As proposed and demonstrated by the Los Alamos team, architectures and techniques proposed to alleviate or completely avoid the barren plateaus in variational quantum computing make them classically simulable. Provided by: LANL
LANL news release
Variational quantum computing is a hybrid quantum-classical approach that has emerged as one of the most promising applications for quantum devices. However, this approach is hampered by the “barren plateau” phenomenon, which impairs the machine learning training capabilities of this approach. The architectures and techniques proposed to mitigate or completely avoid barren plateaus make it possible to classically simulate barren plateaus, as a team of Los Alamos researchers suggested in a recent Perspective article in Nature Communications and continues to demonstrate with simulated quantum neural networks.
“Barren plateaus typically result from a phenomenon known in the field as the ‘curse of dimensionality.’ Models have to travel through very large spaces, and finding a solution is like finding a needle in a haystack,” said Marco Cerezo, a physicist at Los Alamos and lead author of this perspective. “By restricting the model to a small subspace, we avoid the barren plateau and avoid the curse of dimensionality. But the solution may mean that the model can be simulated as efficiently as before.”
If the relationship between the lack of a barren plateau (e.g., by restricting the model to a small subspace) and classical simulability holds, then the remedies for the barren plateau may turn out to be worse than the problem. The advantage of quantum computers in solving machine learning tasks faster than classical supercomputers is limited only to models without sterile plateaus.
Subspaces and classical simulation possibilities
Variational quantum computing hybrid approaches aim to solve tasks by classically optimizing the parameters of quantum circuits and extend the benefits of classical neural networks to the quantum domain. However, because the space of possible quantum states is too large (i.e., the “curse of dimensionality”), the optimization landscape becomes very flat, leading to a barren plateau where the approach’s algorithms fail.
The team’s recent work showed that the presence of barren plateaus has a clear bearing on whether the algorithm operates within small subspaces. The research team analyzed all known models and techniques on a case-by-case basis, uncovering common patterns hidden in plain sight. This means that once a valid small subspace has been identified and identified, all we need to do is emulate what a quantum computer would do within it.
This means that quantum computing approaches could potentially be simulated by classical computing. Across all known models without sterile plateaus, the team’s research found that classical computers can do the same things as quantum computers. This is a surprising result that undermines the quantum-only case for promising architectures and techniques for quantum machine learning. The Los Alamos team recently undertook a concrete demonstration using a specific architecture, the results of which were published in PRX Quantum, demonstrating end-to-end simulation potential.
“It seems like the math to get us worked out really well,” Cerezo said. “If you want to create a complete quantum architecture that can process information, there are barren plateaus and the curse of dimensionality. Also, if you make your model work in a subspace, that subspace will always be small enough to give you classical simulability; there will appear to be no intermediate or in-between spaces.”
End-to-end simulation potential of quantum convolutional neural networks
To test their understanding of simulability, the team analyzed a widely used variant of quantum convolutional neural networks. Quantum convolutional neural networks are an architecture considered by many to be one of the most promising models for quantum machine learning.
By identifying the correct subspace in which the model works, the team built and trained a purely classical surrogate for a quantum convolutional neural network. The surrogate matched or outperformed standard quantum convolutional neural networks on all benchmark datasets, running simulations with as many as 1,024 qubits. This test suggests that the success of quantum networks can be attributed to benchmarking simple problems, and the insights the team gleaned point to the need for non-trivial datasets to advance quantum machine learning.
Cautions and signs of hope
The researchers’ work does not suggest that quantum computers cannot operate in large spaces. In fact, successful quantum algorithms, such as those that simulate quantum systems, are highly structured and avoid the curse of dimensionality by carefully navigating large quantum spaces.
“Unlike standard quantum algorithms, where every logical operation has a specific purpose, quantum machine learning algorithms follow the learning methodology of classical neural networks and try to find the correct order of logical operations by training the algorithm on data,” said Nahuel Díaz, a postdoctoral fellow at the institute. “This means they can get lost in large spaces that are unstructured by design.”
By emulating how standard quantum algorithms work, researchers offer a path forward to overcome the barren plateau of classical simulation possibilities. The examples provided by the team of models that can be trained but cannot be simulated could provide inspiration for building new quantum learning algorithms.
Finally, the research team emphasized that quantum computers may be needed to initialize classical simulations. In this case, the authors proposed a new hybrid paradigm. In this paradigm, quantum devices are used not to train models, but to acquire data and build efficient classical algorithms.
paper: “Does the lack of a provable barren plateau mean classical simulation possibility? Or why we need to reconsider variational quantum computing.” Nature Communications. DOI: 10.1038/s41467-025-63099-6
funding: This research was supported by Los Alamos’ Institute-Directed Research and Development Program, Los Alamos’ Center for Nonlinear Research, and the Institute’s ASC Beyond Moore’s Law project.
paper: “Quantum Convolutional Neural Networks Can Be Effectively Simulated Classically.” PRX Quantum. DOI: 10.1103/8qt9-72ts
funding: This research was supported by Los Alamos’ Institute-Directed Research and Development Program and the Institute’s ASC Beyond Moore’s Law Project.
