Mixed algorithmic-analog simulation of many body dynamics using interaction of fixed-frequency superconducting qubits

In recent years there was a huge experimental progress towards the development of prototypes of algorithmic quantum processors. These quantum machines are not free from imperfections and various technological and scientific problems remain to be solved in the following years. Until that moment computational schemes different from the digital approach can be used in order to perform calculations using state-of-the-art quantum hardware. A prospective idea is to combine positive aspects of both digital and analog computation. Particularly, it is possible to use qubit-qubit interaction embedded in architecture in order to replace those parts of algorithms which are responsible for the quantum entanglement. In this paper, we provide an example of such an approach based on unwanted couplings between fixed-frequency superconducting qubits (crosstalks). These couplings are normally considered as a source of errors in standard digital quantum computation, but we argue that they can be utilized instead of two-qubit gates in some quantum algorithms thus avoiding an accumulation of errors associated with these gates. We illustrate our ideas with quantum processors of IBM Quantum Experience, which are used by us for simulating the dynamics of spin clusters through the Trotterized evolution. We demonstrate a significant improvement in the quality of results compared to the conventional digital approach with the same processor. We also show that crosstalks result in a highly non-markovian dynamics of qubits. This fact must be taken into account while developing error-correction strategies with qubits of this type.