Quantum control in the presence of strongly coupled non-Markovian noise

TL;DR

This work tackles quantum control under strongly coupled, non-Markovian noise by introducing a graybox approach that blends physics-based whitebox components with a GRU-based blackbox emulator to model noise-affected dynamics offline. The method is demonstrated on a single qubit subject to random telegraph noise with unknown frequency parameters, achieving universal gate sets with fidelity exceeding $90\%$ across a wide range of coupling strengths, and significantly outperforming traditional whitebox strategies. The GB framework is shown to generalize to arbitrary open finite-dimensional systems and noise classes, offering a practical route to reliable quantum control in realistic noisy environments and providing insights into noise mitigation via data-driven dynamics learning.

Abstract

Controlling quantum systems under correlated non-Markovian noise, particularly when strongly coupled, poses significant challenges in the development of quantum technologies. Traditional quantum control strategies, heavily reliant on precise models, often fail under these conditions. Here, we address the problem by utilizing a data-driven graybox model, which integrates machine learning structures with physics-based elements. We demonstrate single-qubit control, implementing a universal gate set as well as a random gate set, achieving high fidelity under unknown, strongly-coupled non-Markovian non-Gaussian noise, significantly outperforming traditional methods. Our method is applicable to all open finite-dimensional quantum systems, regardless of the type of noise or the strength of the coupling.

Figures (4)

• Figure 1: The model studied in the paper. A qubit is subjected to a random telegraph noise along the Z-axis. Control pulses are applied on the X- and Y- axes, and the target is to implement a desired quantum gate.
• Figure 2: The qubit coherence under RTN vs the coupling strength between system and noise. The blue line shows the actual calculation using Monte-Carlo simulation. The green and orange lines show the theoretical calculation using the Dyson expansion with truncation orders $N = 2,4$ respectively. The dotted red lines define the boundaries between the different noise strength regions.
• Figure 3: The gate fidelity results for RTN case. Fidelity comparison across $g/\gamma$ values for different gates: a) I, b) X, c) Y, d) Z, e) H, f) $R_x(\frac{\pi}{4})$. For each level of noise strength, three points in the $g/\gamma \in [0,30]$ are selected for the GB approach. In the case of the CS-WB approach, 10 optimal pulses are applied on the noiseless system to simulate performance across all $g$ values. The results are shown in the blue shade. The black line inside of the blue shade represents the average fidelity. In a) the pulse sequence obtained using the CS-WB method is reported. This sequence is used for all values of noise strength. For the GB control, two examples are reported for $g/\gamma$ = 1.8 and 28.8.
• Figure 4: Quantum control results for $\boldsymbol{g/\gamma = 30}$. a) A violin plot displaying MSE statistics of GB control for both training and testing datasets. Each example in the dataset is compared against the predictions of the GB, and the MSE is then computed. The lower, middle and upper horizontal lines indicate the minimum, median, and maximum values respectively. b) GB control of $200$ random unitaries for a system under RTN with $g/\gamma = 30$, compared to CS-WB approach on a noiseless system and CS-WB approach on a system under RTN with $g/\gamma = 5.5$, which is the limit for the truncated Dyson expansion to be physical. The optimized pulses from all three methods are then simulated for a system with $g/\gamma = 30$, and the process matrix fidelity is calculated. The GB method outperforms gradient descent, with over $85\%$ of unitaries achieving fidelity greater than $80\%$. c) The average distance between $V_O$ operator and $I$ for $200$ random unitaries. GB shows distance less than $0.5$ for unitaries with fidelity higher than $70\%$.