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One of the central problems for near-term quantum devices is to understand their ultimate potential and limitations. We address this problem in terms of quantum error mitigation by introducing a framework taking into account the full…
This paper introduces the Quantum Covariance Embedding, which embeds Positive Operator-Valued Measures into a tensor product of a Reproducing Kernel Hilbert Space and the quantum state space via a tensorized Bochner integral. This…
Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial…
Quantum-enhanced measurements exploit quantum mechanical effects to provide ultra-precise estimates of physical variables for use in advanced technologies, such as frequency calibration of atomic clocks, gravitational waves detection, and…
QBism regards quantum mechanics as an addition to probability theory. The addition provides an extra normative rule for decision-making agents concerned with gambling across experimental contexts, somewhat in analogy to the double-slit…
We introduce a new framework for quantifying the complexity of quantum channels, grounded in a suitably chosen resource set. This class of convex functions is designed to analyze the complexity of both open and closed quantum systems. By…
We consider the problem of recovering low-rank matrices from random rank-one measurements, which spans numerous applications including covariance sketching, phase retrieval, quantum state tomography, and learning shallow polynomial neural…
We present and analyze a quantum algorithm to estimate credit risk more efficiently than Monte Carlo simulations can do on classical computers. More precisely, we estimate the economic capital requirement, i.e. the difference between the…
Measurement incompatibility is a cornerstone of quantum mechanics. In the context of estimating multiple parameters of a quantum system, this manifests as a fundamental trade-off between the precisions with which different parameters can be…
The EM algorithm is a novel numerical method to obtain maximum likelihood estimates and is often used for practical calculations. However, many of maximum likelihood estimation problems are nonconvex, and it is known that the EM algorithm…
Uncertainty representation and quantification are paramount in machine learning and constitute an important prerequisite for safety-critical applications. In this paper, we propose novel measures for the quantification of aleatoric and…
A multivariate quantile regression model with a factor structure is proposed to study data with many responses of interest. The factor structure is allowed to vary with the quantile levels, which makes our framework more flexible than the…
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…
Quantum process tomography is often used to completely characterize an unknown quantum process. However, it may lead to an unphysical process matrix, which will cause the loss of information respect to the tomography result. Convex…
In the task of discriminating between nonorthogonal quantum states from multiple copies, the key parameters are the error probability and the resources (number of copies) used. Previous studies have considered the task of minimizing the…
Quadrature rules estimate the value of an integral when the function is given by a table of values. Every binary string defines a quadrature rule by choosing which endpoint of each interval represents the interval. The standard rules, such…
Motivated by recent progress in quantum hardware and algorithms researchers have developed quantum heuristics for optimization problems, aiming for advantages over classical methods. To date, quantum hardware is still error-prone and…
We introduce the concept of boundariness capturing the most efficient way of expressing a given element of a convex set as a probability mixture of its boundary elements. In other words, this number measures (without the need of any…
Reinforcement learning for the optimization of quantum circuits uses an agent whose goal is to maximize the value of a reward function that decides what is correct and what is wrong during the exploration of the search space. It is an open…
Quantum inequalities are bounds on negative time-averages of the energy density of a quantum field. They can be used to rule out exotic spacetimes in general relativity. We study quantum inequalities for a scalar field with a background…