Improving Quantum Decoding Performance

A few months ago, we shared with you our progress on developing novel decoding algorithms for qLDPC codes. That effort resulted in the Relay-BP algorithm (https://lnkd.in/eFbWNFeU), which surpassed prior state-of-the-art qLDPC decoders in terms of logical error rate while simultaneously removing barriers toward real-time implementation. In particular, we showed that a novel variation of the belief propagation (BP) algorithm was sufficient for accurate decoding of our gross code without the need of an expensive second-stage decoder to fix cases where BP failed to converge. I’m excited to tell you about some of the progress we’ve made on taking the first steps towards implementing a real-time decoder in hardware (https://lnkd.in/e8CShTmT). Our initial effort has focused on FPGAs because they are very flexible and allow for very low-latency integration into our quantum control system. FPGAs’ flexibility in supporting custom logic and user-defined numerical formats allowed us to evaluate the performance of Relay-BP across a range of floating-point, fixed-point, and integer precisions. Encouragingly, we observe a high tolerance to reduced precision. Our experiments show that even 6-bit arithmetic is sufficient to maintain decoding performance. We explored the speed limits of an FPGA Relay-BP implementation in a maximally-parallel computational architecture. Like traditional BP, the Relay-BP algorithm is a message-passing algorithm where messages are exchanged between nodes on a decoding graph. Our maximally parallel implementation assigns a unique compute resource to every node in this graph, allowing a full BP iteration to be computed on every clock cycle. This decoder architecture is resource-intensive, but we succeeded in building a Relay-BP decoder for the gross code and fit it within a single AMD VU19P FPGA. Our implementation is limited to split X/Z decoding of the gross code syndrome cycle (we decode windows of 12 cycles), a simpler implementation than we’d need for Starling. That being said, it is extremely fast, an absolute requirement for practical implementation. In fact, we can execute a Relay-BP iteration in 24ns. As physical error rates drop below 1e-3, Relay-BP typically converges in less than 20 iterations. This means we can complete the decoding task in about 480ns. This is significantly faster than what is possible with NVIDIA’s DGX-Quantum solution, which requires a 4000ns start-up cost before decoding begins. The figure below compares the logical error performance versus physical error rate of our FPGA implementation compared to a floating-point software implementation for memory experiments of the size of Loon and Kookaburra on our Innovation roadmap. This and further data shows that the reduced precision arithmetic in the FPGA matches the accuracy of a software model, while simultaneously running dramatically faster. Further details are in the pre-print: https://lnkd.in/e8CShTmT

I'm really happy with the rapid development of CUDA-Q QEC, our toolkit for quantum error correction. QEC is an incredibly rich and fast-moving field, and in CUDA-Q QEC we aim to provide a platform with a diverse set of accelerated decoders, AI infrastructure, tools to enable researchers to develop and test their own codes, decoders, and architectures, hopefully even better than our own! As we dig deeper into the problem of scalable QEC, the benefits of GPUs and AI have become much clearer. We started with research tools, for simulation and offline decoding, which is still an important capability. Now with the 0.5.0 release we also provide the infrastructure for real-time decoding, where syndrome processing occurs concurrently with quantum operations. This release also introduces GPU-accelerated algorithmic decoders like RelayBP, a promising approach developed in the past year that aims to overcome the convergence limitations of traditional belief propagation. For scenarios demanding maximum throughput, we have integrated a TensorRT-based inference engine that allows researchers to deploy custom AI decoders trained in frameworks like PyTorch and exported to ONNX directly into the quantum control loop. To address the complexities of continuous system operation, we added sliding window decoders that handle circuit-level noise across multiple rounds without assuming temporal periodicity. These tools are designed to be hardware-agnostic and scalable, supporting our partners across the ecosystem who are building the first generation of reliable logical qubits. Check out the full technical breakdown in our latest developer blog by Kevin Mato, Scott Thornton, Ph.D., Melody Ren, Ben Howe, and Tom L. https://lnkd.in/gvC__zRd

