Not all quantum protocols require entanglement to outperform their classical alternatives. The nonclassical correlations that lead to this quantum advantage are conjectured to be captured by quantum discord. Here we demonstrate that discord can be ex
plicitly used as a resource: certifying untrusted entangling gates without generating entanglement at any stage. We implement our protocol in the single-photon regime, and show its success in the presence of high levels of noise and imperfect gate operations. Our technique offers a practical method for benchmarking entangling gates in physical architectures in which only highly-mixed states are available.
The relationship between efficient quantum gate synthesis and control theory has been a topic of interest in the quantum control literature. Motivated by this work, we describe in the present article how the dynamic programming technique from optimal
control may be used for the optimal synthesis of quantum circuits. We demonstrate simulation results on an example system on SU(2), to obtain plots related to the gate complexity and sample paths for different logic gates.
