Algorithms
Barren Plateau
A training obstacle in quantum machine learning where gradients become vanishingly small as circuits scale up, stalling optimization.
Definition
A barren plateau is a phenomenon observed in training variational quantum algorithms (like quantum neural networks) where, as the number of qubits increases, the gradient signal used to guide optimization becomes exponentially small, making it nearly impossible for classical optimizers to find improvements.
In depth
A barren plateau is a flat region in the landscape of a variational quantum circuit's cost function, where gradients are exponentially small. McClean and coauthors identified it in 2018: for sufficiently random parameterized circuits, the variance of the gradient shrinks as 2 to the minus n, where n is the number of qubits. Training then needs exponentially many measurements to find a direction downhill, because the signal is buried under shot noise, and no optimizer can help, since the problem is a lack of information rather than a poor search strategy.
Several causes have been found. Deep random circuits form approximate 2-designs that spread the state uniformly over Hilbert space. Global cost functions, which compare the whole state with a target, flatten the landscape, while local costs that look at a few qubits at a time are better, as Cerezo and coauthors showed in 2021. Excess entanglement and noise also cause plateaus: Wang and coauthors in 2021 showed that hardware noise alone can flatten the landscape for deep circuits, so barren plateaus can appear even for circuits designed to avoid the first causes.
Mitigation strategies include initializing parameters near good values, training layer by layer, using shallow or symmetry-respecting circuits, and local cost functions. Larocca and coauthors surveyed the field in 2025. A troubling theme is that many circuits proven to avoid barren plateaus also turn out to be efficiently simulated by classical methods, as argued by Cerezo and others, which raises the question of whether trainable variational circuits can ever be useful for quantum advantage. The issue has pushed research toward fault-tolerant algorithms and toward quantum data tasks.
Technical Definition
Research has shown barren plateaus arise under fairly general conditions for randomly initialized parameterized quantum circuits, motivating research into smarter initialization strategies and circuit structures specifically designed to avoid this vanishing gradient problem.
Visual Explanation: An Analogy
Think of a barren plateau like trying to find the lowest point in an enormous, almost perfectly flat desert — with no slope to guide you in any direction, you have essentially no information about which way to walk to improve your position.
Key facts
| Item | Detail |
|---|---|
| Identified | McClean, Boixo, Smelyanskiy, Babbush, and Neven, 2018 |
| Gradient variance | Falls roughly as 2^(-n) for random deep circuits |
| Causes | Random circuits, global costs, high entanglement, and hardware noise |
| Mitigations | Local costs, good initialization, layerwise training, and structured ansatzes |
| Open question | Whether trainable circuits are classically simulable |
Where the idea comes from
The 2018 Nature Communications paper introduced the term. Subsequent work from 2020 to 2025 mapped its causes, including noise-induced plateaus in 2021, and reviewed mitigation strategies.
Real-World Use Cases
- A major practical obstacle limiting how large variational quantum machine learning models can realistically be trained
- An active area of mitigation research, including specialized initialization techniques
How it differs from related ideas
- A barren plateau is a flat landscape, while a local minimum is a trap with some gradient around it.
- Vanishing gradients in classical deep learning are a similar-sounding but different problem with different fixes.
- Gradient-free optimizers do not escape a barren plateau, because the cost signal itself is exponentially small.
Frequently asked questions
What is a barren plateau?
A region of a variational circuit's cost landscape where gradients vanish exponentially with the number of qubits, making training infeasible.
What causes barren plateaus?
Deep random circuits, global cost functions, too much entanglement, and hardware noise.
How can they be avoided?
By using local cost functions, shallow or structured circuits, careful initialization, and layerwise training.
Related Terms
Keep exploring
- Algorithm: Variational Quantum Eigensolver (VQE)
- Algorithm: Quantum Approximate Optimization Algorithm (QAOA)
- Algorithm: Quantum Natural Gradient Descent
- Algorithm: Quantum Support Vector Machine
- Hardware: IBM Heron (r1, r2, and r3)