Surviving The Barren Plateau in Variational Quantum Circuits with Bayesian Learning Initialization

Rad, Ali Bahrami; Seif, Alireza; Linke, Norbert

doi:10.48550/arxiv.2203.02464

Cited by 8 publications

(12 citation statements)

References 52 publications

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“…In [101], it was believed that correlated parameters in the ansatz can effectively reduce the parameter space and result in large gradients of cost function. A Bayesian learning initialization approach was employed in [102] to first identify a promising region in the parameter space and then employ the gradient-based or gradient-free optimizer for local search. Via simulations, [75] found an initial region of parameters that can improve the trainability and keep a high level of expressive power.…”

Section: Related Workmentioning

confidence: 99%

Trainability Enhancement of Parameterized Quantum Circuits via Reduced-Domain Parameter Initialization

Wang¹,

Qi²,

Ferrie³

et al. 2023

Preprint

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Parameterized quantum circuits (PQCs) have been widely used as a machine learning model to explore the potential of achieving quantum advantages for various tasks. However, the training of PQCs is notoriously challenging owing to the phenomenon of plateaus and/or the existence of (exponentially) many spurious local minima. In this work, we propose an efficient parameter initialization strategy with theoretical guarantees. We prove that if the initial domain of each parameter is reduced inversely proportional to the square root of circuit depth, then the magnitude of the cost gradient decays at most polynomially as a function of the depth. Our theoretical results are verified by numerical simulations of variational quantum eigensolver tasks. Moreover, we demonstrate that the reduced-domain initialization strategy can protect specific quantum neural networks from exponentially many spurious local minima. Our results highlight the significance of an appropriate parameter initialization strategy and can be used to enhance the trainability of PQCs in variational quantum algorithms.

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Section: Related Workmentioning

confidence: 99%

Trainability Enhancement of Parameterized Quantum Circuits via Reduced-Domain Parameter Initialization

Wang¹,

Qi²,

Ferrie³

et al. 2023

Preprint

View full text Add to dashboard Cite

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“…As discussed in the Refs. [15][16][17][18][19][20][21][22][23], better parameters initialization methods can help VQA reach better performance. In this section, we investigate the plain training where the initial parameters of 10% two-qubit gates are sampled uniformly from [0, 2π] and the remaining initial parameters are set to 0.…”

Section: Comparsion With the Initialization Strategymentioning

confidence: 99%

“…Even the gradient-free optimization approaches are also suppressed by the barren plateaus [14]. In order to mitigate the barren plateaus and achieve better performance from VQA, a series of strategies have been proposed, including parameters initialization methods [15][16][17][18][19][20][21][22][23], local objective function [24,25] and special quantum circuit ansatz [26][27][28][29][30][31].…”

mentioning

confidence: 99%

Training variational quantum algorithms with random gate activation

Liu¹,

Zhang²,

Jian³

et al. 2023

Preprint

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Variational quantum algorithms (VQAs) hold great potentials for near-term applications and are promising to achieve quantum advantage on practical tasks. However, VQAs suffer from severe barren plateau problem as well as have a large probability of being trapped in local minima. In this Letter, we propose a novel training algorithm with random quantum gate activation for VQAs to efficiently address these two issues. This new algorithm processes effectively much fewer training parameters than the conventional plain optimization strategy, which efficiently mitigates barren plateaus with the same expressive capability. Additionally, by randomly adding two-qubit gates to the circuit ansatz, the optimization trajectories can escape from local minima and reach the global minimum more frequently due to more sources of randomness. In real quantum experiments, the new training algorithm can also reduce the quantum computational resources required and be more quantum noise resilient. We apply our training algorithm to solve variational quantum simulation problems for ground states and present convincing results that showcase the advantages of our novel strategy where better performance is achieved by the combination of mitigating barren plateaus, escaping from local minima, and reducing the effect of quantum noises. We further propose that the entanglement phase transition could be one underlying reason why our RA training is so effective.

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“…it does not use gradient information) which is popular among VQA practitioners [18][19][20]. Bayesian optimisation can, however, be used within first-order methods to tune the stepsize [21] or initialisation [22]. Wang et al [23] uses Bayesian methods to infer the value of the cost function from a reduced number of measurements.…”

Section: Introductionmentioning

confidence: 99%

Bayesian learning of parameterised quantum circuits

Samuel¹,

Benedetti²,

Rosenkranz³

2023

Mach. Learn.: Sci. Technol.

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Currently available quantum computers suffer from constraints including hardware noise and a limited number of qubits. As such, variational quantum algorithms that utilise a classical optimiser in order to train a parameterised quantum circuit have drawn significant attention for near-term practical applications of quantum technology. In this work, we take a probabilistic point of view and reformulate the classical optimisation as an approximation of a Bayesian posterior. The posterior is induced by combining the cost function to be minimised with a prior distribution over the parameters of the quantum circuit. We describe a dimension reduction strategy based on a maximum a posterior point estimate with a Laplace prior. Experiments on the Quantinuum H1-2 computer show that the resulting circuits are faster to execute and less noisy than the circuits trained without the dimension reduction strategy. We subsequently describe a posterior sampling strategy based on stochastic gradient Langevin dynamics. Numerical simulations on three different problems show that the strategy is capable of generating samples from the full posterior and avoiding local optima.

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Surviving The Barren Plateau in Variational Quantum Circuits with Bayesian Learning Initialization

Cited by 8 publications

References 52 publications

Trainability Enhancement of Parameterized Quantum Circuits via Reduced-Domain Parameter Initialization

Trainability Enhancement of Parameterized Quantum Circuits via Reduced-Domain Parameter Initialization

Training variational quantum algorithms with random gate activation

Bayesian learning of parameterised quantum circuits

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