Reduced-dynamics approach for optimally designing unitary transformations
Kenta Arai, Yukiyoshi Ohtsuki · Physical Review A · 2015
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.