Machine-learning based noise characterization and correction on neutral atoms NISQ devices

TL;DR

This work addresses noise in Pasqal neutral-atom NISQ devices by combining ML-based noise characterization with a reinforcement-learning approach to noise mitigation. It trains supervised regressors to map final occupation probabilities $\bm{\mathcal{P}}$ to noise parameters $(\sigma_R, w, T, \varepsilon, \varepsilon')$ and employs an RL loop to design a post-pulse correction $P'$, aiming to bring the measured dynamics closer to the ideal. Key contributions include demonstrating that ANN-based single- and multi-parameter estimations can outperform baseline linear models, revealing favorable scaling with measurement statistics, and showing that RL can reduce the distance to ideal outcomes as quantified by $D_{KL}$. The results advance understanding and practical mitigation of quantum noise on neutral-atom NISQ devices and point to future directions in integrating quantum ML techniques and deploying these methods on real hardware.

Abstract

Neutral atoms devices represent a promising technology that uses optical tweezers to geometrically arrange atoms and modulated laser pulses to control the quantum states. A neutral atoms Noisy Intermediate Scale Quantum (NISQ) device is developed by Pasqal with rubidium atoms that will allow to work with up to 100 qubits. All NISQ devices are affected by noise that have an impact on the computations results. Therefore it is important to better understand and characterize the noise sources and possibly to correct them. Here, two approaches are proposed to characterize and correct noise parameters on neutral atoms NISQ devices. In particular the focus is on Pasqal devices and Machine Learning (ML) techniques are adopted to pursue those objectives. To characterize the noise parameters, several ML models are trained, using as input only the measurements of the final quantum state of the atoms, to predict laser intensity fluctuation and waist, temperature and false positive and negative measurement rate. Moreover, an analysis is provided with the scaling on the number of atoms in the system and on the number of measurements used as input. Also, we compare on real data the values predicted with ML with the a priori estimated parameters. Finally, a Reinforcement Learning (RL) framework is employed to design a pulse in order to correct the effect of the noise in the measurements. It is expected that the analysis performed in this work will be useful for a better understanding of the quantum dynamic in neutral atoms devices and for the widespread adoption of this class of NISQ devices.

Figures (5)

• Figure 1: Scheme of the noise estimation pipeline. A global pulse is defined by the shapes of Rabi frequency $\Omega$ and detuning $\delta$ (a). A register is prepared with the positions of a set of $n$ atoms (6 in the specific case) that are irradiated by the laser pulse (b). When the pulse ends, the excitation states of the atoms are measured and the process is repeated to gather statistics on the occupation probabilities $\bm{\mathcal{P}}=\mathcal{P}_1,\dots,\mathcal{P}_{2^n}$ (c). The probabilities are used as input to an ann that predicts the noise parameters (d). The ann is trained collecting a simulated dataset of probabilities labelled with the corresponding values of noise. The depicted setting is for the more general multiple parameters estimation. The difference for the single parameter estimation is that the neural network have only one output for $\sigma_R$ and the adopted pulses and atoms registers are different.
• Figure 2: Scaling of single measurement for systems with an increasing number of atoms (a) and scaling in the number of measurements for systems with four atoms (b). We report the average absolute errors and standard deviations for 20 linear regression (in black and green) and 20 ann (in blue and red) models in the predictions of $\sigma_R$ on the synthetic validation set. The models in (a) uses as input the measurements of $s_2$, $s_3$, $s_{4a}$ and $s_5$. The models in (b) uses as input one or more concatenated measurements of runs of the settings with four atoms (the fourth pair of points in (a) is equal to the first pair in (b)). Indicating with $\cdot\oplus\cdot$ the concatenation of the measurements of the settings, we report in (b) in black and blue ${s_{4a},}\, {s_{4a}\oplus s_{4c},}\, {s_{4a}\oplus s_{4c}\oplus s_{4d},}\, {s_{4a}\oplus s_{4c}\oplus s_{4d}\oplus s_{4e},}\, {s_{4a}\oplus s_{4c}\oplus s_{4d}\oplus s_{4e}\oplus s_{4f}}$ and in green and red ${s_{4a}\oplus s_{4b}}$.
• Figure 3: Predictions on real data of the value of $\sigma_R$ for the models trained for the scaling in the number of atoms (a) and in the number of measurements (b) reported in \ref{['fig:scaling']}. We report the average values and standard deviations for the 20 linear regression (in black and green) and the 20 ann (in blue and red) models in the predictions of $\sigma_R$ using a set of real measurements of the settings described in \ref{['tab:registers']} run on the Pasqal nisq devices. The models in (a) uses as input the measurements of $s_2$, $s_3$, $s_{4a}$ and $s_5$. The models in (b) uses as input one or more concatenated measurements of runs of the settings with four atoms (the fourth pair of points in (a) is equal to the first pair in (b)). We report in (b) in black and blue the incremental concatenation of $s_{4a}$, $s_{4c}$, $s_{4d}$, $s_{4e}$ and $s_{4f}$. In green and red we report the concatenation of $s_{4a}$ and $s_{4b}$. The order of the real measurements for the latter concatenation is irrelevant, thus we report two green and two red points (almost overlapping and not clearly discernible) to consider the two possible concatenations. The horizontal red line indicates the value of $3\%$ for $\sigma_R$ estimated by Pasqal.
• Figure 4: Standard pulse $P$ (a) to be corrected with a correction pulse $P'$ (b) to be added after $P$ to counteract the effects of the noise. The Rabi frequency $\Omega$ is depicted in green and the detuning $\delta$ in purple. $P$ is a pulse of duration $T=500 ns$, Gaussian Rabi profile with area equal to $\pi/2$ and detuning in the form of a ramp from $\delta_0 = -20$ rad/$\mu s$ and $\delta_T = 20$ rad/$\mu s$. $P'$ is a pulse with the same duration and characteristics of $P$ but with variable Rabi area $a$, initial detuning $\delta_i$ and final detuning $\delta_f$.
• Figure 5: Evolution of the kl divergence between the corrected noisy simulation and the ideal one averaged for each episode. The red line is the reference value of $0.0011$ for the kl divergence between the uncorrected noisy simulation and the ideal one averaged over $100$ simulations.