Christian Gogolin

We present the first hardware implementation of electrostatic interaction energies using a trapped-ion quantum computer. As test system for our computation, we focus on the reduction of $\mathrm{NO}$ to $\mathrm{N}_2\mathrm{O}$ catalyzed by a nitric oxide reductase (NOR). The quantum computer is used to generate an approximate ground state within the NOR active space. To efficiently measure the necessary one-particle density matrices, we incorporate fermionic basis rotations into the quantum circuit without extending the circuit length, laying the groundwork for further efficient measurement routines using factorizations. Measurements in the computational basis are then used as inputs for computing the electrostatic interaction energies on a classical computer. Our experimental results strongly agree with classical noise-less simulations of the same circuits, finding electrostatic interaction energies within chemical accuracy despite hardware noise. This work shows that algorithms tailored to specific observables of interest, such as interaction energies, may require significantly fewer quantum resources than individual ground state energies would in the straightforward supermolecular approach.

Exploiting quantum properties to outperform classical ways of information-processing is an outstanding goal of modern physics. A promising route is quantum simulation, which aims at implementing relevant and computationally hard problems in controllable quantum systems. Here we demonstrate that in a trapped ion setup, with present day technology, it is possible to realize a spin model of the Mattis type that exhibits spin glass phases. Remarkably, our method produces the glassy behavior without the need for any disorder potential, just by controlling the detuning of the spin-phonon coupling. Applying a transverse field, the system can be used to benchmark quantum annealing strategies which aim at reaching the ground state of the spin glass starting from the paramagnetic phase. In the vicinity of a phonon resonance, the problem maps onto number partitioning, and instances which are difficult to address classically can be implemented.