Optimal and two-step adaptive quantum detector tomography
- URL: http://arxiv.org/abs/2106.09255v2
- Date: Wed, 12 Jan 2022 03:17:20 GMT
- Title: Optimal and two-step adaptive quantum detector tomography
- Authors: Shuixin Xiao, Yuanlong Wang, Daoyi Dong, Jun Zhang
- Abstract summary: We design optimal probe states for detector estimation based on the minimum upper bound of the mean squared error (UMSE) and the maximum robustness.
We also propose a two-step adaptive detector tomography algorithm to optimize the probe states adaptively.
Numerical results demonstrate the effectiveness of both the proposed optimal and adaptive quantum detector tomography methods.
- Score: 5.989827606075226
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum detector tomography is a fundamental technique for calibrating
quantum devices and performing quantum engineering tasks. In this paper, we
design optimal probe states for detector estimation based on the minimum upper
bound of the mean squared error (UMSE) and the maximum robustness. We establish
the minimum UMSE and the minimum condition number for quantum detectors and
provide concrete examples that can achieve optimal detector tomography. In
order to enhance the estimation precision, we also propose a two-step adaptive
detector tomography algorithm to optimize the probe states adaptively based on
a modified fidelity index. We present a sufficient condition on when the
estimation error of our two-step strategy scales inversely proportional to the
number of state copies. Moreover, the superposition of coherent states is used
as probe states for quantum detector tomography and the estimation error is
analyzed. Numerical results demonstrate the effectiveness of both the proposed
optimal and adaptive quantum detector tomography methods.
Related papers
- QestOptPOVM: An iterative algorithm to find optimal measurements for quantum parameter estimation [17.305295658536828]
We introduce an algorithm, termed QestPOVM, designed to directly identify optimal positive operator-Opt measure (POVM)
Through rigorous testing on several examples for multiple copies of qubit states (up to six copies), we demonstrate the efficiency and accuracy of our proposed algorithm.
Our algorithm functions as a tool for elucidating the explicit forms of optimal POVMs, thereby enhancing our understanding of quantum parameter estimation methodologies.
arXiv Detail & Related papers (2024-03-29T11:46:09Z) - A two-stage solution to quantum process tomography: error analysis and
optimal design [6.648667887733229]
We propose a two-stage solution for both trace-preserving and non-trace-preserving quantum process tomography.
Our algorithm exhibits a computational complexity of $O(MLd2)$ where $d$ is the dimension of the quantum system.
Numerical examples and testing on IBM quantum devices are presented to demonstrate the performance and efficiency of our algorithm.
arXiv Detail & Related papers (2024-02-14T05:45:11Z) - Finding the optimal probe state for multiparameter quantum metrology
using conic programming [61.98670278625053]
We present a conic programming framework that allows us to determine the optimal probe state for the corresponding precision bounds.
We also apply our theory to analyze the canonical field sensing problem using entangled quantum probe states.
arXiv Detail & Related papers (2024-01-11T12:47:29Z) - Retrieving space-dependent polarization transformations via near-optimal
quantum process tomography [55.41644538483948]
We investigate the application of genetic and machine learning approaches to tomographic problems.
We find that the neural network-based scheme provides a significant speed-up, that may be critical in applications requiring a characterization in real-time.
We expect these results to lay the groundwork for the optimization of tomographic approaches in more general quantum processes.
arXiv Detail & Related papers (2022-10-27T11:37:14Z) - Adaptive POVM implementations and measurement error mitigation
strategies for near-term quantum devices [0.0]
We present adaptive measurement techniques tailored for variational quantum algorithms on near-term small and noisy devices.
Our numerical simulations clearly indicate that the presented strategies can significantly reduce the number of needed shots to achieve chemical accuracy in variational quantum eigensolvers.
arXiv Detail & Related papers (2022-08-16T16:05:40Z) - Dynamical learning of a photonics quantum-state engineering process [48.7576911714538]
Experimentally engineering high-dimensional quantum states is a crucial task for several quantum information protocols.
We implement an automated adaptive optimization protocol to engineer photonic Orbital Angular Momentum (OAM) states.
This approach represents a powerful tool for automated optimizations of noisy experimental tasks for quantum information protocols and technologies.
arXiv Detail & Related papers (2022-01-14T19:24:31Z) - Bosonic field digitization for quantum computers [62.997667081978825]
We address the representation of lattice bosonic fields in a discretized field amplitude basis.
We develop methods to predict error scaling and present efficient qubit implementation strategies.
arXiv Detail & Related papers (2021-08-24T15:30:04Z) - Fast and robust quantum state tomography from few basis measurements [65.36803384844723]
We present an online tomography algorithm designed to optimize all the aforementioned resources at the cost of a worse dependence on accuracy.
The protocol is the first to give provably optimal performance in terms of rank and dimension for state copies, measurement settings and memory.
Further improvements are possible by executing the algorithm on a quantum computer, giving a quantum speedup for quantum state tomography.
arXiv Detail & Related papers (2020-09-17T11:28:41Z) - Estimation of pure quantum states in high dimension at the limit of
quantum accuracy through complex optimization and statistical inference [0.0]
Quantum tomography has become a key tool for the assessment of quantum states, processes, and devices.
In the case of mixed states of a single 2-dimensional quantum system adaptive methods have been recently introduced that achieve the theoretical accuracy limit deduced by Hayashi and Gill and Massar.
Here we present an adaptive tomographic method and show through numerical simulations, that it is difficult to approach the fundamental accuracy of pure quantum states in high dimension.
arXiv Detail & Related papers (2020-07-02T21:33:16Z) - Semi-device-dependent blind quantum tomography [1.3075880857448061]
Current schemes typically require measurement devices for tomography that are a priori calibrated to high precision.
We show that exploiting the natural low-rank structure of quantum states of interest suffices to arrive at a highly scalable blind' tomography scheme.
We numerically demonstrate that robust blind quantum tomography is possible in a practical setting inspired by an implementation of trapped ions.
arXiv Detail & Related papers (2020-06-04T18:00:04Z) - Quantum probes for universal gravity corrections [62.997667081978825]
We review the concept of minimum length and show how it induces a perturbative term appearing in the Hamiltonian of any quantum system.
We evaluate the Quantum Fisher Information in order to find the ultimate bounds to the precision of any estimation procedure.
Our results show that quantum probes are convenient resources, providing potential enhancement in precision.
arXiv Detail & Related papers (2020-02-13T19:35:07Z)
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.