An initialization strategy for addressing barren plateaus in parametrized quantum circuits

By Edward Grant, Leonard Wossnig, Mateusz Ostaszewski, Marcello Benedetti. Quantum, 2019

514 citations recorded by the source corpus.

Parametrized quantum circuits initialized with random initial parameter values are characterized by barren plateaus where the gradient becomes exponentially small in the number of qubits. In this technical note we theoretically motivate and empirically validate an initialization strategy which can resolve the barren plateau problem for practical applications. The technique involves randomly selecting some of the initial parameter values, then choosing the remaining values so that the circuit is a sequence of shallow blocks that each evaluates to the identity. This initialization limits the effective depth of the circuits used to calculate the first parameter update so that they cannot be stuck in a barren plateau at the start of training. In turn, this makes some of the most compact ansätze usable in practice, which was not possible before even for rather basic problems. We show empirically that variational quantum eigensolvers and quantum neural networks initialized using this strategy can be trained using a gradient based method.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/0becaba0b9d5d025a3cb2ef2b7e8d6fa55cad95d

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

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Noise-induced barren plateaus in variational quantum algorithms (2020, background): “Fortunately, investigations into bar-ren plateaus have spawned several promising strategies to avoid them, including local cost functions [34, 40], parameter correlation [37], pre-training [41], and layer-by-layer training [42, 43].”
Connecting ansatz expressibility to gradient magnitudes and barren plateaus (2021, methodology): “That is, one could start the variational algorithm using a shallow, highly correlated ansatz and as the cost is iteratively minimized gradually grow the ansatz [8, 15, 38] and decorrelate the parameters [37].”
Variational Quantum Linear Solver (2019, background): “Strategies such as layer-by-layer training [45] and correlating the α parameters [46] have been shown to be effective to address these trainability issues.”
Barren plateaus in variational quantum computing (2024, unknown): “Interestingly, one can still bound how much the variance will deviate from that in equation (8) when the circuit is not a two-design (see Box 4 and the results in refs.”
Entanglement Induced Barren Plateaus (2020, background): “The ﬁrst is to choose an atypical initial state which has been already explored in [32].”
Absence of Barren Plateaus in Quantum Convolutional Neural Networks (2020, background): “[46] Edward Grant, Leonard Wossnig, Mateusz Ostaszewski, and Marcello Benedetti, “An initialization strategy for addressing barren plateaus in parametrized quantum circuits,” Quantum 3, 214 (2019).”
Diagnosing Barren Plateaus with Tools from Quantum Optimal Control (2021, background): “[53] Edward Grant, Leonard Wossnig, Mateusz Ostaszewski, and Marcello Benedetti, “An initialization strategy for addressing barren plateaus in parametrized quantum circuits,” Quantum 3, 214 (2019).”
Parameterized quantum circuits as machine learning models (2019, background): “While this limits the eﬀectiveness of variational circuits initialized at random, the use of highly structured circuits could alleviate the problem (e.g., see Grant et al. [53] for a structured initialization strategy).”