Related papers: Optimal lower bounds for Quantum Learning via Info…
We consider the problem of testing and learning from data in the presence of resource constraints, such as limited memory or weak data access, which place limitations on the efficiency and feasibility of testing or learning. In particular,…
Reinforcement learning studies how an agent should interact with an environment to maximize its cumulative reward. A standard way to study this question abstractly is to ask how many samples an agent needs from the environment to learn an…
We develop a quantum learning scheme for binary discrimination of coherent states of light. This is a problem of technological relevance for the reading of information stored in a digital memory. In our setting, a coherent light source is…
Information theory provides tools to predict the performance of a learning algorithm on a given dataset. For instance, the accuracy of learning an unknown parameter can be upper bounded by reducing the learning task to hypothesis testing…
Quantum Neural Networks (QNNs) are a promising variational learning paradigm with applications to near-term quantum processors, however they still face some significant challenges. One such challenge is finding good parameter initialization…
The goal of a learning algorithm is to receive a training data set as input and provide a hypothesis that can generalize to all possible data points from a domain set. The hypothesis is chosen from hypothesis classes with potentially…
Classical probabilistic models of (noisy) quantum systems are not only relevant for understanding the non-classical features of quantum mechanics, but they are also useful for determining the possible advantage of using quantum resources…
The coupon collector is a prototypical model for evaluating the number of samples for identifying a set. By superposing all elements in the set as a pure quantum state, a quantum version of the coupon collector aims to learn the state,…
Learning an unknown $n$-qubit quantum state $\rho$ is a fundamental challenge in quantum computing. Information-theoretically, it is known that tomography requires exponential in $n$ many copies of $\rho$ to estimate it up to trace…
In this paper, we address the problem how to represent a classical data distribution in a quantum system. The proposed method is to learn quantum Hamiltonian that is such that its ground state approximates the given classical distribution.…
For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…
We study sequential decision-making with known rewards and unknown constraints, motivated by situations where the constraints represent expensive-to-evaluate human preferences, such as safe and comfortable driving behavior. We formalize the…
In unitary property testing a quantum algorithm, also known as a tester, is given query access to a black-box unitary and has to decide whether it satisfies some property. We propose a new technique for proving lower bounds on the quantum…
Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accessed. This paper shows in three settings that quantum messages have only…
Rejection sampling is a well-known method to sample from a target distribution, given the ability to sample from a given distribution. The method has been first formalized by von Neumann (1951) and has many applications in classical…
The classical PAC sample complexity bounds are stated for any Empirical Risk Minimizer (ERM) and contain an extra logarithmic factor $\log(1/{\epsilon})$ which is known to be necessary for ERM in general. It has been recently shown by…
Learning about physical systems from quantum-enhanced experiments, relying on a quantum memory and quantum processing, can outperform learning from experiments in which only classical memory and processing are available. Whereas quantum…
After carrying out a protocol for quantum key agreement over a noisy quantum channel, the parties Alice and Bob must process the raw key in order to end up with identical keys about which the adversary has virtually no information. In…
Quantum information theory studies the fundamental limits that physical laws impose on information processing tasks such as data compression and data transmission on noisy channels. This thesis presents general techniques that allow one to…
As learning solutions reach critical applications in social, industrial, and medical domains, the need to curtail their behavior has become paramount. There is now ample evidence that without explicit tailoring, learning can lead to biased,…