Real-time decoding and control of fault-tolerant systems

Title

Scaling Surface Code Decoding with Multi-FPGA Architectures

Abstract

Real-time error correction is essential for fault-tolerant quantum computing. This necessitates efficient code designs as well as fast classical decoders that can decode faster than the rate of measurement. Most prior implementations of classical decoders focus on a single logical qubit which results in a static decoding graph. However, a practical quantum computer would contain multiple logical qubits that interact through lattice surgery operations. This requires decoders to be scalable in compute and I/O resources and capable of handling dynamic decoding graphs. Multi-FPGA architectures offer a promising solution for scaling decoding across multiple logical qubits with minimal latency impact. This talk explores the requirements and strategies for distributing decoding across multiple FPGAs to address scalability challenges.

Title

Decoding the Gross Code

Abstract

We introduce the problem of decoding the Gross code and its relevance to IBM Quantum’s quantum error correction roadmap. We then briefly introduce the belief propagation (BP) + ordered statistics decoder (OSD) decoding algorithm and discuss the relevant aspects and difficulties in performing an FPGA implementation. We present a high-level survey of recent literature exploring enhancements and alternatives to BP and/or OSD. Finally, we close by considering some of the future difficulties we expect to encounter when decoding for a large-scale computer architecture based on the Gross code.

Title

Decoding below the surface code threshold

Abstract

In this talk, I'll discuss some of the decoding methods we use in our recent below-threshold surface code experiment (arXiv:2408.13687). This includes both highly accurate machine learning and minimum-weight perfect matching techniques, alongside a faster but less accurate real-time decoder. I'll touch on some ideas for combining fast and accurate decoders, and other challenges decoders might face in real-life quantum systems.

Title

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

Abstract

The decoding problem in fault-tolerant quantum computation needs to be solved accurately and at speeds sufficient for real-time feedback. Strong error suppression in the code distance is vital to avoid prohibitive increases in the number of qubits required to facilitate computation at a given logical error rate. Similarly, speed is needed to avoid the backlog problem that would otherwise effectively halt the computation. We present an FPGA implementation of the Local Clustering Decoder (LCD) as a solution that balances the accuracy and throughput 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 the distributed union-find algorithm 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 refine 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 1us per round when implemented on a Xilinx Zynq Ultrascale+ FPGA, a rate that is sufficient to avoid the backlog problem on a superconducting quantum computer. We demonstrate that high-accuracy real-time decoding is possible, relaxing the qubit requirements to bring forward the era of fault-tolerant quantum computation.

Title

A systems perspective of spatially parallel window decoding

Abstract

Most prior work on real time decoding has focused on an isolated logical qubit encoded in the surface code. However, for codes including the surface code, a large merged patch can arise during lattice surgery --- possibly as large as the entire device. This puts a significant strain on a real time decoder, which must decode errors on this merged patch and maintain the level of fault-tolerance that it achieves on isolated logical qubits. 

These requirements are relaxed by using spatially parallel decoding, which can be accomplished by dividing the physical qubits on the device into multiple overlapping groups and assigning a decoder module to each. We refer to this approach as spatially parallel windows. While previous work has explored similar ideas, none have addressed system-specific considerations pertinent to the task or the constraints from using hardware accelerators. In this talk, I will show how to configure spatially parallel windows, so that the scheme (1) is compatible with hardware accelerators, (2) supports general lattice surgery operations, (3) maintains the fidelity of the logical qubits, and (4) meets the throughput requirement for real time decoding. Furthermore, our results reveal the importance of optimally choosing the buffer width to achieve a balance between accuracy and throughput --- a decision that should be influenced by the device's physical noise.

Title

Real time-decoding at Quantinuum

Abstract

We will discuss Quantinuum's results on decoding quantum error-correcting codes in real-time. This will include decoding with flagged syndrome extraction for the Steane code as well as real-time decoding for the surface code using minimum weight perfect matching and multiple rounds of syndrome extraction. Time-permitting, unpublished results using real-time decoding for other codes may be discussed.

Title

Promatch: Extending the Reach of Real-Time Quantum Error Correction with Adaptive Predecoding

Abstract

Real-time quantum error correction is essential for fault-tolerant quantum computing, requiring the decoding of measured parity bits into error types and locations within tight time constraints. Minimum Weight Perfect Matching (MWPM) is an accurate decoding algorithm for surface codes, with recent advancements achieving real-time implementations (RT-MWPM) for limited distances. However, at high distances, the number of flipped parity bits in the syndrome, referred to as the Hamming weight, often exceeds the capabilities of existing decoders. In this work, our goal is to enable larger distance RT-MWPM decoders by using adaptive predecoding that converts high Hamming weight syndromes into low Hamming weight syndromes, which are accurately decoded by the RT-MWPM decoder.
An effective predecoder must balance both accuracy (as any erroneous decoding by the predecoder contributes to the overall Logical Error Rate) and coverage (as the predecoder must ensure that the Hamming weight of the syndrome is within the capability of the final decoder). In this work, we propose Promatch, a real-time adaptive predecoder that predecodes both simple and complex patterns using a locality-aware, greedy approach. Our approach ensures two crucial factors: 1) high accuracy in prematching flipped bits, ensuring that the decoding accuracy is not hampered by the predecoder, and 2) sufficient coverage adjusted based on the main decoder’s capability given the time constraints. Promatch enables real-time decoding of surface codes at greater distances. When run concurrently with the state-of-the-art decoder, it achieves Logical Error Rates equivalent to MWPM at distances beyond the reach of the decoder alone.