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Avoiding barren plateaus via Gaussian Mixture Model
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abstract
Variational quantum algorithms is one of the most representative algorithms in quantum computing, which has a wide range of applications in quantum machine learning, quantum simulation and other related fields. However, they face challenges associated with the barren plateau phenomenon, especially when dealing with large numbers of qubits, deep circuit layers, or global cost functions, making them often untrainable. In this paper, we propose a novel parameter initialization strategy based on Gaussian Mixture Models. We rigorously prove that, the proposed initialization method consistently avoids the barren plateaus problem for hardware-efficient ansatz with arbitrary length and qubits and any given cost function. Specifically, we find that the gradient norm lower bound provided by the proposed method is independent of the number of qubits $N$ and increases with the circuit depth $L$. Our results strictly highlight the significance of Gaussian Mixture model initialization strategies in determining the trainability of quantum circuits, which provides valuable guidance for future theoretical investigations and practical applications.
Forward citations
Cited by 6 Pith papers
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Concentration-Free Quantum Kernel Learning in the Rydberg Blockade
A Rydberg blockade based quantum kernel is claimed to avoid exponential concentration while remaining classically hard to simulate.
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Pitfalls when tackling the exponential concentration of parameterized quantum models
Exponentially concentrated measurement outcomes are statistically indistinguishable from fixed noise after polynomial shots, so classical post-processing cannot fix them, and common proposed remedies do not escape this.
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LCQNN: Linear Combination of Quantum Neural Networks
LCQNN combines several trainable unitaries through a learned superposition on control qubits, yielding gradient variance bounds that scale polynomially with local system size rather than exponentially with total qubit count.
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Quantum Recurrent Embedding Neural Network
A quantum recurrent embedding neural network is proven to avoid barren plateaus via a dynamical Lie algebra decomposition, with applications to Hamiltonian and topological phase classification.
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A unifying account of warm start guarantees for patches of quantum landscapes
A new theorem shows that a patch of parameter space around any point with non-exponentially small curvature retains polynomially large loss variance, unifying and extending prior warm-start results for variational qua...
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Demonstration of Efficient Predictive Surrogates for Large-scale Quantum Processors
Classical surrogates using truncated trigonometric expansions emulate noisy quantum processors and cut measurement overhead in VQE pre-training and Floquet phase identification.
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