Tensor-network optimal control for multi-qubit systems

Quantum devices in the NISQ era are being built with an increasing number of qubits. Many-body interaction can be purposefully engineered, or in some cases considered a parasitic interaction that cannot be avoided. The many-body Hamiltonian of these devices are also imperfect due to significant uncertainty in multiple parameters. This necessitates the development of a many-body optimal control algorithm capable of realising quantum operations, i.e., a target state or target gate, which is robust against uncertainty. We develop a robust optimal control algorithm based on tensor networks, and demonstrate its effectiveness for implementing multi-qubit entangled states and unitary gates. We show that robustness against variation in the Hamiltonian's parameters can be achieved by optimising only the extreme points of the uncertain region, and an exponential speed up of the optimisation is possible by focusing on the subspaces of the most correlated parameters. The algorithm is used for generating high-fidelity GHZ states and CNOT gates in an interacting multi-qubit system. Implications for near term quantum processors are discussed."