Related papers: Efficient quantum tomography II
Quantum device characterization via state tomography plays an important role in both validating quantum hardware and processing quantum information, but it needs the exponential number of the measurements. For the systems with XX+YY-type…
Constrained optimization plays a crucial role in the fields of quantum physics and quantum information science and becomes especially challenging for high-dimensional complex structure problems. One specific issue is that of quantum process…
Without large quantum computers to empirically evaluate performance, theoretical frameworks such as the quantum statistical query (QSQ) are a primary tool to study quantum algorithms for learning classical functions and search for quantum…
Let $(X_n)_{n\ge 0}$ be an irreducible, aperiodic, and homogeneous binary Markov chain and let $LI_n$ be the length of the longest (weakly) increasing subsequence of $(X_k)_{1\le k \le n}$. Using combinatorial constructions and weak…
We provide a new quantum algorithm that efficiently determines the quality of a least-squares fit over an exponentially large data set by building upon an algorithm for solving systems of linear equations efficiently (Harrow et al., Phys.…
In the problem of quantum state discrimination, one has to determine by measurements the state of a quantum system, based on the a priori side information that the true state is one of two given and completely known states, rho or sigma. In…
Traditional quantum state tomography requires a number of measurements that grows exponentially with the number of qubits n. But using ideas from computational learning theory, we show that "for most practical purposes" one can learn a…
The ability to efficiently simulate random quantum circuits using a classical computer is increasingly important for developing Noisy Intermediate-Scale Quantum devices. Here we present a tensor network states based algorithm specifically…
Decoy-state quantum key distribution (QKD) is undoubtedly the most efficient solution to handle multi-photon signals emitted by laser sources, and provides the same secret key rate scaling as ideal single-photon sources. It requires,…
In this paper we provide new quantum algorithms with polynomial speed-up for a range of problems for which no such results were known, or we improve previous algorithms. First, we consider the approximation of the frequency moments $F_k$ of…
The experimental realization of increasingly complex quantum states underscores the pressing need for new methods of state learning and verification. In one such framework, quantum state tomography, the aim is to learn the full quantum…
Let $(X_n)_{n \ge 0}$ be an irreducible, aperiodic, homogeneous Markov chain, with state space a totally ordered finite alphabet of size $m$. Using combinatorial constructions and weak invariance principles, we obtain the limiting shape of…
Topological Data Analysis methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially…
Pattern recognition is a central topic in Learning Theory with numerous applications such as voice and text recognition, image analysis, computer diagnosis. The statistical set-up in classification is the following: we are given an i.i.d.…
This PhD thesis combines two of the most exciting research areas of the last decades: quantum computing and machine learning. We introduce dissipative quantum neural networks (DQNNs), which are designed for fully quantum learning tasks, are…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
Quantum state tomography is a technique in quantum information science used to reconstruct the density matrix of an unknown quantum state, providing complete information about the quantum state. It is of significant importance in fields…
Distributed quantum computing offers a promising approach to scaling quantum devices by networking multiple quantum processors. We present a quantum state tomography protocol tailored for distributed quantum computers that avoids assuming…
In maximum-likelihood quantum state tomography, both the sample size and dimension grow exponentially with the number of qubits. It is therefore desirable to develop a stochastic first-order method, just like stochastic gradient descent for…
Quantum data loading plays a central role in quantum algorithms and quantum information processing. Many quantum algorithms hinge on the ability to prepare arbitrary superposition states as a subroutine, with claims of exponential speedups…