  The mass production and the practical number of cryogenic quantum devices
producible in a single chip are limited to the number of electrical contact
pads and wiring of the cryostat or dilution refrigerator. It is, therefore,
beneficial to contrast the measurements of hundreds of devices fabricated in a
single chip in one cooldown process to promote the scalability, integrability,
reliability, and reproducibility of quantum devices and to save evaluation
time, cost and energy. Here, we use a cryogenic on-chip multiplexer
architecture and investigate the statistics of the 0.7 anomaly observed on the
first three plateaus of the quantized conductance of semiconductor quantum
point contact (QPC) transistors. Our single chips contain 256 split gate field
effect QPC transistors (QFET) each, with two 16-branch multiplexed source-drain
and gate pads, allowing individual transistors to be selected, addressed and
controlled through an electrostatic gate voltage process. A total of 1280
quantum transistors with nano-scale dimensions are patterned in 5 different
chips of GaAs heterostructures. From the measurements of 571 functioning QPCs
taken at temperatures T= 1.4 K and T= 40 mK, it is found that the spontaneous
polarisation model and Kondo effect do not fit our results. Furthermore, some
of the features in our data largely agreed with van Hove model with short-range
interactions. Our approach provides further insight into the quantum mechanical
properties and microscopic origin of the 0.7 anomaly in QPCs, paving the way
for the development of semiconducting quantum circuits and integrated cryogenic
electronics, for scalable quantum logic control, readout, synthesis, and
processing applications.
