Low-latency machine learning FPGA accelerator for multi-qubit-state discrimination

arXiv:2407.03852 · quant-ph, cs.AR, cs.LG · Submitted 2024-08-14 · Read on arXiv

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Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: Next we'll be talking about the paper "Low-latency machine learning FPGA accelerator for multi-qubit-state discrimination".

Jane: The paper was written by Pradeep Kumar Gautam, Shantharam Kalipatnapu, Shankaranarayanan H, Ujjawal Singhal, Benjamin Lienhard et al. from Indian Institute of Science and Defence Research and Development Organisation and Princeton University.

Tom: Stay tuned as we take you through the paper and discuss its implications.

Title: Tom: Welcome back to the show, everyone. Today we're diving into a paper that's got a mouthful of a title: "Low-latency machine learning FPGA accelerator for multi-qubit-state discrimination."

Jane: And Tom, I have to say, that title packs in so much. We're talking about quantum computing, machine learning, and specialized hardware all in one. It's like a triple threat of cutting-edge tech.

Tom: Exactly, Jane. And for our listeners who might be new, let's break down the core idea. This is about reading the state of superconducting qubits—the building blocks of quantum computers—and doing it incredibly fast.

Jane: Right. When a quantum computer does a calculation, you need to know what state each qubit is in at the end. That's the "readout." The problem is, this readout process is slow and error-prone, especially when you have multiple qubits.

Tom: And that's where the "machine learning" part comes in. Instead of using traditional signal processing, they're using a neural network to figure out the qubit states. It's like teaching a computer to recognize the subtle differences in the signals.

Jane: But neural networks are usually big and slow. So the "FPGA accelerator" is the clever part. They're putting that neural network onto a special type of chip that can process information in parallel, making it super fast.

Tom: So the whole title is basically saying: "We made a really fast, specialized brain for reading quantum computers." And the results, as we'll get into, are pretty wild. The team is from the Indian Institute of Science, and they've managed to get this working in under fifty nanoseconds.

Jane: Under fifty nanoseconds. For context, that's faster than the blink of an eye by a factor of millions. This is the kind of speed you need if you want to build a quantum computer that can actually correct its own errors.

Tom: And that's the big picture, right? Quantum error correction is the holy grail for making these machines useful. So this paper is a serious step in that direction. Let's get into the details of how they actually pulled this off.

Paper discussion segment 1: Tom: So Jane, we've set the stage. Now let's talk about the actual problem they're solving. The paper is called "Low-latency machine learning FPGA accelerator for multi-qubit-state discrimination," and the core issue is that reading a qubit is messy.

Jane: It really is. The signals you get back from a qubit are noisy. It's like trying to hear a whisper in a crowded room. And when you have five qubits all sending their whispers at once, it gets even harder to tell them apart.

Tom: They call that "frequency-multiplexed readout." All five qubits are sending their signals down the same wire, but at different frequencies. It's efficient, but it creates crosstalk—the signals interfere with each other.

Jane: And that's where the neural network shines. The authors, led by Pradeep Kumar Gautam and the team, trained a neural network to look at the raw, noisy signal and pick out the state of each qubit. It learns the patterns of the crosstalk and compensates for it.

Tom: But here's the catch. A full-blown neural network, like the one they used in a previous paper, is huge. It has over one point six million parameters. You can't just drop that onto an FPGA and expect it to be fast.

Jane: So they had to make it smaller and smarter. They used something called "quantization-aware training." That's a fancy way of saying they trained the network to work with very low-precision numbers. Instead of using thirty-two-bit floating-point numbers, they used just two or four bits.

Tom: Right. It's like the difference between writing a number with a full decimal point versus just rounding it to the nearest whole number. It's less precise, but it's way faster and takes up way less space.

Jane: And the amazing thing is, the fidelity—the accuracy of the readout—only dropped by about zero point nine percent compared to the full-precision model. That's a tiny cost for a massive speedup.

Tom: So they've proven you can shrink the brain without losing much of its intelligence. But then they had to figure out how to wire it up on the FPGA to make it actually fast. That's where the real engineering magic happens, and I think Meng would love this part.

Paper discussion segment 2: Meng: Thanks, Tom. Yeah, I was listening to that, and the quantization part is great, but the real trick is the hardware architecture. The paper is called "Low-latency machine learning FPGA accelerator for multi-qubit-state discrimination," and they did something really clever to get the speed down.

Jane: Tell us, Meng. What was the breakthrough?

Meng: So, a standard way to implement a neural network on an FPGA is to process each layer one after another, and within each layer, you might have to time-multiplex the computation. That means you're reusing the same hardware multiple times to save space, but it costs you speed.

Tom: And they didn't want to do that. They wanted everything to run in parallel.

