Fast and virtually exact quantum gate generation in U(n) via iterative Lyapunov methods
Paulo Sérgio Pereira da Silva, Hector Bessa Silveira, Pierre Rouchon · International Journal of Control · 2019
A new approach called Reference Input Generation Algorithm (RIGA) is introduced for quantum gate generation. Let X¯ℓ−1(t) be the trajectory that is obtained in step ℓ−1, with X¯ℓ−1(t)=I. In step ℓ, X¯ℓ−1 is right-translated in order to displace X¯ℓ−1(Tf) to Xgoal. The translated trajectory is used as a reference for a Lyapunov-based tracking control law, generating X¯ℓ(T), and so on. A proof of the exponential convergence of X¯ℓ−1(Tf) to zero is provided for Tf large enough. Two examples present numerical experiments regarding N coupled qubits. The first example considers N = 3 with a known minimum time T∗. It presents excellent results for Tf=T∗. The second example is a benchmark for the comparison between RIGA and GRAPE, considering a Hadamard gate for the systems with N = 2, 3, …, 10 qubits. The runtime of RIGA could be improved, and GRAPE was implemented in a faster CPU. However, RIGA presents results that are similar to GRAPE, with faster runtime in some cases, showing that the RIGA is indeed a promising algorithm.