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We demonstrate a post-quench dynamics simulation of a Heisenberg model onpresent-day IBM quantum hardware that extends beyond the coherence time of thedevice. This is achieved using a hybrid quantum-classical algorithm thatpropagates a state using Trotter evolution and then performs a classicaloptimization that effectively compresses the time-evolved state into avariational form. When iterated, this procedure enables simulations toarbitrary times with an error controlled by the compression fidelity and afixed Trotter step size. We show how to measure the required cost function, theoverlap between the time-evolved and variational states, on present-dayhardware, making use of several error mitigation methods. In addition tocarrying out simulations on real hardware, we investigate the performance andscaling behavior of the algorithm with noiseless and noisy classicalsimulations. We find the main bottleneck in going to larger system sizes to bethe difficulty of carrying out the optimization of the noisy cost function.

Quantum dynamics simulations beyond the coherence time on NISQ hardware by variational Trotter compression