Meng: Exactly. So they took the first hidden layer of their network—which has sixty-four nodes—and split it into eight separate segments, each with eight nodes. All eight segments run at the same time, in parallel. This is what they call "Arch-seven" in the paper.

Jane: So instead of one big processing unit doing all the work, you have eight smaller ones working simultaneously. That's like having eight cashiers at a supermarket instead of one.

Meng: Precisely. And this cut the latency from thirty-three clock cycles down to nineteen cycles. That's a forty-two percent improvement. The final latency, including the initial signal processing, was about forty-nine point six nanoseconds.

Tom: And they didn't stop there. They also designed a deeper network, "Arch-nine" that processes the input in a piecewise manner. That one got down to just twenty-six point seven nanoseconds total.

Meng: Right. That one's a bit more complex, but the idea is that only the last layer contributes to the latency. The earlier layers are just pre-processing while the data streams in. It's a really elegant way to hide the latency of a deep network.

Jane: So they've got two different designs, both under fifty nanoseconds. But what does that mean for the broader field? Lu, you're the big-picture person here. What's the impact?

Conclusion: Lu: Well, Jane, this is about making quantum error correction actually feasible. The paper, "Low-latency machine learning FPGA accelerator for multi-qubit-state discrimination," is a crucial piece of the puzzle.

Tom: How so, Lu?

Lu: Quantum error correction requires you to constantly measure the qubits and then make corrections based on those measurements. The faster you can do that measurement and decision-making loop, the more error correction cycles you can fit into the qubit's lifetime.

Jane: And these qubits only stay in their quantum state for a few microseconds. So every nanosecond you save on readout is precious.

Lu: Exactly. With a fifty-nanosecond readout, you can do many more rounds of error correction before the qubit loses its information. This paper shows a clear path to achieving that with neural networks, which are much better at handling the crosstalk than traditional methods.

Meng: And it's not just about speed. The fact that they used a fully automated flow, from training to FPGA implementation, means this can be scaled to more qubits. You don't have to hand-craft the hardware for each new quantum processor.

Tom: So, to wrap it up: they've shown you can take a powerful neural network, shrink it down, and run it on specialized hardware to read out five qubits in under fifty nanoseconds, all while keeping the accuracy high.

Jane: And that's a massive step towards building a fault-tolerant quantum computer. It's a beautiful piece of engineering, and we're excited to see where this goes next.

Tom: Absolutely. That's all for today's discussion on "Low-latency machine learning FPGA accelerator for multi-qubit-state discrimination." Thanks for listening, and we'll see you on the next episode.

Jane: Goodbye, everyone!

Pradeep Kumar Gautam, Shantharam Kalipatnapu, Shankaranarayanan H, Ujjawal Singhal, Benjamin Lienhard, Vibhor Singh, Chetan Singh Thakur

Indian Institute of Science · Defence Research and Development Organisation · Princeton University

quant-ph, cs.AR, cs.LG

Submitted: 2024-08-14

Updated: 2026-08-18

Comments: 10 pages, 6 figures

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 66/100

Key concepts

Multi-qubit-state discrimination
This refers to the process of reading the state of multiple superconducting qubits simultaneously. The challenge is that these signals are noisy and interfere with each other, making it difficult to accurately determine the state of every qubit at once.
FPGA accelerator
An FPGA (Field-Programmable Gate Array) is a specialized chip used to implement the neural network. It allows the complex machine learning model to process information in parallel, which significantly increases speed compared to standard processing methods.
Quantization-aware training
This technique involves training a neural network to use very low-precision numbers, such as two or four bits, instead of standard high-precision floating-point numbers. This makes the model smaller and faster for hardware implementation with minimal loss in accuracy.

Terminology

Summary

Summary

This paper presents an integrated approach for implementing neural network (NN)-based qubit-state discriminators on field-programmable gate arrays (FPGAs) for multi-qubit superconducting quantum processors, achieving ultra-low latency readout. The work demonstrates that by employing quantization-aware training (QAT) and automated flows for mapping NNs onto FPGAs, it is possible to design ultra-low latency NN-based qubit-state discriminators that balance computational complexity with low latency requirements without significant loss in accuracy.

The experimental setup involves a five-qubit superconducting transmon quantum processor housed in a dilution refrigerator at around 20 mK, interfaced with a Xilinx RFSoC ZCU111 FPGA board. The readout signal is frequency-multiplexed, combining five readout tones at intermediate frequencies of 64.729 MHz, 25.366 MHz, 24.79 MHz, 70.269 MHz, and 127.282 MHz, upconverted to resonator frequencies in the GHz range using a local oscillator frequency of 7.127 GHz. The signal is digitized at a sampling rate of 500 MHz, and the RF-ADC converts the frequency-multiplexed readout signal into in-phase (I) and quadrature (Q) components for post-processing.

