Few-photon microwave fields for superconducting transmon-based qudit control

Increasing the efficiency of quantum processors is possible by moving from two-level qubits to elements with a larger computational base. An example would be a transmon-based superconducting atom, but the new basic elements require new approaches to control. To solve the control problem, we propose the use of nonclassical fields in which the number of photons is comparable to the number of levels in the computational basis. Using theoretical analysis, we have shown that (i) our approach makes it possible to efficiently populate on demand even relatively high energy levels of the qudit starting from the ground state; (ii) by changing the difference between the characteristic frequencies of the superconducting atom and a single field mode, we can choose which level to populate; and (iii) even the highest levels can be effectively populated on a sub-nanosecond time scale. We also propose the quantum circuit design of a real superconducting system in which the predicted rapid control of the transmon-based qudit can be demonstrated.