Related papers: A simpler algorithm to mark the unknown eigenstate…
We consider the problem of quantum multi-parameter estimation with experimental constraints and formulate the solution in terms of a convex optimization. Specifically, we outline an efficient method to identify the optimal strategy for…
The Expectation Maximization (EM) algorithm is widely used as an iterative modification to maximum likelihood estimation when the data is incomplete. We focus on a semi-supervised case to learn the model from labeled and unlabeled samples.…
Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. We prove two complementary results that confirm this intuition.…
Reflections are omnipresent tools in quantum algorithms. We consider the task of reflecting through the eigenspace of an implementable unitary. Such reflections are generally designed using phase estimation or linear combination of…
Quantum entanglement lies at the heart in quantum information processing tasks. Although many criteria have been proposed, efficient and scalable methods to detect the entanglement of generally given quantum states are still not available…
We present a quantum eigenstate filtering algorithm based on quantum signal processing (QSP) and minimax polynomials. The algorithm allows us to efficiently prepare a target eigenstate of a given Hamiltonian, if we have access to an initial…
Non-Hermitian generalized eigenvalue problems (GEPs) play a significant role in many practical applications, such as mechanical engineering. Based on the generalized Schur decomposition, we propose a variational quantum algorithm for…
Algorithms based on non-unitary evolution have attracted much interest for ground state preparation on quantum computers. One recently proposed method makes use of ancilla qubits and controlled unitary operators to implement weak…
We establish a sharp quantum advantage in determining the parity (even/odd) of an unknown permutation applied to any number $n \ge 3$ of particles. Classically, this is impossible with fewer than $n$ labels, being that the success is…
The variational quantum eigensolver is one of the most promising algorithms for near-term quantum computers. It has the potential to solve quantum chemistry problems involving strongly correlated electrons, which are otherwise difficult to…
Estimating the eigenvalues of non-normal matrices is a foundational problem with far-reaching implications, from modeling non-Hermitian quantum systems to analyzing complex fluid dynamics. Yet, this task remains beyond the reach of standard…
Quantum tomography is a process of quantum state reconstruction using data from multiple measurements. An essential goal for a quantum tomography algorithm is to find measurements that will maximize the useful information about an unknown…
The eigenstate thermalization hypothesis (ETH) attempts to bridge the gap between quantum mechanical and statistical mechanical descriptions of isolated quantum systems. Here, we define unbiased measures for how well the ETH works in…
Unlabeled shape analysis is a rapidly emerging and challenging area of statistics. This has been driven by various novel applications in bioinformatics. We consider here the situation where two configurations are matched under various…
This article reveals the future prospects of quantum algorithms in high energy physics (HEP). Particle identification, knowing their properties and characteristics is a challenging problem in experimental HEP. The key technique to solve…
Quantum state tomography is the experimental procedure of determining an unknown state. It is not only essential for the verification of resources and processors of quantum information but is also important in its own right with regard to…
Quantum steering inequalities allow to demonstrate the presence of entanglement between two parties when one of the two measurement device is not trusted. In this paper we show that quantum steering can be demonstrated for arbitrary low…
Construction of a fault-tolerant quantum computer remains a challenging problem due to unavoidable noise in quantum states and the fragility of quantum entanglement. However, most of the error-correcting codes increases the complexity of…
This paper proposes a new estimation algorithm for the parameters of an HMM as to best account for the observed data. In this model, in addition to the observation sequence, we have \emph{partial} and \emph{noisy} access to the hidden state…
In quantum information theory, the reliable and effective detection of entanglement is of paramount importance. However, given an unknown state, assessing its entanglement is a challenging task. To attack this problem, we investigate the…