Enhancing Quantum Computing’s Expressive Power with Randomized Circuits: A New Approach

Quantum computing’s potential is often limited by the number of quantum gates, which can be compromised by noise, leading to errors. Variational quantum algorithms (VQAs) have been developed to minimize gate count, but their success depends on the expressive power of the variational wave function. A recent study proposed a new approach for VQAs using randomized quantum circuits and artificial neural networks to optimize the distribution function of these circuits. This approach could enhance the performance of VQAs, making them more reliable and accurate and potentially accelerating the development of quantum computing applications.

What is the Expressive Power of Quantum Computing?

Quantum computing is a rapidly evolving field that promises to revolutionize the way we process information. At the heart of this technology is the concept of quantum gates, which are the building blocks of quantum circuits. However, the accuracy of these gates is often compromised by noise, leading to potential errors in each gate operation. As the number of gates increases, quantum computing becomes less reliable, ultimately resulting in failure. Therefore, minimizing the number of gates is crucial for any quantum computing application. This issue is particularly relevant for noisy intermediate-scale quantum (NISQ) computers, where large-scale quantum error correction is unavailable.

Over the past decade, significant effort has been invested in developing quantum applications that take the number of gates into account. Among these applications, variational quantum algorithms (VQAs) have attracted the most interest. The key idea behind VQAs is to construct an Ansatz quantum circuit with parametrized quantum gates. The parameters of these gates are optimized in a feedback loop between quantum and classical computing. The circuit generates a variational wave function, which ideally, once the optimal parameters are found, is the answer to the given problem. This approach allows VQAs to solve certain problems while keeping the gate count minimal.

How Does the Expressive Power of Quantum Computing Impact VQAs?

The success of VQAs depends on the expressive power of the variational wave function. Since the variational wave function can only express a subset of all possible quantum states, a fundamental assumption is that the target quantum state is within this subset. Therefore, it is desirable to use a variational wave function with higher expressive power, capable of exploring a larger portion of the entire state space. By employing such a variational wave function, VQA has a better chance of finding the solution or attaining higher accuracy.

However, maximizing the expressive power presents two challenges. First, the gate number limits the circuit size and the number of parameters. Second, highly expressive circuits usually resemble the unitary t-design, which can lead to difficulties during the training process due to the problem of vanishing gradients. Despite these challenges, much attention has been devoted to designing circuits. However, it remains largely unexplored that the expressive power can be improved by optimizing the strategy of using circuits in the quantum-classical feedback loop.

What is the Proposed Solution to Enhance the Expressive Power of Quantum Computing?

In a recent paper, a team of researchers proposed a new approach for VQAs utilizing randomized quantum circuits to generate the variational wave function. They parametrize the distribution function of these random circuits using artificial neural networks and optimize it to find the solution. This random circuit approach presents a trade-off between maximizing the expressive power of the variational wave function and minimizing the associated time cost, specifically the sampling cost of quantum circuits.

Given a fixed gate number, the researchers demonstrated that they could systematically increase the expressive power by extending the quantum computing time. With a sufficiently large permissible time cost, the variational wave function can approximate any quantum state with arbitrary accuracy. Furthermore, they established explicit relationships between expressive power, time cost, and gate number for variational quantum eigensolvers.

What is the Potential Impact of this Research?

This research highlights the promising potential of the random circuit approach in achieving high expressive power in quantum computing. By utilizing randomized quantum circuits and artificial neural networks, the researchers were able to overcome the limitations of gate numbers and the presence of barren plateaus, which are common challenges in quantum computing.

The proposed approach could significantly enhance the performance of VQAs, making them more reliable and accurate. This could, in turn, accelerate the development and implementation of quantum computing applications, bringing us one step closer to realizing the full potential of this revolutionary technology.

What are the Future Directions of this Research?

While this research presents a promising approach to maximizing the expressive power of quantum computing, further work is needed to fully realize its potential. Future research could focus on refining the random circuit approach and exploring its applicability to different types of quantum computing problems. Additionally, more work is needed to understand the trade-off between expressive power and time cost, and how to optimize it for different applications.

In conclusion, this research represents a significant step forward in our understanding of the expressive power of quantum computing and its impact on VQAs. It opens up new avenues for the development of more powerful and efficient quantum computing applications, bringing us closer to the quantum revolution.