Linear Filtering of Pulses for Cross-Talk Elimination in Frequency-Multiplexed Qubit Control

Frequency multiplexed microwave driving of a large array of spin qubits is a potential solution to scalable control of a fault-tolerant quantum computer. Such control of spin qubits closely spaced in frequency using a common interconnect is susceptible to cross-talk due to the leakage of energy outside the bandwidth of the driven qubit. While pulse shaping can reduce leakage to adjacent victim qubits, general pulse shapes are typically not easily programmable to accommodate varying qubit frequencies, particularly when implemented within low-power, mostly-digital integrated cryogenic controllers. In this work, we show that the loss of fidelity due to X and Y rotations of a victim qubit is approximately proportional to the spectral density of the pulse shape, thereby motivating the use of frequency domain linear filtering to eliminate cross-talk. We then describe low-power, programmable, discrete-time pulse filtering techniques that eliminate leakage and thereby cross-talk at a victim qubit's Larmor Frequency. A digital implementation of the filter is described that is easily scalable by cascading multiple programmable filters to eliminate cross-talk for several qubits. Finally, using simulations we demonstrate that the cross-talk elimination technique restores fidelity to 99.9% for the victim qubit.