Optimally Band-Limited Noise Filtering and Crosstalk Mitigation for Single Qubit Gates in Multi-Qubit Systems

In the NISQ era, accurate and scalable quantum computation is hindered by noise that is often difficult to mitigate. A particularly prevalent source of noise in NISQ devices is quantum crosstalk, where qubits experience always-on or gate-induced parasitic interactions. In this work, we construct optimized control sequences that mitigate temporally correlated noise and quantum crosstalk during the implementation of simultaneous single-qubit gates on multi-qubit systems. We utilize the Filter Function Formalism to define conditions for achieving crosstalk mitigation and filtering system-environment noise. This formalism allows us to analytically derive intuitive initial conditions that are used within the Filter Gradient Ascent in Function Space (F-GRAFS) optimization framework to achieve optimal noise filtering, via slepian based control. We showcase our work on multi-qubit systems with variable topology. In addition, we examine the interplay between control bandwidth, crosstalk mitigation, and system-environment noise filtering, to develop bandwidth conditions for achieving high-fidelity gates.