Related papers: Fast Phase Factor Finding for Quantum Signal Proce…
A new, computationally- and statistically-efficient algorithm, the Fast $\chi^2$ algorithm, can find a periodic signal with harmonic content in irregularly-sampled data with non-uniform errors. The algorithm calculates the minimized…
Entanglement plays a crucial role in quantum physics and is the key resource in quantum information processing. However, entanglement detection and quantification are believed to be hard due to the operational impracticality of existing…
In this brief paper, we go through the theoretical steps of the spectral clustering on quantum computers by employing the phase estimation and the amplitude amplification algorithms. We discuss circuit designs for each step and show how to…
Quantum Process Tomography (QPT) is a powerful tool to characterize quantum operations, but it requires considerable resources making it impractical for more than 2-qubit systems. This work proposes an alternative approach that requires…
We develop procedures, based on minimization of the composition $f(x) = h(c(x))$ of a convex function $h$ and smooth function $c$, for solving random collections of quadratic equalities, applying our methodology to phase retrieval problems.…
Quantum linear system algorithms (QLSAs) for gate-based quantum computing can provide exponential speedups for solving linear systems but face challenges when applied to finite element problems due to the growth of the condition number with…
Given a time series vector, how can we efficiently compute a specified part of Fourier coefficients? Fast Fourier transform (FFT) is a widely used algorithm that computes the discrete Fourier transform in many machine learning applications.…
A fundamental step of any quantum algorithm is the preparation of qubit registers in a suitable initial state. Often qubit registers represent a discretization of continuous variables and the initial state is defined by a multivariate…
In this work we investigate a binned version of Quantum Phase Estimation (QPE) set out by [Somma 2019] and known as the Quantum Eigenvalue Estimation Problem (QEEP). Specifically, we determine whether the circuit decomposition techniques we…
Quantum Phase Estimation is a crucial component of several front-running quantum algorithms. Improving the efficiency and accuracy of QPE is currently a very active field of research. In this work, we present a hybrid quantum-classical…
High efficiency postprocessing of continuous-variable quantum key distribution system has a significant impact on the secret key rate and transmission distance of the system. Currently, the postprocessing mainly contains four steps in the…
This paper reported a general noninterferometric high-accuracy quantitative phase imaging (QPI) method for arbitrary complex valued objects. Given by a typical 4f optical configuration as the imaging system, three frames of small-window…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…
The problem of signal recovery from its Fourier transform magnitude is of paramount importance in various fields of engineering and has been around for over 100 years. Due to the absence of phase information, some form of additional…
We propose a new quantum state reconstruction method that combines ideas from compressed sensing, non-convex optimization, and acceleration methods. The algorithm, called Momentum-Inspired Factored Gradient Descent (\texttt{MiFGD}), extends…
Quantum signal processing is a framework for implementing polynomial functions on quantum computers. To implement a given polynomial $P$, one must first construct a corresponding complementary polynomial $Q$. Existing approaches to this…
Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…
In computational molecular science, calculation of electrostatic interactions involving charged atoms - the strongest interactions in condensed phases, is a major bottleneck. We propose a quantum-classical algorithm for fast, yet, accurate…
We propose a phase-difference estimation algorithm based on the tensor-network circuit compression, leveraging time-evolution data to pursue scalability and higher accuracy on a quantum phase estimation (QPE)-type algorithm. Using tensor…
Motivated by the need for accurate frequency information, a novel algorithm for estimating the fundamental frequency and its rate of change in three-phase power systems is developed. This is achieved through two stages of Kalman filtering.…