Reduced-dynamics approach for optimally designing unitary transformations

Quantum optimal control is a powerful tool for designing a pulse that executes a specified gate, i.e., a unitary transformation in quantum computation. If we consider qubits characterized by different spectroscopic properties, we may design a pulse that executes a specified gate on a specified qubit (S qubit) with the inclusion of neighboring qubits (B qubits) but does not explicitly include the other qubits. In this situation, first we introduce sets of reduced time-evolution operators associated with the S and B qubits. Then, we apply quantum optimal control to these sets to design optimal pulses that could selectively execute the specified gate on the S qubit while actively removing the effects of the pulse on the B qubits, which would lead to a scalable pulse-design procedure. The present pulse design is applied to the quantum computation proposed by DeMille with the aim of executing the Hadamard and controlled-not gates on the S qubits while actively suppressing the pulse-induced population transitions of the B qubit states. The numerical results illustrate high fidelity even after introducing the extra qubits that are not included in the pulse design.