Related papers: Quantum Hypothesis Testing with Group Structure
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…
Using the recent ability of quantum computers to initialize quantum states rapidly with high fidelity, we use a function operating on a discrete set to create a simple class of quantum channels. Fixed points and periodic orbits, that are…
Quantum algorithms based on quantum kernel methods have been investigated previously [1]. A quantum advantage is derived from the fact that it is possible to construct a family of datasets for which, only quantum processing can recognise…
Characterization of quantum processes is a preliminary step necessary in the development of quantum technology. The conventional method uses standard quantum process tomography, which requires $d^2$ input states and $d^4$ quantum…
Modern quantum engineering techniques enabled successful foundational tests of quantum mechanics. Yet, the universal validity of quantum postulates is an open question. Here we propose a new theoretical framework of Q-data tests, which…
This paper presents a systematic study of adversarial hypothesis testing for both quantum-quantum (QQ) and classical-quantum (CQ) channels. Unlike conventional channel discrimination, we consider a framework where the sender, Alice, selects…
Quantum channel discrimination has been studied from an information-theoretic perspective, wherein one is interested in the optimal decay rate of error probabilities as a function of the number of unknown channel accesses. In this paper, we…
Quantum state discrimination is a fundamental concept in quantum information theory, which refers to a class of techniques to identify a specific quantum state through a positive operator-valued measure. In this work, we investigate how…
We present quantum query complexity bounds for testing algebraic properties. For a set S and a binary operation on S, we consider the decision problem whether $S$ is a semigroup or has an identity element. If S is a monoid, we want to…
A fully homomorphic encryption system hides data from unauthorized parties, while still allowing them to perform computations on the encrypted data. Aside from the straightforward benefit of allowing users to delegate computations to a more…
Quantum process tomography, the standard procedure to characterize any quantum channel in nature, is affected by a circular argument: in order to characterize the channel, the tomographic preparation and measurement need in turn to be…
Quantum theory departs from classical probabilistic theories in foundational ways. These departures--termed quantumness here--power quantum information and computation. This thesis charts the role of discrete structures in assessing…
This paper introduces a completely new approach to encryption based on group theoretic quantum framework. Quantum cryptography has essentially focused only on key distribution and proceeded with classical encryption algorithm with the…
Given a unitary representation of a finite group on a finite-dimensional Hilbert space, we show how to find a state whose translates under the group are distinguishable with the highest probability. We apply this to several quantum oracle…
A quantum algorithm for general combinatorial search that uses the underlying structure of the search space to increase the probability of finding a solution is presented. This algorithm shows how coherent quantum systems can be matched to…
I assess the potential of quantum computation. Broad and important applications must be found to justify construction of a quantum computer; I review some of the known quantum algorithms and consider the prospects for finding new ones.…
We introduce a general framework to design and analyze algorithms for the problem of testing homomorphisms between finite groups in the low-soundness regime. In this regime, we give the first constant-query tests for various families of…
In order to perform Quantum Cryptography procedures it is often essencial to ensure that the parties of the communication are authentic. Such task is accomplished by quantum authentication protocols which are distributed algorithms based on…
A fundamental problem in statistics and learning theory is to test properties of distributions. We show that quantum computers can solve such problems with significant speed-ups. In particular, we give fast quantum algorithms for testing…
The temporal evolution of a quantum system can be characterized by quantum process tomography, a complex task that consumes a number of physical resources scaling exponentially with the number of subsystems. An alternative approach to the…