New Algorithm Mitigates Noise in Quantum Algorithms, Enhancing Gradient Descent Performance

The article discusses a new algorithm designed to reduce the impact of noise on gradient descent in variational quantum algorithms (VQAs). The algorithm computes a regularized local classical approximation to the objective function at every gradient descent step, with the computational overhead being entirely classical. The algorithm’s effectiveness has been demonstrated on randomized parametrized quantum circuits. However, its general-purpose nature means it may not mitigate certain types of noise as effectively as specialized methods. Future research could focus on improving the algorithm’s ability to mitigate specific types of noise.

What is the New Algorithm for Mitigating Noise in Variational Quantum Algorithms?

The article introduces a new algorithm designed to mitigate the adverse effects of noise on gradient descent in variational quantum algorithms (VQAs). The algorithm achieves this by computing a regularized local classical approximation to the objective function at every gradient descent step. The computational overhead of this algorithm is entirely classical, meaning the number of circuit evaluations is the same as when carrying out gradient descent using the parameter-shift rules.

The algorithm’s effectiveness is demonstrated empirically on randomized parametrized quantum circuits. The algorithm is agnostic to the type of noise that evaluation of the objective function is subjected to, making it a general-purpose method with applications in a variety of settings. However, this agnosticism also means that the algorithm might fail to mitigate certain types of noise and could be outperformed by specialized methods for specific types of noise.

How Does the Algorithm Work?

The algorithm works by computing an approximation to the objective function at every gradient descent step. This computation is facilitated by the fact that the set of possible objective functions naturally embeds into a certain reproducing kernel Hilbert space, whose structure can be exploited. The quality of the approximation will generally not be good on the entire parameter space, but at every gradient descent step, a good approximation is guaranteed locally around the current point in parameter space.

The benefit of computing a local approximation is that samples from past iterations can be taken into account to make the approximation more robust to noise. Additionally, computing an approximation allows the use of regularization techniques from classical machine learning. The algorithm is agnostic to the type of noise that evaluation of the objective function is subjected to, making it a general-purpose method with applications in a variety of settings.

What are the Advantages and Drawbacks of the Algorithm?

The algorithm offers several advantages. Firstly, it mitigates the adverse effects of noise on gradient descent in VQAs, which is generally detrimental to their performance. Secondly, the computational overhead of the algorithm is entirely classical, meaning the number of circuit evaluations is the same as when carrying out gradient descent using the parameter-shift rules.

However, the algorithm also has some disadvantages. Its agnosticism to the type of noise means that it might fail to mitigate certain types of noise. Moreover, for specific types of noise, the algorithm is likely to be outperformed by specialized methods.

How are Gradients in VQAs Calculated?

Gradients in VQAs are usually calculated using the so-called parameter-shift rules. However, the computational cost of the latter scales very unfavorably with the number of trainable parameters. The computational overhead of the new algorithm is entirely classical, meaning the number of circuit evaluations is exactly the same as when carrying out gradient descent using the parameter-shift rules.

What is the Future of the Algorithm?

The article concludes by pointing out some possible directions for future research. The algorithm’s effectiveness is demonstrated empirically on a large number of randomized parametrized quantum circuits, considering both measurement shot noise and simulated quantum hardware noise. However, the algorithm’s agnosticism to the type of noise means that it might fail to mitigate certain types of noise, and for specific types of noise, the algorithm is likely to be outperformed by specialized methods. Therefore, future research could focus on improving the algorithm’s ability to mitigate specific types of noise.