Quantum Multi-Parameter Adaptive Bayesian Estimation and Application to Super-Resolution Imaging

• URL: http://arxiv.org/abs/2202.09980v2
• Date: Thu, 9 Jun 2022 17:58:16 GMT
• Title: Quantum Multi-Parameter Adaptive Bayesian Estimation and Application to Super-Resolution Imaging
• Authors: Kwan Kit Lee, Christos Gagatsos, Saikat Guha, Amit Ashok
• Abstract summary: In quantum sensing tasks, the user gets $rho_theta$, the quantum state that encodes $theta$. Personick found the optimum POVM $Pi_l$ that minimizes the MMSE over all possible measurements. This result from 1971 is less-widely known than the quantum Fisher information (QFI), which lower bounds the variance of an unbiased estimator.
• Score: 1.4222887950206657
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In Bayesian estimation theory, the estimator ${\hat \theta} = E[\theta|l]$ attains the minimum mean squared error (MMSE) for estimating a scalar parameter of interest $\theta$ from the observation of $l$ through a noisy channel $P_{l|\theta}$, given a prior $P_\theta$ on $\theta$. In quantum sensing tasks, the user gets $\rho_\theta$, the quantum state that encodes $\theta$. They choose a measurement, a positive-operator valued measure (POVM) $\Pi_l$, which induces the channel $P_{l|\theta} = {\rm Tr}(\rho_\theta \Pi_l)$ to the measurement outcome $l$, on which the aforesaid classical MMSE estimator is employed. Personick found the optimum POVM $\Pi_l$ that minimizes the MMSE over all possible measurements, and that MMSE. This result from 1971 is less-widely known than the quantum Fisher information (QFI), which lower bounds the variance of an unbiased estimator over all measurements, when $P_\theta$ is unavailable. For multi-parameter estimation, i.e., when $\theta$ is a vector, in Fisher quantum estimation theory, the inverse of the QFI matrix provides an operator lower bound to the covariance of an unbiased estimator. However, there has been little work on quantifying quantum limits and measurement designs, for multi-parameter quantum estimation in the {\em Bayesian} setting. In this paper, we build upon Personick's result to construct a Bayesian adaptive measurement scheme for multi-parameter estimation when $N$ copies of $\rho_\theta$ are available. We illustrate an application to localizing a cluster of point emitters in a highly sub-Rayleigh angular field-of-view, an important problem in fluorescence microscopy and astronomy. Our algorithm translates to a multi-spatial-mode transformation prior to a photon-detection array, with electro-optic feedback to adapt the mode sorter. We show that this receiver performs far superior to quantum-noise-limited focal-plane direct imaging.

Related papers

• Calculating response functions of coupled oscillators using quantum phase estimation [40.31060267062305]
  We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer. Our proposed quantum algorithm operates in the standard $s-sparse, oracle-based query access model. We show that a simple adaptation of our algorithm solves the random glued-trees problem in time.
  arXiv  Detail & Related papers  (2024-05-14T15:28:37Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• On the bias in iterative quantum amplitude estimation [0.0]
  This paper investigates the bias in iterative quantum amplitude estimation (IQAE) We show that IQAE is biased and the bias is enhanced for some specific values of $a$. We present a bias mitigation method: just re-executing the final round with the Grover number and the shot number fixed.
  arXiv  Detail & Related papers  (2023-11-28T07:02:29Z)
• A Specialized Semismooth Newton Method for Kernel-Based Optimal Transport [92.96250725599958]
  Kernel-based optimal transport (OT) estimators offer an alternative, functional estimation procedure to address OT problems from samples. We show that our SSN method achieves a global convergence rate of $O (1/sqrtk)$, and a local quadratic convergence rate under standard regularity conditions.
  arXiv  Detail & Related papers  (2023-10-21T18:48:45Z)
• Quantum Metropolis-Hastings algorithm with the target distribution calculated by quantum Monte Carlo integration [0.0]
  Quantum algorithms for MCMC have been proposed, yielding the quadratic speedup with respect to the spectral gap $Delta$ compered to classical counterparts. We consider not only state generation but also finding a credible interval for a parameter, a common task in Bayesian inference. In the proposed method for credible interval calculation, the number of queries to the quantum circuit to compute $ell$ scales on $Delta$, the required accuracy $epsilon$ and the standard deviation $sigma$ of $ell$ as $tildeO(sigma/epsilon
  arXiv  Detail & Related papers  (2023-03-10T01:05:16Z)
• Distributed quantum sensing with optical lattices [0.0]
  In distributed quantum sensing the correlations between multiple modes, typically of a photonic system, are utilized to enhance the measurement precision of an unknown parameter. We show that it can allow for parameter estimation at the Heisenberg limit of $(N(M-1)T)2$, where $N$ is the number of particles, $M$ is the number of modes, and $T$ is the measurement time.
  arXiv  Detail & Related papers  (2022-08-10T03:47:44Z)
• DP-PCA: Statistically Optimal and Differentially Private PCA [44.22319983246645]
  DP-PCA is a single-pass algorithm that overcomes both limitations. For sub-Gaussian data, we provide nearly optimal statistical error rates even for $n=tilde O(d)$.
  arXiv  Detail & Related papers  (2022-05-27T02:02:17Z)
• Parameter Estimation with Reluctant Quantum Walks: a Maximum Likelihood approach [0.0]
  A coin action is presented, with the real parameter $theta$ to be estimated. For $k$ large, we show that the likelihood is sharply peaked at a displacement determined by the ratio $d/k$.
  arXiv  Detail & Related papers  (2022-02-24T00:51:17Z)
• Sharp regret bounds for empirical Bayes and compound decision problems [42.397889421982555]
  In a Bayes setting the optimal estimator is given by the prior-dependent conditional mean. We show that for the Poisson model with compactly supported and subexponential priors, the optimal regret scales as $Theta(fraclog nloglog n)2)$ and $Theta(log3 n)$.
  arXiv  Detail & Related papers  (2021-09-08T21:34:47Z)
• Bi-frequency illumination: a quantum-enhanced protocol [0.0]
  Quantum-enhanced, idler-free sensing protocol to measure the response of a target object to the frequency of a probe is proposed. This work opens the way to applications in both radar and medical imaging, in particular in the microwave domain.
  arXiv  Detail & Related papers  (2020-10-28T17:21:56Z)
• Quantum Algorithms for Simulating the Lattice Schwinger Model [63.18141027763459]
  We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$. We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
  arXiv  Detail & Related papers  (2020-02-25T19:18:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.