Related papers: Random-depth Quantum Amplitude Estimation
Nonparametric empirical Bayes methods provide a flexible and attractive approach to high-dimensional data analysis. One particularly elegant empirical Bayes methodology, involving the Kiefer-Wolfowitz nonparametric maximum likelihood…
Quantum error mitigation is an important technique to reduce the impact of noise in quantum computers. With more and more qubits being supported on quantum computers, there are two emerging fundamental challenges. First, the number of shots…
Accurately inferring the state of a quantum device from the results of measurements is a crucial task in building quantum information processing hardware. The predominant state estimation procedure, maximum likelihood estimation (MLE),…
Local Hamiltonian Problems (LHPs) are important problems that are computationally QMA-complete and physically relevant for many-body quantum systems. Quantum MaxCut (QMC), which equates to finding ground states of the quantum Heisenberg…
Quantum algorithm involves the manipulation of amplitudes and computational basis, of which manipulating basis is largely a quantum analogue of classical computing that is always a major contributor to the complexity. In order to make full…
Over the last decades, the family of $\alpha$-stale distributions has proven to be useful for modelling in telecommunication systems. Particularly, in the case of radar applications, finding a fast and accurate estimation for the amplitude…
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.…
Amplitude estimation, in its original form, is formulated as phase estimation upon the Grover iterate. Subsequent improvements to the algorithm have eliminated the need for phase estimation and introduced low-depth variants that trade…
This paper introduces quantum computing methods for Monte Carlo simulations in power systems which are expected to be exponentially faster than their classical computing counterparts. Monte Carlo simulations is a fundamental method, widely…
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…
Training the parameters of statistical models to describe a given data set is a central task in the field of data mining and machine learning. A very popular and powerful way of parameter estimation is the method of maximum likelihood…
Maximum likelihood estimation (MLE) is one of the most important methods in machine learning, and the expectation-maximization (EM) algorithm is often used to obtain maximum likelihood estimates. However, EM heavily depends on initial…
Noise is the greatest obstacle in quantum metrology that limits it achievable precision and sensitivity. There are many techniques to mitigate the effect of noise, but this can never be done completely. One commonly proposed technique is to…
Maximum likelihood estimation is one of the most used methods in quantum state tomography, where the aim is to reconstruct the density matrix of a physical system from measurement results. One strategy to deal with positivity and unit trace…
Conventional methods for computing maximum-likelihood estimators (MLE) often converge slowly in practical situations, leading to a search for simplifying methods that rely on additional assumptions for their validity. In this work, we…
Accurate noise estimation is essential for fault-tolerant quantum computing, as decoding performance depends critically on the fidelity of the circuit-level noise parameters. In this work, we introduce a differentiable Maximum Likelihood…
Quantum metrology is a general term for methods to precisely estimate the value of an unknown parameter by actively using quantum resources. In particular, some classes of entangled states can be used to significantly suppress the…
We address several estimation problems in quantum optics by means of the maximum-likelihood principle. We consider Gaussian state estimation and the determination of the coupling parameters of quadratic Hamiltonians. Moreover, we analyze…
A new likelihood based AR approximation is given for ARMA models. The usual algorithms for the computation of the likelihood of an ARMA model require $O(n)$ flops per function evaluation. Using our new approximation, an algorithm is…
Accelerated algorithms for maximum likelihood image reconstruction are essential for emerging applications such as 3D tomography, dynamic tomographic imaging, and other high dimensional inverse problems. In this paper, we introduce and…