The performance metric used is the geometric mean fidelity (FGM) of the five qubits, defined as the fifth root of the product of individual qubit fidelities, where each fidelity is calculated as 1 minus the average of the conditional probabilities of misassigning ground and excited states. The authors also use cross-fidelity to assess crosstalk between qubits.

The authors systematically optimized the NN architecture. Starting from a base model with input size 1000 (500 I and 500 Q samples), three hidden layers with 1000, 500, and 250 nodes, and 32 output nodes, they reduced the input feature size to 512 and the number of output nodes to 5 (one per qubit) using BCEWithLogitsLoss as the loss function. This reduction exponentially decreases the output layer size. They found that reducing input feature size has a minimal impact on fidelity (maximum 0.3% drop), and decreasing hidden layers to 2 with fewer nodes only marginally affects FGM. The selected configuration was 512 × 64 × 5.

For quantization, the authors used Brevitas for QAT within the PyTorch framework. They varied bit-widths for input, weights, and activations from 8-bit to 2-bit. Results showed that FGM degrades for input quantization below 4-bit (dropping to approximately 0.7 for 2-bit input), indicating at least 4-bit representation is necessary for accurate state discrimination in a five-qubit system. Mixed precision quantization of weights and activations (from 8-bit to 2-bit) did not significantly impact fidelity. However, binary quantization (1-bit weights and activations) showed a notable decrease in accuracy, with fidelity dropping by 4-21%. The chosen quantization scheme was 4-bit for input and 2-bit for both weights and activations, achieving a geometric mean fidelity of 0.904, only 0.9% below the floating-point model reported in Ref. [13].

For FPGA implementation, the authors used the FINN-R framework, which employs a dataflow architecture with multi-vector threshold units (MVTUs) for low-precision matrix multiplication. To maximize parallelism, they designed a novel architecture where the first hidden layer (64 nodes) is divided into eight equal segments, each containing eight nodes, with all 512 input nodes connected to all segments. This eliminates time-multiplexing and reduces latency. The outputs of these segments are concatenated using a Concat layer. To make the model fully dataflow-convertible, they inserted uniform QuantIdentity layers before the Concat layer and added model graph modification steps within the FINN-R transformation process. This novel architecture fully parallelizes the FPGA implementation and reduces latency.

The paper reports several NN archetypes with their resource utilization and latency. Key results include:

  • Arch-1 (1000 × 1000 × 500 × 250 × 32): 1,634,782 parameters, 4/2/2 quantization, FGM 90.40%, latency 3802.26 ns, using 39.28% LUTs and 15.88% FFs.

  • Arch-5 (512 × 64 × 5): 33,217 parameters, 4/2/2 quantization, FGM 89.91%, latency 127.05 ns, using 10.37% LUTs and 6.26% FFs.

  • Arch-6 (512 × 64 × 5, binarized): 33,217 parameters, 4/1/1 quantization, FGM 80.1%, latency 38.59 ns, using 4.30% LUTs and 1.78% FFs.

  • Arch-7 ((512 × 8) × 8) × 5): 33,295 parameters, 4/2/2 quantization, FGM 89.72%, latency 47.12 ns, using 25.16% LUTs and 7.13% FFs.

  • Arch-8 (256 × 128 × 128 × 128 × 128 × 5): 42,124 parameters, 4/2/4 quantization, FGM 89.78%, latency 32.23 ns, using 25.94% LUTs and 14.52% FFs.

  • Arch-9 (256 × 128 × 128 × 128 × 128 × 5): 42,124 parameters, 4/1/4 quantization, FGM 89.07%, latency 24.03 ns, using 24.58% LUTs and 11.28% FFs.

The novel approach of splitting the first hidden layer of Arch-5 into eight parallel segments (Arch-7) reduced latency from 33 cycles to 19 cycles, a 42% improvement, at the cost of increased resource consumption due to additional QuantIdentity layers and heightened parallelism.

The authors also implemented an ultra-low latency SVM-based state discriminator on FPGA for single-qubit state discrimination. The SVM was trained using LinearSVC with 1,000 random samples from each of 32 possible state combinations, with a vector size of 512 for both IQ-data. The floating-point SVM outperformed matched filters, achieving a 1.53% increase in overall geometric mean fidelity (0.8982 vs 0.8846). The quantized SVM (8-bit weights and inputs) achieved a discriminator latency of 5.74 ns and utilized only 1675 LUTs for the five-qubit system, with two variants (2 multipliers and 1 multiplier per qubit) achieving FGM of 0.8980 and 0.8985, respectively.

Comparisons with state-of-the-art methods show that the NN-based discriminators (Arch-7, Arch-8, Arch-9) achieve latencies (including boxcar operation) of 49.6 ns, 35.16 ns, and 26.7 ns, respectively, comparable to or better than existing implementations. The presented approach has 18 to 29 times more learnable parameters than prior work (e.g., Reuer et al. with 1,891 parameters and 48 ns latency; Satvik et al. with 1,112 parameters), making it more robust and versatile for complex readout scenarios. The SVM discriminator achieves a processing latency of 5.74 ns (multi-cycle) and 3.67 ns (single-cycle), outperforming other traditional signal processing discriminators in latency and resource utilization.

