Simulating open quantum systems with molecular spin qudits.

Noise affecting quantum processors still limits quantum simulations to a small number of units and operations. This is especially true for the simulation of open quantum systems, which involve additional units and operations to map environmental degrees of freedom. Hence, finding efficient approaches for the simulation of open quantum systems is an open issue. In this work, we demonstrate how using units with d > 2 levels (qudits) results in a reduction of up to two orders of magnitude in the number of operations (gates) required to implement state-of-the-art algorithms. We explore two conceptually distinct families of these algorithms that were initially designed for qubits and discuss the gate complexity scaling that different platforms (qubit-based vs. qudit-based) offer. Additionally, we present realistic simulations of an experimental platform based on molecular spin qudits coupled to superconducting resonators, where the main hardware error sources are included. We show that, in all cases considered, the use of qudits leads to a remarkable reduction in circuit complexity and that molecular nanomagnets are ideal qudit hosts.