LCD: a real-time adaptive hardware decoder for the surface code

To avoid prohibitive overheads in performing fault-tolerant quantum computation, the decoding problem needs to be solved accurately and at speeds sufficient for fast feedback. We present an FPGA implementation of the Local Clustering Decoder (LCD) as a solution that balances the accuracy and speed requirements of a real-time decoding system. It contains two main components: (1) a decoding engine that projects an arbitrary decoding graph onto a coarse-grained parallel architecture and implements a distributed clustering algorithm based on Union-Find to achieve an average per round decoding time that scales sublinearly with the surface code distance; and (2) an adaptivity engine that uses a pre-learned set of adaptions to update the decoding graph at runtime in response to control signals, such as heralded leakage measurements. Under a realistic circuit-level noise model where leakage is a dominant error source, our decoder enables a million error-free quantum operations with a distance 17 surface code patch—a four-fold reduction in the number of physical qubits when compared to standard non-adaptive decoding. This is achieved whilst decoding in under 1 μs per round with modest FPGA resources. This demonstrates that high-accuracy real-time decoding is possible, relaxing the qubit requirements to bring forward the era of fault-tolerant quantum computation.