Obtaining effective noisy systems by simulating noiseless systems on NISQ hardware.

Quantum Computers promise to revolutionize the simulation of large quantum systems. In the NISQ era of quantum computing, the simulation of "perfect" coherent model systems without noise or disorder is hindered by errors introduced in the simulation by the imperfection of the NISQ device. Typically these errors can either be mitigated with error mitigation schemes or simulating the system must wait for the availability of fully error corrected quantum computers.

Here we follow a different approach. We consider the simulation of "imperfect" systems that are themselves noisy and can include disorder on NISQ quantum computers. We study the noisy systems that are effectively simulated when a NISQ quantum computer is used to run a quantum program to simulate the time-evolution of a perfect quantum system without disorder or coupling to a noise source.

We discuss which classes of noise coupling or disorder can appear in the effective model, for specific types of errors in the quantum device. We also use an automated computer program to extract the effectively simulated model from a quantum-circuit-level description of the simulation of one Trotter step and show how the effective model compares to a full simulation of the quantum circuit