Diffusion-Inspired Quantum Noise Mitigation in Parameterized Quantum Circuits

TL;DR

This work addresses the degradation of parameterized quantum circuits (PQCs) caused by noise that accumulates across layers toward the maximally mixed state $\mathbbm{1}_n = I/2^n$. It introduces a diffusion-inspired learning framework that models the quantum noise as a forward diffusion and learns a noise distribution to enable a denoising (inverse) process, guided by a forward-backward quantum divergence loss based on fidelity $F(\rho,\sigma)$. Task-specific training combines this denoising with a supervised loss, producing a total objective $\mathcal{L}_{total} = \alpha_{fb}\mathcal{L}_{fb} + \alpha_{task}\mathcal{L}_{task}$. Empirical results on MNIST and Fashion classification under quantum noise demonstrate state-of-the-art robustness, highlighting the approach's potential to enhance PQC performance on NISQ devices.

Abstract

Parameterized Quantum Circuits (PQCs) have been acknowledged as a leading strategy to utilize near-term quantum advantages in multiple problems, including machine learning and combinatorial optimization. When applied to specific tasks, the parameters in the quantum circuits are trained to minimize the target function. Although there have been comprehensive studies to improve the performance of the PQCs on practical tasks, the errors caused by the quantum noise downgrade the performance when running on real quantum computers. In particular, when the quantum state is transformed through multiple quantum circuit layers, the effect of the quantum noise happens cumulatively and becomes closer to the maximally mixed state or complete noise. This paper studies the relationship between the quantum noise and the diffusion model. Then, we propose a novel diffusion-inspired learning approach to mitigate the quantum noise in the PQCs and reduce the error for specific tasks. Through our experiments, we illustrate the efficiency of the learning strategy and achieve state-of-the-art performance on classification tasks in the quantum noise scenarios.

Figures (7)

• Figure 1: The divergence between the quantum state and maximally mixed state when running operations on the IBM Quito quantum system. After a number of quantum state operations with noise, the quantum state becomes closer to the full quantum noise, i.e., maximally mixed state. It shows the relation between the effect of quantum noise and the number of quantum operations in PQCs. Note that although the amplitude damping makes the quantum state close to the $|0\rangle$ state, the quantum state distribution still gets closer to the maximally mixed state in the first 1200 operations.
• Figure 2: (a) In the traditional diffusion model, the distribution of the data $q(\mathbf{x}_i)$ becomes closer to the Gaussian noise $\mathcal{N}_G$ through diffusion steps. (b) In the noise-free scenario, each quantum transformation $V_i(\theta_i)$ can be reversed and maintain the quantum information of the previous circuit layer via reverse operation $V_i^\dagger(\theta_i)$. (c) In the PQCs having quantum noise case, the quantum state transformations $\tilde{V}_i(\theta_i) = \Lambda_i \circ V_i(\theta_i)$ are affected by noise $\Lambda_i$ that makes the reversed quantum state different from the original one. Motivated by this, we propose a learning-based method to mitigate the quantum noise via computing the divergence between the quantum state and its noisy forward-and-backward state.
• Figure 3: An overall framework of PQCs with quantum noise mitigation. For every quantum circuit layer $\tilde{V}_i(\theta_i) = \Lambda_i \circ V_i(\theta_i)$, a quantum noise mitigation layer $\Lambda_i^{-1}$ is applied to reduce the error.
• Figure 4: The forward-backward quantum divergence loss in a quantum circuit. For each layer $V_i(\theta_i)$ of the quantum circuit, the current quantum state $\tilde{\rho}_i$ is denoised by a learnable noise mitigation layer $\Lambda_i^{-1}$.
• Figure 5: Ablation studies on different numbers of circuit layers.