Related papers: Query complexity of unitary operation discriminati…
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
Hamiltonian oracles are the continuum limit of the standard unitary quantum oracles. In this limit, the problem of finding the optimal query algorithm can be mapped into the problem of finding shortest paths on a manifold. The study of…
Checking whether two quantum circuits are approximately equivalent is a common task in quantum computing. We consider a closely related identity check problem: given a quantum circuit $U$, one has to estimate the diamond-norm distance…
We consider the problem of quantum channel certification to unitary, where one is given access to an unknown $d$-dimensional channel $\mathcal{E}$, and wants to test whether $\mathcal{E}$ is equal to a target unitary channel or is…
Our problem is to evaluate a multi-valued Boolean function $F$ through oracle calls. If $F$ is one-to-one and the size of its domain and range is the same, then our problem can be formulated as follows: Given an oracle $f(a,x):…
In the exact quantum query model a successful algorithm must always output the correct function value. We investigate the function that is true if exactly $k$ or $l$ of the $n$ input bits given by an oracle are 1. We find an optimal…
Quantum search is a technique for searching N possibilities in only O(sqrt(N)) steps. It has been applied in the design of quantum algorithms for several structured problems. Many of these algorithms require significant amount of quantum…
We explore potential quantum speedups for the fundamental problem of testing the properties of closeness and $k$-wise uniformity of probability distributions. Closeness testing is the problem of distinguishing whether two $n$-dimensional…
Motivated by limitations on the depth of near-term quantum devices, we study the depth-computation trade-off in the query model, where the depth corresponds to the number of adaptive query rounds and the computation per layer corresponds to…
We investigate how to efficiently compute the difference result of two (or multiple) conjunctive queries, which is the last operator in relational algebra to be unraveled. The standard approach in practical database systems is to…
Consider the following generalization of the classic binary search problem: A searcher is required to find a hidden target vertex $x$ in a graph $G$. To do so, they iteratively perform queries to an oracle, each about a chosen vertex $v$.…
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…
Undoing a unitary operation, $i.e$. reversing its action, is the task of canceling the effects of a unitary evolution on a quantum system, and it may be easily achieved when the unitary is known. Given a unitary operation without any…
People have been studying the following problem: Given a finite set S with a hidden (black box) binary operation * on S which might come from a group law, and suppose you have access to an oracle that you can ask for the operation x*y of…
We present a novel use case for quantum computation: the sensitivity analysis for a risk model used at Deutsche B\"orse Group. Such an analysis is computationally too expensive to perform on classical computers. We show in detail how the…
We address quantum decision theory as a convenient framework to analyze process discrimination and estimation in qubit systems. In particular we discuss the following problems: i) how to discriminate whether or not a given unitary…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points. A choice among these…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
Many convex optimization problems have structured objective function written as a sum of functions with different types of oracles (full gradient, coordinate derivative, stochastic gradient) and different evaluation complexity of these…