Related papers: Rademacher Complexity Bounds for Parameterized Qua…
Quantum machine learning offers a transformative approach to solving complex problems, but the inherent noise hinders its practical implementation in near-term quantum devices. This obstacle makes it difficult to understand the…
Quantum computers hold unprecedented potentials for machine learning applications. Here, we prove that physical quantum circuits are PAC (probably approximately correct) learnable on a quantum computer via empirical risk minimization: to…
This paper provides a general result on controlling local Rademacher complexities, which captures in an elegant form to relate the complexities with constraint on the expected norm to the corresponding ones with constraint on the empirical…
Hybrid quantum-classical systems make it possible to utilize existing quantum computers to their fullest extent. Within this framework, parameterized quantum circuits can be regarded as machine learning models with remarkable expressive…
We show that classical and quantum Kolmogorov complexity of binary strings agree up to an additive constant. Both complexities are defined as the minimal length of any (classical resp. quantum) computer program that outputs the…
In this paper we present the partial wave unitarity bound in the parameter space of dimension-5 and dimension-6 effective operators that arise in a compositeness scenario. These are routinely used in experimental searches at the LHC to…
Understanding and certifying the generalization performance of machine learning algorithms -- i.e. obtaining theoretical estimates of the test error from the training error -- is a central theme of statistical learning theory. Among the…
We study the problem of learning nearly $(s,\epsilon)$-sparse unitaries, meaning that the Pauli spectrum is concentrated on at most $s$ components with at most $\epsilon$ residual mass in Pauli $\ell_1$-norm. This class generalizes…
This paper studies the problem of learning weighted automata from a finite labeled training sample. We consider several general families of weighted automata defined in terms of three different measures: the norm of an automaton's weights,…
We present a lower bound for Pauli Manipulation Detection (PMD) codes, a class of quantum codes that detect every Pauli error with high probability. Our lower bound reveals the first trade-off between the error parameter and the coding…
Parameterized quantum circuits play an essential role in the performance of many variational hybrid quantum-classical (HQC) algorithms. One challenge in implementing such algorithms is to choose an effective circuit that well represents the…
Characterizing the quantum complexity of local random quantum circuits is a very deep problem with implications to the seemingly disparate fields of quantum information theory, quantum many-body physics and high energy physics. While our…
Parameterized quantum circuits have been extensively used as the basis for machine learning models in regression, classification, and generative tasks. For supervised learning, their expressivity has been thoroughly investigated and several…
Understanding the complexity of quantum states and circuits is a central challenge in quantum information science, with broad implications in many-body physics, high-energy physics and quantum learning theory. A common way to model the…
We study the sample complexity of learning neural networks, by providing new bounds on their Rademacher complexity assuming norm constraints on the parameter matrix of each layer. Compared to previous work, these complexity bounds have…
A principal concern in the optimisation of parametrised quantum circuits is the presence of barren plateaus, which present fundamental challenges to the scalability of applications, such as variational algorithms and quantum machine…
We derive an upper bound on the local Rademacher complexity of $\ell_p$-norm multiple kernel learning, which yields a tighter excess risk bound than global approaches. Previous local approaches aimed at analyzed the case $p=1$ only while…
Quantum learning encounters fundamental challenges when estimating non-linear properties, owing to the inherent linearity of quantum mechanics. Although recent advances in single-copy randomized measurement protocols have achieved optimal…
Statistical learning theory provides bounds of the generalization gap, using in particular the Vapnik-Chervonenkis dimension and the Rademacher complexity. An alternative approach, mainly studied in the statistical physics literature, is…
Following the seminal approach by Talagrand, the concept of Rademacher complexity for independent sequences of random variables is extended to Markov chains. The proposed notion of "block Rademacher complexity" (of a class of functions)…