Quantum Computing: Error Mitigation’s Mixed Impact on Variational Algorithm Trainability

Variational Quantum Algorithms (VQAs) are seen as a promising path to quantum advantage, but noise can limit their trainability. Error Mitigation (EM) strategies have been proposed to reduce noise impact, but a new study shows that some, like Virtual Distillation, can actually make it harder to resolve cost function values. However, the study also found that Clifford Data Regression can aid the training process in certain settings. The research underscores the need for careful application of EM protocols and highlights the potential of specific strategies to improve trainability, a crucial factor for VQA scalability and near-term quantum advantage.

Can Error Mitigation Improve the Trainability of Noisy Variational Quantum Algorithms?

The Role of Variational Quantum Algorithms and Error Mitigation

Variational Quantum Algorithms (VQAs) are often seen as the most promising avenue for achieving quantum advantage in the near future. These algorithms adapt to the constraints of Noisy Intermediate-Scale Quantum (NISQ) devices by minimizing a cost function through training a parameterized quantum circuit via a classical-quantum feedback loop. The cost is computed efficiently on a quantum computer, while the parameter optimization is carried out classically. VQAs have been proposed for a wide range of problems, from dynamical quantum simulation to machine learning and beyond.

However, recent studies have shown that noise can severely limit the trainability of VQAs, by exponentially flattening the cost landscape and suppressing the magnitudes of cost gradients. This is where Error Mitigation (EM) comes in. EM has shown promise in reducing the impact of noise on near-term devices, leading to the question of whether EM can improve the trainability of VQAs.

The Limitations of Error Mitigation Strategies

In this study, the researchers first demonstrate that for a broad class of EM strategies, exponential cost concentration cannot be resolved without committing exponential resources elsewhere. This class of strategies includes Zero-Noise Extrapolation, Virtual Distillation, Probabilistic Error Cancellation, and Clifford Data Regression.

The researchers performed analytical and numerical analysis of these EM protocols and found that some of them, such as Virtual Distillation, can make it harder to resolve cost function values compared to running no EM at all. This suggests that care should be taken in applying EM protocols as they can either worsen or not improve trainability.

The Potential of Clifford Data Regression

Despite the limitations of some EM strategies, the researchers found numerical evidence that Clifford Data Regression (CDR) can aid the training process in certain settings where cost concentration is not too severe. This positive result highlights the possibility of engineering error mitigation methods to improve trainability.

However, it’s important to note that noise impacts the trainability of VQAs, that is, the ability of the classical optimizer to find the global cost minimum. For ansatzes, or parameterized quantum circuits with depth linear or superlinear in the number of qubits and local Pauli noise, the cost function landscape exponentially flattens, leading to an exponentially vanishing cost gradient, a phenomenon known as Noise-Induced Barren Plateaus (NIBPs). This means that noise impedes the training process of VQAs, requiring an exponential number of shots per optimization step to resolve the cost landscape against finite sampling noise.

The Future of Error Mitigation in Quantum Computing

Given the great success of EM methods in suppressing error in observable expectation values, it’s natural to ask whether EM methods could address NIBPs. More generally, one could simply ask, does it help to use error mitigation during the training process for VQAs? This question is precisely the topic of this article.

The researchers note that error mitigation has been successfully implemented during the VQA training process for a finite sample statistics. However, new challenges have recently been discovered for this approach. It is now recognized that noise impacts the trainability of VQAs, potentially posing a serious issue for VQA scalability and could ultimately be a roadblock for near-term quantum advantage. It is therefore crucial to investigate potential methods to mitigate them.

In conclusion, while error mitigation shows promise in reducing the impact of noise on near-term quantum devices, its effectiveness in improving the trainability of VQAs is still a topic of ongoing research. The findings of this study highlight the need for careful application of EM protocols and the potential of strategies like Clifford Data Regression in certain settings.