Related papers: Quantum Phase Estimation by Compressed Sensing
Quantum phase estimation is a fundamental subroutine in many quantum algorithms, including Shor's factorization algorithm and quantum simulation. However, so far results have cast doubt on its practicability for near-term, non-fault…
Quantum Phase Estimation (QPE) is a cornerstone algorithm in quantum computing, with applications ranging from integer factorization to quantum chemistry simulations. However, the resource demands of standard QPE, which require a large…
We develop a phase estimation method with a distinct feature: its maximal runtime (which determines the circuit depth) is $\delta/\epsilon$, where $\epsilon$ is the target precision, and the preconstant $\delta$ can be arbitrarily close to…
This paper introduces Witnessed Quantum Time Evolution (WQTE), a novel quantum algorithm for efficiently computing the eigen-energy spectra of arbitrary quantum systems without requiring eigenstate preparation-a key limitation of…
The Quantum Phase Difference Estimation (QPDE) algorithm, as an extension of the Quantum Phase Estimation (QPE), is a quantum algorithm designed to compute the differences of two eigenvalues of a unitary operator by exploiting the quantum…
In the light of the progress in quantum technologies, the task of verifying the correct functioning of processes and obtaining accurate tomographic information about quantum states becomes increasingly important. Compressed sensing, a…
We address the issue of applying quantized compressed sensing (CS) on low-energy telemonitoring. So far, few works studied this problem in applications where signals were only approximately sparse. We propose a two-stage data compressor…
Let $x\in\mathbb{C}^n$ be a spectrally sparse signal consisting of $r$ complex sinusoids with or without damping. We consider the spectral compressed sensing problem, which is about reconstructing $x$ from its partial revealed entries. By…
Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples.…
Quantum phase estimation is one of the critical building blocks of quantum computing. For early fault-tolerant quantum devices, it is desirable for a quantum phase estimation algorithm to (1) use a minimal number of ancilla qubits, (2)…
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…
Compressed sensing is a technique for recovering a high-dimensional signal from lower-dimensional data, whose components represent partial information about the signal, utilizing prior knowledge on the sparsity of the signal. For further…
We develop several algorithms for performing quantum phase estimation based on basic measurements and classical post-processing. We present a pedagogical review of quantum phase estimation and simulate the algorithm to numerically determine…
The number of measurements demanded by hybrid quantum-classical algorithms such as the variational quantum eigensolver (VQE) is prohibitively high for many problems of practical value. For such problems, realizing quantum advantage will…
Compressed sensing is a method that allows a significant reduction in the number of samples required for accurate measurements in many applications in experimental sciences and engineering. In this work, we show that compressed sensing can…
In order to leverage the full power of quantum noise squeezing with unavoidable decoherence, a complete understanding of the degradation in the purity of squeezed light is demanded. By implementing machine learning architecture with a…
The accumulation of noise in quantum computers is the dominant issue stymieing the push of quantum algorithms beyond their classical counterparts. We do not expect to be able to afford the overhead required for quantum error correction in…
Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear…
We consider faithfully combining phase retrieval with classical compressed sensing. Inspired by the recent novel formulation for phase retrieval called PhaseMax, we present and analyze SparsePhaseMax, a linear program for phaseless…
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…