Quantum Motion has implemented a streaming error correction decoder for the surface code, called Snowflake. It runs on commercial field-programmable gate arrays (FPGAs) at cryogenic temperatures. This work demonstrates that a streaming decoder can operate in real-time on standard commercial hardware at cryogenic temperatures, with in-built mechanisms for flagging difficult decoding problems. The results are a step towards the integrated classical-quantum systems that a large-scale fault-tolerant quantum computer will require.
Qubits are inherently noisy, they make mistakes and errors accumulate over the course of a computation. Quantum error correction (QEC) addresses this by distributing the computation across many qubits working together. The most widely studied approach to QEC is the surface code, in which some of the qubits are repeatedly measured throughout the computation to check for errors. The pattern of these measurement results is called the syndrome. It tells us where and when errors are likely to have occurred.
A classical computer interprets this syndrome and has to work out where errors have occurred. This is the job of a decoder. In a quantum computer syndrome measurements happen up to roughly every microsecond. The decoder must keep up, processing each round of syndrome data in under a microsecond, continuously. If the decoder falls behind, errors accumulate and the computation becomes meaningless.
Most decoders operate by collecting several rounds of syndrome data and then process them as a batch for each block of the computation. This introduces latency in the computation because the computation can not progress to the next block until the decoder has received all the syndrome data and made a decision.
Snowflake, developed by the team at Quantum Motion and the University of Oxford, is a streaming decoder, which processes syndrome data as it receives it, creating a continuous decoding process, reducing the time to reach the end of the computation.
However speed isn’t everything, the decoder must also be accurate in its decisions. Recent work has proposed running a two tier decoder: a fast lightweight decoder that can handle most of the simpler decoding work on its own, while a second, more powerful decoder only steps in when needed. For that handover to work, the fast decoder needs a way to flag its own uncertainty. This is called a decoder confidence score (DCS). When the score is high, there is no need for the fast decoder to ask for help.
This paper adds three DCSs directly with Snowflake’s implementation. The implementation of these confidence scores shows they cost almost nothing to compute. They have low impact on decoding speed and have minimal impact on the resource utilisation of the FPGA.
The team implemented Snowflake on two commercial FPGAs and tested the decoder at room temperature and, critically, at cryogenic temperatures inside a cryostat. Operating a decoder close to the quantum processor at cryogenic temperatures inside the fridge reduces the latency introduced by metres of cabling between the dilution fridge and room-temperature electronics.
Embedded Software & FPGA Engineer at Quantum Motion, Maries Tahaab said: “Decoding is one of the central engineering problems of fault-tolerant quantum computing. A quantum processor running error correction at scale will require many decoders operating in parallel, processing syndromes continuously and with low latency. This work shows that stream decoding can achieve sub-microsecond throughput and zero-latency confidence scoring on commercial off-the-shelf FPGAs at the temperatures relevant to quantum computing systems.”
The paper details that Snowflake achieves sub-microsecond average decoding time for the surface code up to distances of 21, satisfying the timing budget for superconducting quantum devices. These results were also validated experimentally on hardware for smaller code distances.
The results are promising but operating a highly-utilised FGPA at cryogenic temperatures generates substantial heat, raising the temperature inside the cryostat above the temperature to preserve qubit coherence. The paper discusses two ways forward, one is to operate the decoders at the 50K stage of the refrigerator, where more cooling power is available, connected via a high-speed bus. The second, which the team has developed in detail in the paper, is a new 2D architecture for Snowflake that would reduce the resource utilisation which leads to a decrease in power consumption, making a 4 K implementation a realistic target for future implementations.
This work included contributions from Maries Tahaab (Quantum Motion), Tim Chan (University of Oxford/University of Osaka), James Kirkman (Quantum Motion), and Simon Benjamin (University of Oxford/Quantum Motion).