Synthesis of discrete-continuous quantum circuits with multimodal diffusion models

TL;DR

A multimodal denoising diffusion model that simultaneously generates a circuit's structure and its continuous parameters for compiling a target unitary and is benchmarked over different experiments, showcasing the ability of the method to outperform existing approaches in gate counts and under noisy conditions.

Abstract

Efficiently compiling quantum operations remains a major bottleneck in scaling quantum computing. Today's state-of-the-art methods achieve low compilation error by combining search algorithms with gradient-based parameter optimization, but they incur long runtimes and require multiple calls to quantum hardware or expensive classical simulations, making their scaling prohibitive. Recently, machine-learning models have emerged as an alternative, though they are currently restricted to discrete gate sets. Here, we introduce a multimodal denoising diffusion model that simultaneously generates a circuit's structure and its continuous parameters for compiling a target unitary. It leverages two independent diffusion processes, one for discrete gate selection and one for parameter prediction. We benchmark the model over different experiments, analyzing the method's accuracy across varying qubit counts and circuit depths, showcasing the ability of the method to outperform existing approaches in gate counts and under noisy conditions. Additionally, we show that a simple post-optimization scheme allows us to significantly improve the generated ansätze. Finally, by exploiting its rapid circuit generation, we create large datasets of circuits for particular operations and use these to extract valuable heuristics that can help us discover new insights into quantum circuit synthesis.

Figures (20)

• Figure 1: Multimodal quantum circuit synthesis pipeline scheme.a) An input circuit is first tokenized and then embedded into two separate modes, from which the forward and backward diffusion processes are defined. b) Schematic of the generative model. c) Inference overview, exemplary for the quantum Fourier transform. See \ref{['sec:methods']} for details.
• Figure 2: Noise schedules and loss weighting.a) Averaged Hamming distance between an initial token $\vb{h}_0$ and the decoded embedding of $\vb{h}_t$ over the diffusion time $t$. Dashed lines represent target schedules and solid lines represent the learned ones (see \ref{['sec:learned_sched']}). b) Circular loss between initial parameter $\vb{\lambda}$ and the decoded parameter $\hat{\lambda}_t$ over the diffusion time $t$ for different noise schedules. c) Loss weighting for the discrete ($\omega_h(t)$) and continuous ($\omega_w(t)$) modes used in \ref{['eq:loss']} over the diffusion time, chosen such that their total areas roughly match.
• Figure 3: Synthesis of random unitaries.a) Histogram of infidelities for 1024 unitaries and 128 circuits sampled per unitary (up to 16 gates). b) Histogram of minimum infidelity for each of the 1024 unitaries in a). The insets showcase the same plot but in logarithmic scale. c) Best infidelity over 128 circuits for target unitaries of varying gate count and percentage of parameterized gates.
• Figure 4: Process infidelity under noise. Average minimum process infidelity of generated circuits under noisy simulation, depending on the value of the error probability $p$ (see \ref{['sec:app_noisy_sim']}). Plotted are infidelities for: a) 3, b) 4, and c) 5 qubits. The circuits are sampled the same way as in \ref{['tab:compiler_comparison']}.
• Figure 5: Improving generative ansatz. Results after a tree-search with generative ansatz circuits as starting points. a) Average infidelity of the generated circuits after performing some actions. Errorbars are the error of the means. b) Histogram of infidelities before and after the improvements are applied. c) Distribution of taken actions at each tree depth. The converged action refers to nodes that have reached an infidelity threshold $\epsilon$ (vertical dashed line in panel b) and are not expanded anymore.