Related papers: A randomized quantum algorithm for statistical pha…
We propose the first near-optimal quantum algorithm for estimating in Euclidean norm the mean of a vector-valued random variable with finite mean and covariance. Our result aims at extending the theory of multivariate sub-Gaussian…
We propose a quantum algorithm based on ridge regression model, which get the optimal fitting parameters w and a regularization hyperparameter {\alpha} by analysing the training dataset. The algorithm consists of two subalgorithms. One is…
We consider deterministic and {\em randomized} quantum algorithms simulating $e^{-iHt}$ by a product of unitary operators $e^{-iA_jt_j}$, $j=1,...,N$, where $A_j\in\{H_1,...,H_m\}$, $H=\sum_{i=1}^m H_i$ and $t_j > 0$ for every $j$.…
Quantum phase estimation algorithm has been successfully adapted as a sub frame of many other algorithms applied to a wide variety of applications in different fields. However, the requirement of a good approximate eigenvector given as an…
Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine…
An estimation method is presented for polynomial phase signals, i.e., those adopting the form of a complex exponential whose phase is polynomial in its indices. Transcending the scope of existing techniques, the proposed estimator can…
An algorithm based on quantum phase estimation, which discriminates quantum states nondestructively within a set of arbitrary orthogonal states, is described and experimentally verified by a NMR quantum information processor. The procedure…
Estimating the overlap between an approximate wavefunction and a target eigenstate of the system Hamiltonian is essential for the efficiency of quantum phase estimation. In this work, we derive upper and lower bounds on this overlap using…
A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems. For this task, there is a well-studied quantum algorithm that performs quantum phase estimation on an initial trial state that…
Hybrid quantum-classical optimization algorithms represent one of the most promising application for near-term quantum computers. In these algorithms the goal is to optimize an observable quantity with respect to some classical parameters,…
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the dimension of the problem space grows exponentially, finding the eigenvalues of certain…
We describe an algorithm for quantum state tomography that converges in polynomial time to an estimate, together with a rigorous error bound on the fidelity between the estimate and the true state. The result suggests that state tomography…
Amplitude estimation algorithms are based on Grover's algorithm: alternating reflections about the input state and the desired outcome. But what if we are given the ability to perform arbitrary rotations, instead of just reflections? In…
Identifying the Hamiltonian of a quantum system from experimental data is considered. General limits on the identifiability of model parameters with limited experimental resources are investigated, and a specific Bayesian estimation…
One of the most promising applications of quantum computing is simulating quantum many-body systems. However, there is still a need for methods to efficiently investigate these systems in a native way, capturing their full complexity. Here,…
We present a quantum algorithm for efficiently sampling transformed Gaussian random fields on $d$-dimensional domains, based on an enhanced version of the classical moving average method. Pointwise transformations enforcing boundedness are…
Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in…
We propose a general-purpose quantum algorithm for preparing ground states of quantum Hamiltonians from a given trial state. The algorithm is based on techniques recently developed in the context of solving the quantum linear systems…
We consider how to characterize the dynamics of a quantum system from a restricted set of initial states and measurements using Bayesian analysis. Previous work has shown that Hamiltonian systems can be well estimated from analysis of noisy…
The computational cost of quantum algorithms for physics and chemistry is closely linked to the spectrum of the Hamiltonian, a property that manifests in the necessary rescaling of its eigenvalues. The typical approach of using the 1-norm…