Related papers: On Testing and Learning Quantum Junta Channels
In unitary property testing a quantum algorithm, also known as a tester, is given query access to a black-box unitary and has to decide whether it satisfies some property. We propose a new technique for proving lower bounds on the quantum…
The goal of quantum channel discrimination and estimation is to determine the identity of an unknown channel from a discrete or continuous set, respectively. The query complexity of these tasks is equal to the minimum number of times one…
We propose several algorithms for learning unitary operators from quantum statistical queries with respect to their Choi-Jamiolkowski state. Quantum statistical queries capture the capabilities of a learner with limited quantum resources,…
Dynamics of many-qubit systems, that may correspond to computational processing with quantum systems, can be efficiently and generally approximated by a sequence of two- and single-qubit gates. In practical applications, however, a quantum…
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…
What is the ultimate performance for discriminating two arbitrary quantum channels acting on a finite-dimensional Hilbert space? Here we address this basic question by deriving a general and fundamental lower bound. More precisely, we…
We show that entangled measurements provide an exponential advantage in sample complexity for Pauli channel estimation, which is both a fundamental problem and a practically important subroutine for benchmarking near-term quantum devices.…
Given a black-box representing an unknown Boolean function $f$ of $n$ variables, in this paper we propose a fast quantum algorithm to test whether or not a certain variable in the function $f$ is a junta variable. The proposed algorithm…
With increasing commercial availability of quantum information processing devices the need for testing them efficiently for their specified functionality will arise. Complete quantum channel characterization is out of the question for…
Understanding the noise affecting a quantum device is of fundamental importance for scaling quantum technologies. A particularly important class of noise models is that of Pauli channels, as randomized compiling techniques can effectively…
We analyze the energy and training data requirements for supervised learning of an $M$-mode linear optical circuit by minimizing an empirical risk defined solely from the action of the circuit on coherent states. When the linear optical…
We study the task of learning mixed unitary channels using Fisher information, under different quantum resource assumptions including ancilla and concatenation. Our result shows that the asymptotic sample complexity scales as…
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…
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…
We are presented with a graph, $G$, on $n$ vertices with $m$ edges whose edge set is unknown. Our goal is to learn the edges of $G$ with as few queries to an oracle as possible. When we submit a set $S$ of vertices to the oracle, it tells…
The computational problem of distinguishing two quantum channels is central to quantum computing. It is a generalization of the well-known satisfiability problem from classical to quantum computation. This problem is shown to be…
Quantum k-SAT is the problem of deciding whether there is a n-qubit state which is perpendicular to a set of vectors, each of which lies in the Hilbert space of k qubits. Equivalently, the problem is to decide whether a particular type of…
Quantum process tomography, the task of estimating an unknown quantum channel, is a central problem in quantum information theory. A long-standing open question is to determine the optimal number of uses of an unknown channel required to…
Random (mixed) unitary channels describe an important subset of quantum channels, which are commonly used in quantum information, noise modeling, and quantum error mitigation. Despite their usefulness, there is substantial complexity in…
Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer…