We present a control and measurement setup for superconducting qubits based on Xilinx 16-channel radio frequency system on chip (RFSoC) device. The proposed setup consists of four parts:multiple RFSoC FPGA boards, a setup to synchronise every DAC and ADC channel across multiple boards, a low-noise DC current supply for qubit biasing and cloud access for remotely performing experiments. We also design the setup to be free of physical mixers. The FPGA boards directly generate microwave pulses using sixteen DAC channels up to the third Nyquist zone which are directly sampled by its eight ADC channels between the fifth and the ninth zones.
A challenge in the Gauss sums factorization scheme is the presence of ghost factors – non-factors that behave similarly to actual factors of an integer – which might leadto the misidentification of non-factors as factors or vice versa, especially in the presence of noise. We investigate Type II ghost factors, which are the class of ghost factors that cannot be suppressed with techniques previously laid out in the literature. The presence of Type II ghost factors and the coherence time of the qubit set an upper limit for the total experiment time, and hence the largest factorizable number with this scheme. Discernability is a figure of merit introduced to characterize this behavior. We introduce preprocessing as a strategy to increase the discernability of a system, and demonstrate the technique with a transmon qubit. This can bring the total experiment time of the system closer to its decoherence limit, and increase the largest factorizable number.