  Reading a qubit is a fundamental operation in quantum computing. It
translates quantum information into classical information enabling subsequent
classification to assign the qubit states `0' or `1'. Unfortunately, qubit
readout is one of the most error-prone and slowest operations on a
superconducting quantum processor. On state-of-the-art superconducting quantum
processors, readout errors can range from 1-10%. High readout accuracy is
essential for enabling high fidelity for near-term noisy quantum computers and
error-corrected quantum computers of the future.
  Prior works have used machine-learning-assisted single-shot qubit-state
classification, where a deep neural network was used for more robust
discrimination by compensating for crosstalk errors. However, the neural
network size can limit the scalability of systems, especially if fast hardware
discrimination is required. This state-of-the-art baseline design cannot be
implemented on off-the-shelf FPGAs used for the control and readout of
superconducting qubits in most systems, which increases the overall readout
latency as discrimination has to be performed in software.
  In this work, we propose HERQULES, a scalable approach to improve qubit-state
discrimination by using a hierarchy of matched filters in conjunction with a
significantly smaller and scalable neural network for qubit-state
discrimination. We achieve substantially higher readout accuracies (16.4%
relative improvement) than the baseline with a scalable design that can be
readily implemented on off-the-shelf FPGAs. We also show that HERQULES is more
versatile and can support shorter readout durations than the baseline design
without additional training overheads.
