminal work by Fortson [Phys. Rev. Lett. {\bf 70}, 2383 (1993)], proposing a scheme for a single trapped ion. In our version, a large sample of neutral atoms should be localised in an optical lattice overlapping a grid of detection sites, all tailored as the single site in Fortson's work. The methodology is of general applicability, but as an example we estimate the achievable signal in an experiment probing a nuclear spin independent parity violation on the line $6\mathrm{s}\,^2\mathrm{S}_{1/2}$--$5\mathrm{d}\,^2\mathrm{D}_{3/2}$ in $^{133}$Cs. The projected result is based on realistic parameters and \textit{ab initio} calculations of transition amplitudes, using the relativistic coupled-cluster method. The final result is a predicted spectroscopic signature, evidencing parity violation, of the order of 1 Hz, for a sample of $10^8$ atoms. We show that a total interrogation time of 30000 s should suffice for achieving a precision of the order of 0.1\% --- surpassing previous determinations of the weak charge in Cs by at least a factor of five.