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Found 31 papers, 6 papers with code
Does provable absence of barren plateaus imply classical simulability? Or, why we need to rethink variational quantum computing
A large amount of effort has recently been put into understanding the barren plateau phenomenon.
Deep quantum neural networks form Gaussian processes
It is well known that artificial neural networks initialized from independent and identically distributed priors converge to Gaussian processes in the limit of large number of neurons per hidden layer.
Challenges and Opportunities in Quantum Machine Learning
At the intersection of machine learning and quantum computing, Quantum Machine Learning (QML) has the potential of accelerating data analysis, especially for quantum data, with applications for quantum materials, biochemistry, and high-energy physics.
On the universality of $S_n$-equivariant $k$-body gates
Our results show that if the QNN is generated by one- and two-body $S_n$-equivariant gates, the QNN is semi-universal but not universal.
Effects of noise on the overparametrization of quantum neural networks
In particular, it has been proposed that a QNN can be defined as overparametrized if it has enough parameters to explore all available directions in state space.
Resource frugal optimizer for quantum machine learning
In this work, we advocate for simultaneous random sampling over both the dataset as well as the measurement operators that define the loss function.
Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks
Despite the great promise of quantum machine learning models, there are several challenges one must overcome before unlocking their full potential.
Theory for Equivariant Quantum Neural Networks
Most currently used quantum neural network architectures have little-to-no inductive biases, leading to trainability and generalization issues.
Representation Theory for Geometric Quantum Machine Learning
Recent advances in classical machine learning have shown that creating models with inductive biases encoding the symmetries of a problem can greatly improve performance.
Exponential concentration in quantum kernel methods
Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration.
Inference-Based Quantum Sensing
We show that, for a general class of unitary families of encoding, $\mathcal{R}(\theta)$ can be fully characterized by only measuring the system response at $2n+1$ parameters.
Group-Invariant Quantum Machine Learning
We present theoretical results underpinning the design of $\mathfrak{G}$-invariant models, and exemplify their application through several paradigmatic QML classification tasks including cases when $\mathfrak{G}$ is a continuous Lie group and also when it is a discrete symmetry group.
Covariance matrix preparation for quantum principal component analysis
We also argue that PCA on quantum datasets is natural and meaningful, and we numerically implement our method for molecular ground-state datasets.
Generalization in quantum machine learning from few training data
Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i. e., generalizing).
Subtleties in the trainability of quantum machine learning models
In this work we bridge the two frameworks and show that gradient scaling results for VQAs can also be applied to study the gradient scaling of QML models.
Theory of overparametrization in quantum neural networks
The prospect of achieving quantum advantage with Quantum Neural Networks (QNNs) is exciting.
Entangled Datasets for Quantum Machine Learning
For this purpose, we introduce the NTangled dataset composed of quantum states with different amounts and types of multipartite entanglement.
Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?
On the other hand, our positive results for CDR highlight the possibility of engineering error mitigation methods to improve trainability.
Equivalence of quantum barren plateaus to cost concentration and narrow gorges
Optimizing parameterized quantum circuits (PQCs) is the leading approach to make use of near-term quantum computers.
A semi-agnostic ansatz with variable structure for quantum machine learning
Our approach, called VAns (Variable Ansatz), applies a set of rules to both grow and (crucially) remove quantum gates in an informed manner during the optimization.
Connecting ansatz expressibility to gradient magnitudes and barren plateaus
Parameterized quantum circuits serve as ans\"{a}tze for solving variational problems and provide a flexible paradigm for programming near-term quantum computers.
Variational Quantum Algorithms
Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers due to the extremely high computational cost.
Effect of barren plateaus on gradient-free optimization
We numerically confirm this by training in a barren plateau with several gradient-free optimizers (Nelder-Mead, Powell, and COBYLA algorithms), and show that the numbers of shots required in the optimization grows exponentially with the number of qubits.
Non-trivial symmetries in quantum landscapes and their resilience to quantum noise
(2) We study the resilience of the symmetries under noise, and show that while it is conserved under unital noise, non-unital channels can break these symmetries and lift the degeneracy of minima, leading to multiple new local minima.
Absence of Barren Plateaus in Quantum Convolutional Neural Networks
To derive our results we introduce a novel graph-based method to analyze expectation values over Haar-distributed unitaries, which will likely be useful in other contexts.
Generalized Measure of Quantum Fisher Information
In this work, we present a lower bound on the quantum Fisher information (QFI) which is efficiently computable on near-term quantum devices.
Quantum Physics Mathematical Physics Mathematical Physics Data Analysis, Statistics and Probability
Noise-Induced Barren Plateaus in Variational Quantum Algorithms
Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits $n$ if the depth of the ansatz grows linearly with $n$.
Reformulation of the No-Free-Lunch Theorem for Entangled Data Sets
With the recent rise of quantum machine learning, it is natural to ask whether there is a quantum analog of the NFL theorem, which would restrict a quantum computer's ability to learn a unitary process (the quantum analog of a function) with quantum training data.
Trainability of Dissipative Perceptron-Based Quantum Neural Networks
Several architectures have been proposed for quantum neural networks (QNNs), with the goal of efficiently performing machine learning tasks on quantum data.
Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
Variational quantum algorithms (VQAs) optimize the parameters $\vec{\theta}$ of a parametrized quantum circuit $V(\vec{\theta})$ to minimize a cost function $C$.
Variational Quantum Linear Solver
Specifically, we prove that $C \geq \epsilon^2 / \kappa^2$, where $C$ is the VQLS cost function and $\kappa$ is the condition number of $A$.
Quantum Physics
