With great interest from the quantum computing community, an immense amount of R&D effort has been invested into improving superconducting qubits. The technologies developed for the design and fabrication of these qubits can be directly applied to applications for ultralow-threshold particle detectors, e.g., low-mass dark matter and far-infrared photon sensing. We propose a novel energy-resolving sensor based on the transmon qubit architecture combined with a signal-enhancing superconducting quasiparticle amplification stage. We refer to these sensors as SQUATs: superconducting quasiparticle-amplifying transmons. We detail the operating principle and design of this new sensor and predict that, with minimal R&D effort, solid-state-based detectors patterned with these sensors can achieve sensitivity to single terahertz photons, and sensitivity to 1meV phonons in the detector absorber substrate on the microsecond timescale.