Related papers: Quantum Phase Estimation by Compressed Sensing
In phase retrieval, the goal is to recover a signal $\mathbf{x}\in\mathbb{C}^N$ from the magnitudes of linear measurements $\mathbf{Ax}\in\mathbb{C}^M$. While recent theory has established that $M\approx 4N$ intensity measurements are…
The resources required to characterise the dynamics of engineered quantum systems-such as quantum computers and quantum sensors-grow exponentially with system size. Here we adapt techniques from compressive sensing to exponentially reduce…
Compressed sensing (CS) is on recovery of high dimensional signals from their low dimensional linear measurements under a sparsity prior and digital quantization of the measurement data is inevitable in practical implementation of CS…
We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on…
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…
Quantum phase estimation (QPE) is a promising quantum algorithm for obtaining molecular ground-state energies with chemical accuracy. However, its computational cost, dominated by the Hamiltonian 1-norm $\lambda$ and the cost of the block…
Quantum Phase Estimation (QPE) is a cornerstone algorithm for fault-tolerant quantum computation, especially for electronic structure calculations of chemical systems. To accommodate the diverse characteristics of quantum chemical systems,…
Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…
Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the…
In this paper, we explore the possibilities and limitations of recovering sparse signals in an online fashion. Employing a mean field approximation to the Bayes recursion formula yields an online signal recovery algorithm that can be…
In the problem of matrix compressed sensing we aim to recover a low-rank matrix from few of its element-wise linear projections. In this contribution we analyze the asymptotic performance of a Bayes-optimal inference procedure for a model…
Can compression algorithms be employed for recovering signals from their underdetermined set of linear measurements? Addressing this question is the first step towards applying compression algorithms for compressed sensing (CS). In this…
This paper presents two efficient and stable algorithms for recovering phase factors in quantum signal processing (QSP), a crucial component of many quantum algorithms. The first algorithm, the ``Half Cholesky" method, which is based on…
The problem of finding the ground state energy of a Hamiltonian using a quantum computer is currently solved using either the quantum phase estimation (QPE) or variational quantum eigensolver (VQE) algorithms. For precision $\epsilon$, QPE…
Quantum Phase Estimation (QPE), the quantum algorithm for estimating eigenvalues of a given Hermitian matrix and preparing its eigenvectors, is considered the most promising approach to finding the ground states and their energies of…
Quantum Phase Estimation (QPE) stands as a pivotal quantum computing subroutine that necessitates an inverse Quantum Fourier Transform (QFT). However, it is imperative to recognize that enhancing the precision of the estimation inevitably…
The phase estimation algorithm is a powerful quantum algorithm with applications in cryptography, number theory, and simulation of quantum systems. We use this algorithm to simulate the time evolution of a system of two spin-1/2 particles…
1-bit compressive sensing aims to recover sparse signals from quantized 1-bit measurements. Designing efficient approaches that could handle noisy 1-bit measurements is important in a variety of applications. In this paper we use the…
Here we revisit the quantum phase estimation (QPE) algorithm, and devise an iterative method to improve the precision of QPE with propagators over a variety of time spans. For a given propagator and a certain eigenstate as input, QPE with…
We consider the problem of compressed sensing and of (real-valued) phase retrieval with random measurement matrix. We derive sharp asymptotics for the information-theoretically optimal performance and for the best known polynomial algorithm…