Barren plateaus in quantum neural network training landscapes

By Jarrod R. McClean, Sergio Boixo, Vadim N. Smelyanskiy, Ryan Babbush, Hartmut Neven. Nature Communications, 2018

2,812 citations recorded by the source corpus.

Many experimental proposals for noisy intermediate scale quantum devices involve training a parameterized quantum circuit with a classical optimization loop. Such hybrid quantum-classical algorithms are popular for applications in quantum simulation, optimization, and machine learning. Due to its simplicity and hardware efficiency, random circuits are often proposed as initial guesses for exploring the space of quantum states. We show that the exponential dimension of Hilbert space and the gradient estimation complexity make this choice unsuitable for hybrid quantum-classical algorithms run on more than a few qubits. Specifically, we show that for a wide class of reasonable parameterized quantum circuits, the probability that the gradient along any reasonable direction is non-zero to some fixed precision is exponentially small as a function of the number of qubits. We argue that this is related to the 2-design characteristic of random circuits, and that solutions to this problem must be studied. Gradient-based hybrid quantum-classical algorithms are often initialised with random, unstructured guesses. Here, the authors show that this approach will fail in the long run, due to the exponentially-small probability of finding a large enough gradient along any direction.

Subfields: Artificial Intelligence

View Paper: https://www.semanticscholar.org/paper/d699e0958fe1d8a4c1d691765f7e11b823fa606f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

Citations in the corpus

Variational Quantum Linear Solver (2019, background): “Let us remark that this ansatz can have trainability issues [38, 44] for large-scale problems.”
Diagnosing Barren Plateaus with Tools from Quantum Optimal Control (2021, background): “For instance, it is known that one should avoid problem-agnostic ansatzes such as deep hardware efficient ansatzes, as these can exhibit barren plateaus due to their high expressibility [37, 38, 47].”
Quantum Generative Adversarial Networks for learning and loading random distributions (2019, background): “Furthermore, although barren plateaus [45] were not observed in our experiments, the possible occurrence of this effect, as well as, counteracting methods should be investigated.”
Robust data encodings for quantum classifiers (2020, background): “More fundamental questions about the computational complexity [7, 19], trainability [20–22] and noise-resilience [23] of VQAs have also been considered.”
Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices (2018, methodology): “Without constructive approaches to perform the parameter optimization, any potential advantages of the hybrid algorithms could be lost [13].”
Quantum machine learning models are kernel methods (2021, background): “In addition, convexity – the property that there is only one global minimum – may help with trainability problems like the notorious “barren plateaus” [16] in variational circuit training.”
QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuits (2021, background): “For example, “barren plateau” [44] is a phenomenon when the cost function landscape is flat, Encoder Trainable Quantum Layers Measurement Encode pixels as angles”
Entanglement Induced Barren Plateaus (2020, methodology): “In recent years, several barren plateau results [12–16] put limitations on the gradient-based training of QNNs.”
Variational quantum algorithms (2020, background): “The phenomenon of BPs was originally discovered in [164] where it was shown that deep unstructured parametrized quantum circuits exhibit BPs when randomly initialized.”
Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator (2018, background): “[120] Jarrod McClean, Sergio Boixo, Vadim Smelyanskiy, Ryan Babbush, and Hartmut Neven, “Barren Plateaus in Quantum Neural Network Training Landscapes,” arXiv.”
Challenges and opportunities in quantum machine learning (2022, background): “Local minima are not the only issue facing QML, as it has been shown that quantum landscapes can exhibit a fascinating property known as a barren plateau [58, 77– 89].”