Related papers: Beating full state tomography for unentangled spec…
Quantum state learning is a fundamental problem in physics and computer science. As near-term quantum devices are error-prone, it is important to design error-resistant algorithms. Apart from device errors, other unexpected factors could…
Learning physical properties of high-dimensional states is crucial for developing quantum technologies but usually consumes an exceedingly large number of samples which are difficult to afford in practice. In this Letter, we use the…
Spectral clustering has shown a superior performance in analyzing the cluster structure. However, its computational complexity limits its application in analyzing large-scale data. To address this problem, many low-rank matrix approximating…
Graph spectral techniques for measuring graph similarity, or for learning the cluster number, require kernel smoothing. The choice of kernel function and bandwidth are typically chosen in an ad-hoc manner and heavily affect the resulting…
The ability of quantum computers to directly manipulate and analyze quantum states stored in quantum memory allows them to learn about aspects of our physical world that would otherwise be invisible given a modest number of measurements.…
Many experiments in quantum information aim at creating multi-partite entangled states. Quantifying the amount of entanglement that was actually generated can, in principle, be accomplished using full-state tomography. This method requires…
In the last years several estimation strategies have been formulated to determine the value of an unknown parameter in the most precise way, taking into account the presence of noise. These strategies typically rely on the use of quantum…
Problems on repeated geometric patterns in finite point sets in Euclidean space are extensively studied in the literature of combinatorial and computational geometry. Such problems trace their inspiration to Erd\H{o}s' original work on that…
We study the computational phase transition in a multi-frequency group synchronization problem, where pairwise relative measurements of group elements are observed across multiple frequency channels and corrupted by Gaussian noise. Using…
Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by…
We study quantum state testing where the goal is to test whether $\rho=\rho_0\in\mathbb{C}^{d\times d}$ or $\|\rho-\rho_0\|_1>\varepsilon$, given $n$ copies of $\rho$ and a known state description $\rho_0$. In practice, not all measurements…
We propose a learning method for estimating unknown pure quantum states. The basic idea of our method is to learn a unitary operation $\hat{U}$ that transforms a given unknown state $|\psi_\tau\rangle$ to a known fiducial state $|f\rangle$.…
We study the problem of learning an unknown graph provided via an oracle using a quantum algorithm. We consider three query models. In the first model ("OR queries"), the oracle returns whether a given subset of the vertices contains any…
For the precise estimation of the unknown quantum state, the independent samples should be prepared. Can we reduce the error of the estimation by the measurement using the quantum correlation between every sample? In this paper, this…
A quantum state's entanglement across a bipartite cut can be quantified with entanglement entropy or, more generally, Schmidt norms. Using only Schmidt decompositions, we present a simple iterative algorithm to maximize Schmidt norms.…
State estimation is key to both analyzing physical mechanisms and enabling real-time control of fluid flows. A common estimation approach is to relate sensor measurements to a reduced state governed by a reduced-order model (ROM). (When…
Drawing the quantum phase diagram of a many-body system in the parameter space of its Hamiltonian can be seen as a learning problem, which implies labelling the corresponding ground states according to some classification criterium that…
We present a quantum algorithm for sampling random spanning trees from a weighted graph in $\widetilde{O}(\sqrt{mn})$ time, where $n$ and $m$ denote the number of vertices and edges, respectively. Our algorithm has sublinear runtime for…
Quantum tomography requires repeated measurements of many copies of the physical system, all prepared by a source in the unknown state. In the limit of very many copies measured, the often-used maximum-likelihood (ML) method for converting…
We present a detailed account of quantum state estimation by joint maximization of the likelihood and the entropy. After establishing the algorithms for both perfect and imperfect measurements, we apply the procedure to data from simulated…