Related papers: Statistical inference for quantum singular models
The basic idea of quantum computing is surprisingly similar to that of kernel methods in machine learning, namely to efficiently perform computations in an intractably large Hilbert space. In this paper we explore some theoretical…
The ability to use quantum technology to achieve useful tasks, be they scientific or industry related, boils down to precise quantum control. In general it is difficult to assess a proposed solution due to the difficulties in characterising…
Within the framework of statistical learning theory it is possible to bound the minimum number of samples required by a learner to reach a target accuracy. We show that if the bound on the accuracy is taken into account, quantum machine…
In this article we derive a useful expectation identity using the language of quantum statistical mechanics, where density matrices represent the state of knowledge about the system. This identity allows to establish relations between…
Quantum Computing and especially Quantum Machine Learning, in a short period of time, has gained a lot of interest through research groups around the world. This can be seen in the increasing number of proposed models for pattern…
As quantum machine-learning architectures mature, a central challenge is no longer their construction, but identifying the regimes in which they offer practical advantages over classical approaches. In this work, we introduce a framework…
The most general examples of quantum learning advantages involve data labeled by cryptographic or intrinsically quantum functions, where classical learners are limited by the infeasibility of evaluating the labeling functions using…
Tackling output sampling noise due to finite shots of quantum measurement is an unavoidable challenge when extracting information in machine learning with physical systems. A technique called Eigentask Learning was developed recently as a…
Stochastic models for quantum state reduction give rise to statistical laws that are in many respects in agreement with those of standard quantum measurement theory. Here we construct a counterexample involving a Hamiltonian with degenerate…
The method of classical shadows heralds unprecedented opportunities for quantum estimation with limited measurements [H.-Y. Huang, R. Kueng, and J. Preskill, Nat. Phys. 16, 1050 (2020)]. Yet its relationship to established quantum…
In quantum information processing quantum operations are often processed alongside measurements which result in classical data. Due to the information gain of classical measurement outputs non-unitary dynamical processes can take place on…
While quantum architectures are still under development, when available, they will only be able to process quantum data when machine learning algorithms can only process numerical data. Therefore, in the issues of classification or…
It has been hypothesized that quantum computers may lend themselves well to applications in machine learning. In the present work, we analyze function classes defined via quantum kernels. Quantum computers offer the possibility to…
Density estimation is a central task in statistics and machine learning. This problem aims to determine the underlying probability density function that best aligns with an observed data set. Some of its applications include statistical…
Deep learning has enjoyed tremendous success in a variety of applications but its application to quantile regressions remains scarce. A major advantage of the deep learning approach is its flexibility to model complex data in a more…
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…
A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where…
Operating quantum sensors and quantum computers would make data in the form of quantum states available for purely quantum processing, opening new avenues for studying physical processes and certifying quantum technologies. In this…
Unsupervised machine learning models build an internal representation of their training data without the need for explicit human guidance or feature engineering. This learned representation provides insights into which features of the data…
There are two major approaches to building good machine learning algorithms: feeding lots of data into large models, or picking a model class with an ''inductive bias'' that suits the structure of the data. When taking the second approach…