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The error rates of quantum devices are orders of magnitude higher than whatis needed to run most quantum applications. To close this gap, Quantum ErrorCorrection (QEC) encodes logical qubits and distributes information usingseveral physical qubits. By periodically executing a syndrome extractioncircuit on the logical qubits, information about errors (called syndrome) isextracted while running programs. A decoder uses these syndromes to identifyand correct errors in real time, which is required to use feedback implementedin quantum algorithms. Unfortunately, software decoders are slow and hardwaredecoders are fast but less accurate. Thus, almost all QEC studies so far haverelied on offline decoding.  To enable real-time decoding in near-term QEC, we propose LILLIPUT-- aLightweight Low Latency Look-Up Table decoder. LILLIPUT consists of two parts--First, it translates syndromes into error detection events that index into aLook-Up Table (LUT) whose entry provides the error information in real-time.Second, it programs the LUTs with error assignments for all possible errorevents by running a software decoder offline. LILLIPUT tolerates an error onany operation in the quantum hardware, including gates and measurement, and thenumber of tolerated errors grows with the size of the code. It needs <7% logicon off-the-shelf FPGAs that allows it to be easily integrated alongside thecontrol and readout circuits in existing systems. LILLIPUT incurs a latency offew nanoseconds and enables real-time decoding. We also propose Compressed LUTs(CLUTs) to reduce the memory needed by LILLIPUT. By exploiting the fact thatnot all error events are equally likely and only storing data for the mostprobable error events, CLUTs reduce the memory needed by up-to 107x (from 148MB to 1.38 MB) without degrading accuracy.

LILLIPUT: A Lightweight Low-Latency Lookup-Table Based Decoder for Near-term Quantum Error Correction