  We experimentally implement the Sz.-Nagy dilation algorithm to simulate open
quantum dynamics on an nuclear magnetic resonance (NMR) quantum processor. The
Sz.-Nagy algorithm enables the simulation of the dynamics of
arbitrary-dimensional open quantum systems, using only a single ancilla qubit.
We experimentally simulate the action of two non-unitary processes, namely, a
phase damping channel acting independently on two qubits and a magnetic field
gradient pulse (MFGP) acting on an ensemble of two coupled nuclear spin-1/2
particles. To evaluate the quality of the experimentally simulated quantum
process, we perform convex optimization-based full quantum process tomography
to reconstruct the quantum process from the experimental data and compare it
with the target quantum process to be simulated.
