Related papers: Low-depth amplitude estimation via statistical eig…
Parameter estimation on gravitational wave signals from compact binary coalescence (CBC) requires the evaluation of computationally intensive waveform models, typically the bottleneck in the analysis. This cost will increase further as low…
In recent years there has been substantial development in algorithms for quantum phase estimation. In this work we provide a new approach to online Bayesian phase estimation that achieves Heisenberg limited scaling that requires…
Sinusoidal parameter estimation is a fundamental task in applications from spectral analysis to time-series forecasting. Estimating the sinusoidal frequency parameter by gradient descent is, however, often impossible as the error function…
The hope of the quantum computing field is that quantum architectures are able to scale up and realize fault-tolerant quantum computing. Due to engineering challenges, such ''cheap'' error correction may be decades away. In the meantime, we…
A central question in high-dimensional statistics is to understand statistical--computational gaps: regimes in which recovering a hidden signal is information-theoretically possible but conjectured to be computationally intractable. The…
We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer. The functional form of these response functions can be mapped to a corresponding eigenproblem of…
There are quantum procedures that encode the solutions to a problem in the phases of quantum amplitudes. This happens in some quantum optimization algorithms in which the value of a function to be maximized or minimized is represented by a…
We propose a quantum lidar protocol to jointly estimate the range and velocity of a target by illuminating it with a single beam of pulsed displaced squeezed light. In the lossless scenario, we show that the mean-squared errors of both…
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…
We develop an energy calculation algorithm leveraging quantum phase difference estimation (QPDE) scheme and a tensor-network-based unitary compression method in the preparation of superposition states and time-evolution gates. Alongside its…
For compact self-adjoint operators in Hilbert spaces, two algorithms are proposed to provide fully computable a posteriori error estimate for eigenfunction approximation. Both algorithms apply well to the case of tight clusters and multiple…
Recently, it has been demonstrated experimentally that adaptive estimation of a continuously varying optical phase provides superior accuracy in the phase estimate compared to static estimation. Here, we show that the mean-square error in…
The superimposed pilot transmission scheme offers substantial potential for improving spectral efficiency in MIMO-OFDM systems, but it presents significant challenges for receiver design due to pilot contamination and data interference. To…
The ultimate bound to the accuracy of phase estimates is often assumed to be given by the Heisenberg limit. Recent work seemed to indicate that this bound can be violated, yielding measurements with much higher accuracy than was previously…
There is widespread interest in calculating the energy spectrum of a Hamiltonian, for example to analyze optical spectra and energy deposition by ions in materials. In this study, we propose a quantum algorithm that samples the set of…
Many quantum algorithms contain an important subroutine, the quantum amplitude estimation. As the name implies, this is essentially the parameter estimation problem and thus can be handled via the established statistical estimation theory.…
In the circuit model of quantum computing, amplitude amplification techniques can be used to find solutions to NP-hard problems defined on $n$-bits in time $\text{poly}(n) 2^{n/2}$. In this work, we investigate whether such general…
This paper establishes a nearly optimal algorithm for estimating the frequencies and amplitudes of a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery…
In this paper, we construct a parameter estimation framework for robust low-rank tensor regression based on a truncation method and Huber loss, specifically focusing on models with random noise having only finite second-order moments.…
In a Hilbert setting, for convex differentiable optimization, we develop a general framework for adaptive accelerated gradient methods. They are based on damped inertial dynamics where the coefficients are designed in a closed-loop way.…