BEINIT: Avoiding Barren Plateaus in Variational Quantum Algorithms

Kulshrestha, Ankit; Safro, Ilya

doi:10.1109/qce53715.2022.00039

Cited by 9 publications

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The BP strongly limits the applicability of most VQAs, so the search for techniques to avoid BP has become a significant problem today. It has been shown that BPs can be avoided in some VQA by employing a local cost function instead of a global one [37,[39][40][41], using better initial parameters for the optimization [42,43], detecting the BPs with classical shadows [44], reducing the expressiveness of the parametric circuit [45], including mid-circuit measurements [46], using quantum annealing [47], geometric quantum machine learning [48], overparametrization [49], or improved gradient methods [50]. Despite the advances on this topic, there is no general indication to avoid BP in a generic VQA, and moreover, it is not clear which technique will help to avoid BPs in VDGE.…”

Section: Introductionmentioning

confidence: 99%

Avoiding barren plateaus in the variational determination of geometric entanglement

Zambrano,

Muñoz-Moller,

Muñoz

et al. 2024

Quantum Sci. Technol.

View full text Add to dashboard Cite

The barren plateau phenomenon is one of the main obstacles to implementing variational quantum algorithms in the current generation of quantum processors. Here, we introduce a method capable of avoiding the barren plateau phenomenon in the variational determination of the geometric measure of entanglement for a large number of qubits. The method is based on measuring compatible two-qubit local functions whose optimization allows for achieving a well-suited initial condition, from which a global function can be further optimized without encountering a barren plateau. We analytically demonstrate that the local functions can be efficiently estimated and optimized. Numerical simulations up to 18-qubit GHZ and W states demonstrate that the method converges to the exact value. In particular, the method allows for escaping from barren plateaus induced by hardware noise or global functions defined on high-dimensional systems. Numerical simulations with noise are in agreement with experiments carried out on IBM’s quantum processors for 7 qubits.

show abstract

Section: Introductionmentioning

confidence: 99%

Avoiding barren plateaus in the variational determination of geometric entanglement

Zambrano,

Muñoz-Moller,

Muñoz

et al. 2024

Quantum Sci. Technol.

View full text Add to dashboard Cite

show abstract

“…Not only are they known to have an optimization landscape riddled with local minima [44,58], they also suffer from the phenomenon of "barren plateaus", in which the gradients with respect to the optimization parameters vanish exponentially with system size [63,99]. Though several strategies have been proposed to deal with this problem [35,52,56,57,64,90,110] it remains an active area of research.…”

Section: Introductionmentioning

confidence: 99%

Characterization of variational quantum algorithms using free fermions

Matos

Self

Papić

et al. 2023

Quantum

View full text Add to dashboard Cite

We study variational quantum algorithms from the perspective of free fermions. By deriving the explicit structure of the associated Lie algebras, we show that the Quantum Approximate Optimization Algorithm (QAOA) on a one-dimensional lattice – with and without decoupled angles – is able to prepare all fermionic Gaussian states respecting the symmetries of the circuit. Leveraging these results, we numerically study the interplay between these symmetries and the locality of the target state, and find that an absence of symmetries makes nonlocal states easier to prepare. An efficient classical simulation of Gaussian states, with system sizes up to 80 and deep circuits, is employed to study the behavior of the circuit when it is overparameterized. In this regime of optimization, we find that the number of iterations to converge to the solution scales linearly with system size. Moreover, we observe that the number of iterations to converge to the solution decreases exponentially with the depth of the circuit, until it saturates at a depth which is quadratic in system size. Finally, we conclude that the improvement in the optimization can be explained in terms of better local linear approximations provided by the gradients.

show abstract

Hyperparameter importance and optimization of quantum neural networks across small datasets

Moussa,

Patel,

Dunjko

et al. 2023

Mach Learn

View full text Add to dashboard Cite

As restricted quantum computers become available, research focuses on finding meaningful applications. For example, in quantum machine learning, a special type of quantum circuit called a quantum neural network is one of the most investigated approaches. However, we know little about suitable circuit architectures or important model hyperparameters for a given task. In this work, we apply the functional ANOVA framework to the quantum neural network architectures to analyze which of the quantum machine learning hyperparameters are most influential for their predictive performance. We restrict our study to 7 open-source datasets from the OpenML-CC18 classification benchmark, which are small enough for simulations on quantum hardware with fewer than 20 qubits. Using this framework, three main levels of importance were identified, confirming expected patterns and revealing new insights. For instance, the learning rate is identified as the most important hyperparameter on all datasets, whereas the particular choice of entangling gates used is found to be the least important on all except for one dataset. In addition to identifying the relevant hyperparameters, for each of them, we also learned data-driven priors based on values that perform well on previously seen datasets, which can then be used to steer hyperparameter optimization processes. We utilize these priors in the hyperparameter optimization method hyperband and show that these improve performance against uniform sampling across all datasets by, on average, $$0.53 \%$$ 0.53 % , up to $$6.11 \%$$ 6.11 % , in cross-validation accuracy. We also demonstrate that such improvements hold on average regardless of the configuration hyperband is run with. Our work introduces new methodologies for studying quantum machine learning models toward quantum model selection in practice. All research code is made publicly available.

show abstract

BEINIT: Avoiding Barren Plateaus in Variational Quantum Algorithms

Cited by 9 publications

References 13 publications

Avoiding barren plateaus in the variational determination of geometric entanglement

Avoiding barren plateaus in the variational determination of geometric entanglement

Characterization of variational quantum algorithms using free fermions

Hyperparameter importance and optimization of quantum neural networks across small datasets

Contact Info

Product

Resources

About