Search Results for author:
Found 23 papers, 6 papers with code
On the expressivity of embedding quantum kernels
After proving the universality of embedding quantum kernels for both shift-invariant and composition kernels, we identify the directions towards new, more exotic, and unexplored quantum kernel families, for which it still remains open whether they correspond to efficient embedding quantum kernels.
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.
Understanding quantum machine learning also requires rethinking generalization
In this work, through systematic randomization experiments, we show that traditional approaches to understanding generalization fail to explain the behavior of such quantum models.
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.
Towards provably efficient quantum algorithms for large-scale machine-learning models
Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process.
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.
Stochastic noise can be helpful for variational quantum algorithms
Saddle points constitute a crucial challenge for first-order gradient descent algorithms.
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.
Classical surrogates for quantum learning models
In this work, we introduce the concept of a classical surrogate, a classical model which can be efficiently obtained from a trained quantum learning model and reproduces its input-output relations.
Exploiting symmetry in variational quantum machine learning
The success of variational quantum learning models crucially depends on finding a suitable parametrization of the model that encodes an inductive bias relevant to the learning task.
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.
Single-component gradient rules for variational quantum algorithms
A popular set of optimization methods work on the estimate of the gradient, obtained by means of circuit evaluations.
Quantum Computational Advantage via High-Dimensional Gaussian Boson Sampling
Theoretically, there is a comparative lack of rigorous evidence for the classical hardness of GBS.
Quantum Physics
Holographic tensor network models and quantum error correction: A topical review
Recent progress in studies of holographic dualities, originally motivated by insights from string theory, has led to a confluence with concepts and techniques from quantum information theory.
Tensor Networks
Quantum Physics
Strongly Correlated Electrons
High Energy Physics - Theory
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.
Tensor network models of AdS/qCFT
Based on these symmetries, we introduce the notion of a quasiperiodic conformal field theory (qCFT), a critical theory less restrictive than a full CFT and with characteristic multi-scale quasiperiodicity.
Tensor Networks
Quantum Physics
Strongly Correlated Electrons
High Energy Physics - Theory
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.
Recovering quantum gates from few average gate fidelities
For the important case of characterising multi-qubit unitary gates, we provide a rigorously guaranteed and practical reconstruction method that works with an essentially optimal number of average gate fidelities measured respect to random Clifford unitaries.
Quantum Physics Information Theory Information Theory
