Related papers: Rademacher Complexity Bounds for Parameterized Qua…
To study generator design for parameterized unitaries in quantum machine learning (QML), we propose an observable-guided generator selection algorithm for $ n $-qubit Pauli-string generator pools. The proposed method selects generators…
Learning an appropriate (dis)similarity function from the available data is a central problem in machine learning, since the success of many machine learning algorithms critically depends on the choice of a similarity function to compare…
Quantum magic is a necessary resource for quantum computers to be not efficiently simulable by classical computers. Previous results have linked the amount of quantum magic, characterized by the number of $T$ gates or stabilizer rank, to…
Quantum machine learning has shown promise for high-dimensional data analysis, yet many existing approaches rely on linear unitary operations and shared trainable parameters across outputs. These constraints limit expressivity and…
Quantum machine learning holds the promise of combining the success of classical machine learning methods with the power of quantum computing, however one of the largest obstacles facing the field is the problem of barren plateaus.…
Transductive learning considers situations when a learner observes $m$ labelled training points and $u$ unlabelled test points with the final goal of giving correct answers for the test points. This paper introduces a new complexity measure…
In this work we establish lower bounds on the size of Clifford circuits that measure a family of commuting Pauli operators. Our bounds depend on the interplay between a pair of graphs: the Tanner graph of the set of measured Pauli…
We propose new bounds on the error of learning algorithms in terms of a data-dependent notion of complexity. The estimates we establish give optimal rates and are based on a local and empirical version of Rademacher averages, in the sense…
Measurement-based quantum computing uses measurement patterns on predefined quantum resource states to execute quantum logic. Quantum simulation offers an important use case on near-term devices. However, pattern optimization depends on the…
Large language models (LLMs) have transformed artificial intelligence, yet classical architectures impose a fundamental constraint: every trainable parameter demands classical memory that scales unfavourably with model size. Quantum…
Modern machine learning algorithms, especially deep learning based techniques, typically involve careful hyperparameter tuning to achieve the best performance. Despite the surge of intense interest in practical techniques like Bayesian…
Quantifying quantum states' complexity is a key problem in various subfields of science, from quantum computing to black-hole physics. We prove a prominent conjecture by Brown and Susskind about how random quantum circuits' complexity…
We present a method that outputs a sequence of simple unitary operations to prepare a given quantum state that is a generalized coherent state. Our method takes as inputs the expectation values of some relevant observables on the state to…
Communication over a random-parameter quantum channel when the decoder is required to reconstruct the parameter sequence is considered. We study scenarios that include either strictly-causal, causal, or non-causal channel side information…
We investigate the dividing line between classical and quantum computational power in estimating properties of matrix functions. More precisely, we study the computational complexity of two primitive problems: given a function $f$ and a…
Variational quantum algorithms that are used for quantum machine learning rely on the ability to automatically differentiate parametrized quantum circuits with respect to underlying parameters. Here, we propose the rules for differentiating…
Period finding and phase estimation are fundamental in quantum computing. Prior work has established lower bounds on their success probabilities. Such quantum algorithms measure a state $|\hat\ell\rangle$ in an $n$-qubit computational…
We study the complexity of learning mixtures of separated Gaussians with common unknown bounded covariance matrix. Specifically, we focus on learning Gaussian mixture models (GMMs) on $\mathbb{R}^d$ of the form $P= \sum_{i=1}^k w_i…
Although the performance of hybrid quantum-classical algorithms is highly dependent on the selection of the classical optimizer and the circuit ansatz, a robust and thorough assessment on-hardware of such features has been missing to date.…
Many modern tools in machine learning and signal processing, such as sparse dictionary learning, principal component analysis (PCA), non-negative matrix factorization (NMF), $K$-means clustering, etc., rely on the factorization of a matrix…