Related papers: Learning unitaries with quantum statistical querie…
Junta testing for Boolean functions has sparked a long line of work over recent decades in theoretical computer science, and recently has also been studied for unitary operators in quantum computing. Tolerant junta testing is more general…
As experiments continue to push the quantum-classical boundary using increasingly complex dynamical systems, the interpretation of experimental data becomes more and more challenging: when the observations are noisy, indirect, and limited,…
Quantum computations promise the ability to solve problems intractable in the classical setting. Restricting the types of computations considered often allows to establish a provable theoretical advantage by quantum computations, and later…
Statistical functions such as the moment-generating function, characteristic function, cumulant-generating function, and second characteristic function are cornerstone tools in classical statistics and probability theory. They provide a…
We propose a variational approach for preparing entangled quantum states on quantum computers. The methodology involves training a unitary operation to match with a target unitary using the Fubini-Study distance as a cost function. We…
To overcome the limitations of classical partially connected Boltzmann machines and mainstream quantum Boltzmann machines (QBMs), this work extends the conventional circuit of the quantum approximate optimization algorithm (QAOA) to a…
The problem of an optimal mapping between Hilbert spaces $IN$ and $OUT$, based on a series of density matrix mapping measurements $\rho^{(l)} \to \varrho^{(l)}$, $l=1\dots M$, is formulated as an optimization problem maximizing the total…
In this note we study the number of quantum queries required to identify an unknown multilinear polynomial of degree d in n variables over a finite field F_q. Any bounded-error classical algorithm for this task requires Omega(n^d) queries…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
We describe a method to upper bound the quantum query complexity of Boolean formula evaluation problems, using fundamental theorems about the general adversary bound. This nonconstructive method can give an upper bound on query complexity…
Qubit-resolved operations and measurements are required for most current quantum information processing schemes. However, these operations can be experimentally costly due to the need for local addressing, demanding significant classical…
We present an iterative method to solve the multipartite quantum state estimation problem. We demonstrate convergence for any informationally complete set of generalized quantum measurements in every finite dimension. Our method exhibits…
We systematically investigate quantum algorithms and lower bounds for mean estimation given query access to non-identically distributed samples. On the one hand, we give quantum mean estimators with quadratic quantum speed-up given samples…
The standard quantum search algorithm lacks a feature, enjoyed by many classical algorithms, of having a fixed-point, i.e. a monotonic convergence towards the solution. Here we present two variations of the quantum search algorithm, which…
Quantum neural networks constitute a key class of near-term quantum learning models, yet their training dynamics remain not fully understood. Here, we present a unified theoretical framework for the frequency principle (F-principle) that…
We prove that any exact quantum algorithm searching an ordered list of N elements requires more than \frac{1}{\pi}(\ln(N)-1) queries to the list. This improves upon the previously best known lower bound of {1/12}\log_2(N) - O(1). Our proof…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
Quantum-phase-estimation algorithms are critical subroutines in many applications for quantum computers and in quantum-metrology protocols. These algorithms estimate the unknown strength of a unitary evolution. By using coherence or…
We propose and analyze a nonunitary variant of the continuous time Grover search algorithm based on frequent Zeno-type measurements. We show that the algorithm scales similarly to the pure quantum version by deriving tight analytical lower…
In this paper, we present an algorithm for preparing quantum states of the form $\sum_{i=0}^{n-1} \alpha_i |i\rangle$, where the coefficients $\alpha_i$ are specified by a quantum oracle. Our method achieves this task twice as fast as the…