LILLIPUT: a lightweight low-latency lookup-table decoder for near-term Quantum error correction

Abstract

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. LIL-LIPUT 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. CCS CONCEPTS• Hardware → Quantum technologies; • Computer systems organization → Quantum computing.

Neural-Network Decoders for Quantum Error Correction Using Surface Codes: A Space Exploration of the Hardware Cost-Performance Tradeoffs

“…The hardware trade-offs for recurrent neural networks should also be explored when using a more realistic error model including measurement errors, such as circuit noise. Employing recurrency and using the circuit noise error model would allow the comparison with other competitive hardware decoders, such as [30], [31]. Currently, our decoder shows competitive delays, while still performing better than the MWPM and Union-Find algorithms under depolarizing error models.…”

Scalable surface code decoders with parallelization in time

“…A window needs no buffer preceding the core because all past defects have been reliably annihilated, rendering its past time boundary closed. As far as we know, the idea of forward decoder first appears in [5] with w = 2s, and is rediscovered in [30] with s = 1 but without specifying the future-boundary conditions of windows. A limitation for the forward decoder is that windows must be processed sequentially due to the defect updates.…”

“…In this work, we introduce the sandwich decoder for the surface code, which solves the throughput problem using parallelism. Our work is inspired by the idea of "overlapping recovery" in [5] (later rediscovered in [30]), which we reformulate as the forward decoder. Both the sandwich and forward decoders are sliding-window decoders, * These two authors contributed equally.…”

Multidimensional Bose quantum error correction based on neural network decoder

“…In the second noise model, the Gaussian error displacement channel N 1 in the data qubit and the auxiliary qubit in the measurement N 2 and N m also exist. The Gaussian error displacement channels N 2 and N m are located behind the CNOT gate, so there is no error propagation from the auxiliary qubits to the data qubits, which corresponds to the phenomenological error model 41 . After applying ME-Steane error Fig.…”