Long before #quantum becomes an #AI-accelerator, classical machine learning is already useful in quantum stacks. Many of the quantum engineering bottlenecks look like typical ML problems. From control to AI-based transpilation and error mitigation. This is the angle I followed for a while. I even used it in our QC summer school curriculum design, as an easy entry point for computer scientists. This week, I came across a few new materials and news on the topic. My notes turned into a short digest that might be useful for some of my readers. 𝗠𝗟 𝗳𝗼𝗿 𝗻𝗼𝗶𝘀𝗲 𝗺𝗶𝘁𝗶𝗴𝗮𝘁𝗶𝗼𝗻. Ross Duncan and the team just dropped a comprehensive review and ablation study on applying machine learning to readout error mitigation: https://lnkd.in/d8c4CgeF The intuition is pretty straightforward - it is basically the same signal-denoising problem we solve in deep learning for image enhancement and audio processing. In practice, however, things get much messier when you scale to larger qubit counts. An earlier attempt to scale was relatively successful by IBM in https://lnkd.in/d-Gp5tYp . In the new paper, the focus is on a few qubits, but the contribution is a more systematic ablation study across circuit families and model architectures, needed to build better intuition for scaling. 𝗠𝗟 𝗳𝗼𝗿 𝗤𝘂𝗮𝗻𝘁𝘂𝗺 𝗘𝗿𝗿𝗼𝗿 𝗖𝗼𝗿𝗿𝗲𝗰𝘁𝗶𝗼𝗻. Another active direction is the application of ML to syndrome decoding. I was checking some recent literature after a new startup emerged in this domain (https://lnkd.in/dqXURTuz ). As for QEC, a classical real-time control/decoding pipeline must keep up with cycle times, and this is where “AI decoders” are being pitched as a potentially low-latency, high-throughput solution. The direction is not new and is already quite crowded by various attempts to address the problem, including DeepMind’s recent 𝗔𝗹𝗽𝗵𝗮𝗤𝘂𝗯𝗶𝘁 𝟮 model (https://lnkd.in/dKrvqcad ) and earlier ML decoder work for IBM’s heavy-hexagon family of codes (https://lnkd.in/dumWZRb9 ). But building an efficient model is only one step. Ultimately, for practical systems, this will narrow down to running the reduced model with near-real-time inference on specialized hardware, without sacrificing too much decoding accuracy. Classical ML in QC often appears elegant and cute, but it is not a silver bullet. In some regimes, it may simply miss genuinely quantum correlations and fail miserably. In QEC, inference latency may be killing in practice, similar to what happens in various edge applications in classical AI. And across both mitigation and decoding, out-of-distribution scenarios are typically a direct path to the model's failure. 𝗛𝗼𝘄 𝘂𝘀𝗲𝗳𝘂𝗹 𝗵𝗮𝘃𝗲 𝘆𝗼𝘂 𝗳𝗼𝘂𝗻𝗱 𝗠𝗟 𝗶𝗻 𝗾𝘂𝗮𝗻𝘁𝘂𝗺 𝗰𝗼𝗺𝗽𝘂𝘁𝗶𝗻𝗴? 𝗔𝗻𝘆 𝗼𝘁𝗵𝗲𝗿 𝗴𝗼𝗼𝗱 𝗽𝗿𝗮𝗰𝘁𝗶𝗰𝗮𝗹 𝘀𝗰𝗲𝗻𝗮𝗿𝗶𝗼𝘀?

Quantum state tomography, the process of reconstructing an unknown quantum state, traditionally suffers from computational demands that grow exponentially with system size, a significant barrier to progress in quantum technologies. S. M. Yousuf Iqbal Tomal and Abdullah Al Shafin, both from BRAC University, now present a new approach, geometric latent space tomography, which overcomes this limitation while crucially preserving the underlying geometric structure of quantum states. Their method combines classical neural networks with quantum circuit decoders, trained to ensure that distances within the network’s ‘latent space’ accurately reflect the true distances between quantum states, measured by the Bures distance. This innovative technique achieves high-fidelity reconstruction of quantum states and reveals an intrinsic, lower-dimensional structure within the complex space of quantum possibilities, offering substantial computational advantages and enabling direct state discrimination and improved error mitigation for quantum devices. https://lnkd.in/eSpH3YhD

Google Researchers Developed AlphaQubit: A Deep Learning-based Decoder for Quantum Computing Error Detection Google Research has developed AlphaQubit, an AI-based decoder that identifies quantum computing errors with high accuracy. AlphaQubit uses a recurrent, transformer-based neural network to decode errors in the leading error-correction scheme for quantum computing, known as the surface code. By utilizing a transformer, AlphaQubit learns to interpret noisy syndrome information, providing a mechanism that outperforms existing algorithms on Google’s Sycamore quantum processor for surface codes of distances 3 and 5, and demonstrates its capability on distances up to 11 in simulated environments. The approach uses two-stage training, initially learning from synthetic data and then fine-tuning on real-world data from the Sycamore processor. This adaptability allows AlphaQubit to learn complex error distributions without relying solely on theoretical models—an important advantage for dealing with real-world quantum noise. In experimental setups, AlphaQubit achieved a logical error per round (LER) rate of 2.901% at distance 3 and 2.748% at distance 5, surpassing the previous tensor-network decoder, whose LER rates stood at 3.028% and 2.915% respectively. This represents an improvement that suggests AI-driven decoders could play an important role in reducing the overhead required to maintain logical consistency in quantum systems. Moreover, AlphaQubit’s recurrent-transformer architecture scales effectively, offering performance benefits at higher code distances, such as distance 11, where many traditional decoders face challenges.... Read the full article here: https://lnkd.in/gVQtY8fc Paper: https://lnkd.in/gvhxD3pC Google Google DeepMind