The paper concludes that the demonstrated substantial reduction in latency while maintaining qubit-state discrimination fidelity enables the implementation of quantum error correction (QEC) protocols with more error correction cycles, significantly improving quantum processor performance. This marks the advent of low-latency NN architectures on FPGAs that do not require qubit-specific signal processing and can be scaled up as the number of qubits increases.

Improvements for AI systems

Based on the paper, here are specific improvements I can make to AI systems and what the improved systems can do:

  • Implement quantization-aware training (QAT) with 4-bit inputs, 2-bit weights, and 2-bit activations to achieve sub-50ns inference latency on FPGA (RFSoC ZCU111)

  • Use the novel segmented parallel architecture (Arch-7: 512×64×5 split into 8 parallel segments) to reduce latency by 42% compared to non-segmented equivalent

  • Achieve 24–47ns total latency including boxcar preprocessing, enabling more quantum error correction cycles per qubit coherence time

  • Replace traditional matched-filter/demodulation pipelines with a single neural network that processes raw I/Q data directly, eliminating per-qubit digital demodulation

  • Use output layer size equal to number of qubits (N) instead of 2 N possible states, reducing output complexity exponentially

  • Handle frequency-multiplexed readout of 5+ qubits simultaneously with geometric mean fidelity of 89.7–90.4% (only 0.9% below full-precision baseline)

  • Use the quantized neural network to reduce readout cross-talk correlations, as demonstrated by the cross-fidelity matrix (off-diagonal elements near zero)

  • Implement the SVM-based discriminator (quantized to 8-bit) that improves geometric mean fidelity by 1.53% over matched filters while using only 1,675 LUTs and 5.74ns processing latency

  • Integrate Brevitas (PyTorch quantization) → ONNX → FINN-R dataflow transformation → Xilinx Vivado synthesis

  • Add custom graph modifications (uniform QuantIdentity layers before Concat) to enable full dataflow conversion of segmented architectures

  • Achieve resource utilization under 26% of available LUTs on XCZU28DR, leaving room for control logic

  1. Real-Time Quantum Feedback: Process qubit readout signals in under 50ns, enabling mid-circuit measurements and dynamic error correction that were previously limited by signal processing latency

  2. Multi-Qubit Readout Without Custom Hardware: Discriminate states of 5+ frequency-multiplexed qubits using a single neural network, eliminating the need for per-qubit demodulation hardware and scaling linearly with qubit count

  3. Robust Operation Under Crosstalk: Maintain high fidelity (89.7%) even with significant readout crosstalk between qubits, outperforming traditional matched filters (88.5%)

  4. Deployable on Existing Quantum Control Platforms: The design fits on the RFSoC ZCU111 evaluation kit, which is already used in quantum labs, requiring no custom hardware

  5. Flexible Architecture Trade-offs: Choose between:

  • Balanced: Arch-7 (49.6ns, 25% LUT utilization)

  • Low-latency: Arch-9 (26.7ns, 24.6% LUT utilization)

  • Resource-constrained: Binarized model (38.6ns, 4.3% LUT utilization)

  1. Scalable to Larger Quantum Processors: The methodology supports networks with 1.6M+ parameters (Arch-1) and can be extended to deeper networks (Arch-8/9) without proportional latency increase due to piecewise input processing

  2. Single-Qubit Ultra-Fast Discrimination: The SVM variant achieves 5.74ns processing latency with only 1,675 LUTs, suitable for single-qubit feedback loops requiring maximum speed

These improvements enable practical quantum error correction, real-time adaptive control, and scalable multi-qubit readout that were previously bottlenecked by classical signal processing latency.

Abstract

Measuring a qubit state is a fundamental yet error-prone operation in quantum computing. These errors can arise from various sources, such as crosstalk, spontaneous state transitions, and excitations caused by the readout pulse. Here, we utilize an integrated approach to deploy neural networks onto field-programmable gate arrays (FPGA). We demonstrate that implementing a fully connected neural network accelerator for multi-qubit readout is advantageous, balancing computational complexity with low latency requirements without significant loss in accuracy. The neural network is implemented by quantizing weights, activation functions, and inputs. The hardware accelerator performs frequency-multiplexed readout of five superconducting qubits in less than 50 ns on a radio frequency system on chip (RFSoC) ZCU111 FPGA, marking the advent of RFSoC-based low-latency multi-qubit readout using neural networks. These modules can be implemented and integrated into existing quantum control and readout platforms, making the RFSoC ZCU111 ready for experimental deployment.

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