  Energy-efficient hardware implementation of machine learning algorithms for
quantum computation requires nonvolatile and electrically-programmable devices,
memristors, working at cryogenic temperatures that enable in-memory computing.
Magnetic topological insulators are promising candidates due to their tunable
magnetic order by electrical currents with high energy efficiency. Here, we
utilize magnetic topological insulators as memristors (termed magnetic
topological memristors) and introduce a chiral edge state-based cryogenic
in-memory computing scheme. On the one hand, the chiral edge state can be tuned
from left-handed to right-handed chirality through spin-momentum locked
topological surface current injection. On the other hand, the chiral edge state
exhibits giant and bipolar anomalous Hall resistance, which facilitates the
electrical readout. The memristive switching and reading of the chiral edge
state exhibit high energy efficiency, high stability, and low stochasticity. We
achieve high accuracy in a proof-of-concept classification task using four
magnetic topological memristors. Furthermore, our algorithm-level and
circuit-level simulations of large-scale neural networks based on magnetic
topological memristors demonstrate a software-level accuracy and lower energy
consumption for image recognition and quantum state preparation compared with
existing memristor technologies. Our results may inspire further topological
quantum physics-based novel computing schemes.
