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Found 14 papers, 5 papers with code
Potential and limitations of random Fourier features for dequantizing quantum machine learning
We build on these insights to make concrete suggestions for PQC architecture design, and to identify structures which are necessary for a regression problem to admit a potential quantum advantage via PQC based optimization.
Classical Verification of Quantum Learning
Finally, we showcase two general scenarios in learning and verification in which quantum mixture-of-superpositions examples do not lead to sample complexity improvements over classical data.
On the average-case complexity of learning output distributions of quantum circuits
In this work, we show that learning the output distributions of brickwork random quantum circuits is average-case hard in the statistical query model.
A super-polynomial quantum-classical separation for density modelling
Specifically, we (a) provide an overview of the relationships between hardness results in supervised learning and distribution learning, and (b) show that any weak pseudo-random function can be used to construct a classically hard density modelling problem.
Scalably learning quantum many-body Hamiltonians from dynamical data
The physics of a closed quantum mechanical system is governed by its Hamiltonian.
A single $T$-gate makes distribution learning hard
We first show that the generative modelling problem associated with depth $d=n^{\Omega(1)}$ local quantum circuits is hard for any learning algorithm, classical or quantum.
Learnability of the output distributions of local quantum circuits
As many practical generative modelling algorithms use statistical queries -- including those for training quantum circuit Born machines -- our result is broadly applicable and strongly limits the possibility of a meaningful quantum advantage for learning the output distributions of local quantum circuits.
Encoding-dependent generalization bounds for parametrized quantum circuits
However, none of these generalization bounds depend explicitly on how the classical input data is encoded into the PQC.
The effect of data encoding on the expressive power of variational quantum machine learning models
Quantum computers can be used for supervised learning by treating parametrised quantum circuits as models that map data inputs to predictions.
On the Quantum versus Classical Learnability of Discrete Distributions
Here we study the comparative power of classical and quantum learners for generative modelling within the Probably Approximately Correct (PAC) framework.
Expressive power of tensor-network factorizations for probabilistic modeling
Inspired by these developments, and the natural correspondence between tensor networks and probabilistic graphical models, we provide a rigorous analysis of the expressive power of various tensor-network factorizations of discrete multivariate probability distributions.
Stochastic gradient descent for hybrid quantum-classical optimization
We formalize this notion, which allows us to show that in many relevant cases, including VQE, QAOA and certain quantum classifiers, estimating expectation values with $k$ measurement outcomes results in optimization algorithms whose convergence properties can be rigorously well understood, for any value of $k$.
Expressive power of tensor-network factorizations for probabilistic modeling, with applications from hidden Markov models to quantum machine learning
Inspired by these developments, and the natural correspondence between tensor networks and probabilistic graphical models, we provide a rigorous analysis of the expressive power of various tensor-network factorizations of discrete multivariate probability distributions.
Reinforcement Learning Decoders for Fault-Tolerant Quantum Computation
Topological error correcting codes, and particularly the surface code, currently provide the most feasible roadmap towards large-scale fault-tolerant quantum computation.
