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

The error rates of quantum devices are orders of magnitude higher than what is needed to run most quantum applications. To close this gap, Quantum Error Correction (QEC) encodes logical qubits and distributes information using several physical qubits. By periodically executing a syndrome extraction circuit on the logical qubits, information about errors (called syndrome) is extracted while running programs. A decoder uses these syndromes to identify and correct errors in real time, which is necessary to prevent accumulation of errors. Unfortunately, software decoders are slow and hardware decoders are fast but less accurate. Thus, almost all QEC studies so far have relied on offline decoding. To enable real-time decoding in near-term QEC, we propose LILLIPUT- a Lightweight Low Latency Look-Up Table decoder. LILLIPUT consists of two parts- First, it translates syndromes into error detection events that index into a Look-Up Table (LUT) whose entry provides the error information in real-time. Second, it programs the LUTs with error assignments for all possible error events by running a software decoder offline. LILLIPUT tolerates an error on any operation in the quantum hardware, including gates and measurements, and the number of tolerated errors grows with the size of the code. LILLIPUT utilizes less than 7% logic on off-the-shelf FPGAs enabling practical adoption, as FPGAs are already used to design the control and readout circuits in existing systems. LILLIPUT incurs a latency of a few nanoseconds and enables real-time decoding. We also propose Compressed LUTs (CLUTs) to reduce the memory required by LILLIPUT. By exploiting the fact that not all error events are equally likely and only storing data for the most probable error events, CLUTs reduce the memory needed by up-to 107x (from 148 MB to 1.38 MB) without degrading the accuracy.