Quantum State Tomography via Linear Regression Estimation
arXiv:1304.6827 · doi:10.1038/srep03496
Abstract
A simple yet efficient method of linear regression estimation (LRE) is presented for quantum state tomography. In this method, quantum state reconstruction is converted into a parameter estimation problem of a linear regression model and the least-squares method is employed to estimate the unknown parameters. The asymptotic mean squared error (MSE) bound of the estimate can be given analytically, which can guide one to choose optimal measurement sets. The LRE is asymptotically optimal in the sense that the MSE may achieve the Cramér-Rao bound asymptotically. The computational complexity of LRE is O(d^4), where d is the dimension of the quantum state. Numerical examples show that LRE is much faster than maximum-likelihood estimation for quantum state tomography.
5 pages, 2 figures, Comments are welcome
References in corpus (12)
- Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
- Efficient quantum state tomography
- Direct measurement of general quantum states using weak measurement
- Permutationally invariant quantum tomography
- Full characterisation of polarisation states of light via direct measurement
- Choice of Measurement Sets in Qubit Tomography
- Knowledge and ignorance in incomplete quantum state tomography
- Weighted complex projective 2-designs from bases: optimal state determination by orthogonal measurements
- Optimal quantum tomography for states, measurements, and transformations
- Optimal data processing for quantum measurements
- Incomplete quantum state estimation: a comprehensive study
- Optimal quantum tomography of permutationally invariant qubits
Cited by in corpus (55)
- Quantum Algorithm Implementations for Beginners
- Sampling-based learning control of inhomogeneous quantum ensembles
- Recursively Adaptive Quantum State Tomography: Theory and Two-qubit Experiment
- Superfast maximum likelihood reconstruction for quantum tomography
- Full reconstruction of a 14-qubit state within four hours
- A Quantum Hamiltonian Identification Algorithm: Computational Complexity and Error Analysis
- Machine learning assisted quantum state estimation
- Local-measurement-based quantum state tomography via neural networks
- Reconstructing quantum states with quantum reservoir networks
- Neural-network quantum state tomography
- Optimal two-qubit tomography based on local and global measurements: Maximal robustness against errors as described by condition numbers
- Experimentally Obtaining Maximal Coherence Via Assisted Distillation Pro cess
- Practical adaptive quantum tomography
- Quantum coherence and state conversion: theory and experiment
- Quantum gate identification: error analysis, numerical results and optical experiment
- Quantum Ensemble Classification: A Sampling-based Learning Control Approach
- Efficient quantum circuit for singular value thresholding
- A comparative study of estimation methods in quantum tomography
- Systematic study of High transmon qudits up to
- Constructing valid density matrices on an NMR quantum information processor via maximum likelihood estimation
- Adaptive quantum tomography
- Priority Choice Experimental Two-qubit Tomography: Measuring One by One All Elements of Density Matrices
- Fiber-compatible photonic feed-forward with 99% fidelity
- Two-stage Estimation for Quantum Detector Tomography: Error Analysis, Numerical and Experimental Results
- Neural network state estimation for full quantum state tomography
- Efficient online quantum state estimation using a matrix-exponentiated gradient method
- Realization of mutually unbiased bases for a qubit with only one wave plate: Theory and experiment
- Quantum State Interferography
- Spin qudit tomography and state reconstruction error
- Neural networks for quantum state tomography with constrained measurements
- Real-time quantum state estimation in circuit QED via Bayesian approach
- Classification and reconstruction of optical quantum states with deep neural networks
- Machine Learning for Estimation and Control of Quantum Systems
- A Tailor-made Quantum State Tomography Approach
- Maximum likelihood quantum state tomography is inadmissible
- Efficient factored gradient descent algorithm for quantum state tomography
- Quantum Steering on IBMQ
- Recovering quantum properties of continuous-variable states in the presence of measurement errors
- Benchmarking maximum-likelihood state estimation with an entangled two-cavity state
- Realizing a Compact, High-Fidelity, Telecom-Wavelength Source of Multipartite Entangled Photons
- The pretty bad measurement
- Fast State Stabilization using Deep Reinforcement Learning for Measurement-based Quantum Feedback Control
- Macroscopic approach to N-qudit systems
- Experimentally Certified Transmission of a Quantum Message through an Untrusted and Lossy Quantum Channel via Bell's Theorem
- A Variational Approach to Unique Determinedness in Pure-state Tomography
- Quantum image processing?
- Matrix-Completion Quantum State Tomography
- Unorthodox parallelization for Bayesian quantum state estimation
- Hybrid filtering for a class of nonlinear quantum systems subject to classical stochastic disturbances
- Investigating Pure State Uniqueness in Tomography via Optimization
- Quantum Tomography by Regularized Linear Regression
- Characterizing errors in parameter estimation by local measurements
- Rigorous Maximum Likelihood Estimation for Quantum States
- Detailed Account of Complexity for Implementation of Some Gate-Based Quantum Algorithms
- Real-time Information, Uncertainty and Quantum Feedback Control