  Simulating quantum channels is a fundamental primitive in quantum computing,
since quantum channels define general (trace-preserving) quantum operations. An
arbitrary quantum channel cannot be exactly simulated using a
finite-dimensional programmable quantum processor, making it important to
develop optimal approximate simulation techniques. In this paper, we study the
challenging setting in which the channel to be simulated varies adversarially
with time. We propose the use of matrix exponentiated gradient descent (MEGD),
an online convex optimization method, and analytically show that it achieves a
sublinear regret in time. Through experiments, we validate the main results for
time-varying dephasing channels using a programmable generalized teleportation
processor.
