Universal stabilization of single-qubit states using a tunable coupler

We theoretically analyze a scheme for fast stabilization of arbitrary qubit states with high fidelities, extending a protocol recently demonstrated experimentally [1]. Our scheme utilizes red and blue sideband transitions in a system composed of a fixed-frequency transmon qubit, a low-Q LC-oscillator, and a coupler enabling us to tune the interaction between them. Under parametric modulations of the coupling strength, the qubit can be steered into any desired pure or mixed single-qubit state. For realistic circuit parameters, we predict that stabilization can be achieved within 100 ns. By varying the ratio between the oscillator's damping rate and the effective qubit-oscillator coupling strength, we can switch between under-damped, critically-damped, and over-damped stabilization and find optimal working points. We further analyze the effect of thermal fluctuations and show that the stabilization scheme remains robust for realistic temperatures.

[1] Yao Lu, S. Chakram, N. Leung, N. Earnest, R. K. Naik, Ziwen Huang, Peter Groszkowski, Eliot Kapit, Jens Koch, and David I. Schuster, Phys. Rev. Lett. 119, 150502 (2017)