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Variational quantum algorithms

Variational quantum algorithms are promising candidates to make use of these devices for achieving a practical quantum advantage over classical computers, and are the leading proposal for achieving quantum advantage using near-term quantum computers.
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Cost function dependent barren plateaus in shallow parametrized quantum circuits

The authors explore the feasibility of training depending on the type of cost functions, showing that local ones are less prone to the barren plateau problem and establish a connection between locality and trainability.
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Cost-Function-Dependent Barren Plateaus in Shallow Quantum Neural Networks

Two results are rigorously proved that establish a connection between locality and trainability in VQAs and illustrate these ideas with large-scale simulations of a particular VQA known as quantum autoencoders.
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Connecting ansatz expressibility to gradient magnitudes and barren plateaus

The resulting bounds indicate that highly expressive ansätze exhibit high cost landscapes and therefore will be harder to train, and the implications for designing strategies to avoid barren plateaus are discussed.
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Diagnosing Barren Plateaus with Tools from Quantum Optimal Control

Variational Quantum Algorithms (VQAs) have received considerable attention due to their potential for achieving near-term quantum advantage. However, more work is needed to understand their…
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Noise resilience of variational quantum compiling

This work finds one often learns the correct gate sequence V despite various sources of incoherent noise acting during the cost-evaluation circuit, and suggests that variational quantum compiling, due to its robustness, could be practically useful for noisy intermediate-scale quantum devices.
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Variational Quantum Linear Solver.

A hybrid quantum-classical algorithm, called Variational Quantum Linear Solver (VQLS), for solving linear systems on near-term quantum computers, and derives an operationally meaningful termination condition that allows one to guarantee that a desired solution precision $\epsilon$ is achieved.

Variational Quantum Linear Solver: A Hybrid Algorithm for Linear Systems

This paper presents a parallel version of the Celada–Seiden cellular automaton that simulates the dynamic response of the immune system tozman, a type of “spatially aggregating” disease.
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Absence of Barren Plateaus in Quantum Convolutional Neural Networks

This work rigorously analyze the gradient scaling for the parameters in the QCNN architecture and finds that the variance of the gradient vanishes no faster than polynomially, implying that QCNNs do not exhibit barren plateaus.
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Theory of overparametrization in quantum neural networks

This paper presents a meta-analyses of the LaSalle–Cerezo–Larocca–Bouchut–Seiden–Stein cellular automaton, a model derived from the model developed by J. J. Giambiagi in 2007, which states that the model derived in this paper can be modified for flows on rugous topographies varying around an inclined plane.
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