Physically, quantum gates (unitary gates) for quantum computation are implemented by controlling the Hamiltonian dynamics of quantum systems. When full descriptions of the Hamiltonians are given, the set of implementable quantum gates is easily characterized by quantum control theory. In many real systems, however, the Hamiltonians may include unknown parameters due to the difficulty of performing precise measurements or instability of the system. In this paper, we consider the situation that some parameters of the Hamiltonian are unknown, but we still want to perform a robust control of the Hamiltonian dynamics to implement a quantum gate irrespectively to the unknown parameters. The existence of the robust control was previously shown for single-qubit systems, and a constructive method was developed for two-qubit systems if a full control of each qubit is available. We analytically investigate the robust controllability of two-qubit systems, and apply Lie-algebraic approaches to handle the cases where only one of the two qubits is controllable. We also numerically analyze the robust controllability of the two-qubit systems where the analytical approach is not necessarily applicable and investigate the relationship between the robust controllability of systems with a discrete and continuous unknown parameter.
|Number of pages||7|
|Journal||Physical Review A: covering atomic, molecular, and optical physics and quantum information|
|Publication status||Published - 8 Oct 2019|