Isoprobability Models of Qubit Dynamics: Demonstration via Time-Dependent Phase Control on IBM Quantum

Abstract

Efficient quantum control is a cornerstone for the advancement of quantum technologies, from computation to sensing and communications. Several approaches in quantum control, e.g. optimal control and inverse engineering, use pulse amplitude and frequency shaping as control tools. Often, these approaches prescribe pulse shapes which are difficult or impossible to implement. To this end, we develop the concept of isoprobability classes of models of qubit dynamics, in which various pairs of time-dependent pulse amplitude and frequency generate the same transition probability profile (albeit different temporal evolutions toward this probability). In this manner, we introduce an additional degree of freedom, and hence flexibility in qubit control. Selection of hardware-aware temporal pulse shapes has the potential to decrease gate duration, overcome platform constraints and increase robustness to noise. We demonstrate this approach with two classes of isoprobability models, which derive from the established Landau-Majorana-St\"uckelberg-Zener (LMSZ) and Allen-Eberly-Hioe (AEH) classes. We experimentally validate the isoprobability equivalence on an IBM Quantum processor, quantifying agreement with numerical simulations via the mean squared error (MSE). Instead of frequency (i.e. detuning) shaping, which is difficult to implement on this platform, we exploit the time-dependent phase of the driving field to induce an effective detuning. Indeed, the temporal derivative of the phase function emulates a variable detuning, thereby avoiding the need for direct detuning control. The experimental validation of the isoprobability concept with the time-dependent phase control underscores the potential of this robust and accessible method for high-fidelity quantum operations, bringing us one step closer to scalable quantum control in various quantum applications.