Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Quantum model averaging

Christopher Ferrie

Published Sep 24, 2014• 15 citations
OpenAlex

Abstract

© 2014 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Standard tomographic analyses ignore model uncertainty. It is assumed that a given model generated the data and the task is to estimate the quantum state, or a subset of parameters within that model. Here we apply a model averaging technique to mitigate the risk of overconfident estimates of model parameters in two examples: (1) selecting the rank of the state in tomography and (2) selecting the model for the fidelity decay curve in randomized benchmarking.

Related papers

Quantum model averaging

Christopher Ferrie

Standard tomographic analyses ignore model uncertainty. It is assumed that a given model generated the data and the task is to estimate the quantum state, or a subset of parameters within that model. Here we apply a model averaging technique to mitigate the risk of overconfident estimates of model parameters in two examples: (1) selecting the rank of the state in tomography and (2) selecting the model for the fidelity decay curve in randomized benchmarking.

arXiv:1405.6329•New Journal of Physics•Sep 24, 2014•22 citations

Practical adaptive quantum tomography

Christopher Granade, Christopher Ferrie, Steven T. Flammia

© 2017 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. We introduce a fast and accurate heuristic for adaptive tomography that addresses many of the limitations of prior methods. Previous approaches were either too computationally intensive or tailored to handle special cases such as single qubits or pure states. By contrast, our approach combines the efficiency of online optimization with generally applicable and well-motivated data-processing techniques. We numerically demonstrate these advantages in several scenarios including mixed states, higher-dimensional systems, and restricted measurements.

•Nov 1, 2017•47 citations

Precision-Guaranteed Quantum Tomography

Takanori Sugiyama, Peter S. Turner, Mio Murao

Quantum state tomography is currently the standard tool for verifying that a state prepared in the lab is close to an ideal target state, but up to now there have been no rigorous methods for evaluating the precision of the state preparation in tomographic experiments. We propose a new estimator for quantum state tomography, and prove that the (always physical) estimates will be close to the true prepared state with a high probability. We derive an explicit formula for evaluating how high the probability is for an arbitrary finite-dimensional system and explicitly give the one- and two-qubit cases as examples. This formula applies for any informationally complete sets of measurements, arbitrary finite number of data sets, and general loss functions including the infidelity, the Hilbert-Schmidt, and the trace distances. Using the formula, we can evaluate not only the difference between the estimated and prepared states, but also the difference between the prepared and target states. This is the first result directly applicable to the problem of evaluating the precision of estimation and preparation in quantum tomographic experiments.

arXiv:1306.4191•Physical Review Letters•Oct 17, 2013•53 citations

Quantum Tomography by Regularized Linear Regression

Biqiang Mu, Hongsheng Qi, Ian R. Petersen +1 more

In this paper, we study extended linear regression approaches for quantum state tomography based on regularization techniques. For unknown quantum states represented by density matrices, performing measurements under certain basis yields random outcomes, from which a classical linear regression model can be established. First of all, for complete or over-complete measurement bases, we show that the empirical data can be utilized for the construction of a weighted least squares estimate (LSE) for quantum tomography. Taking into consideration the trace-one condition, a constrained weighted LSE can be explicitly computed, being the optimal unbiased estimation among all linear estimators. Next, for general measurement bases, we show that $\ell_2$-regularization with proper regularization gain provides even lower mean-square error under a cost in bias. The regularization parameter is tuned by two estimators in terms of a risk characterization. Finally, a concise and unified formula is established for the regularization parameter with complete measurement basis under an equivalent regression model, which proves that the proposed tuning estimators are asymptotically optimal as the number of samples grows to infinity under the risk metric. Additionally, numerical examples are provided to validate the established results.

arXiv:1904.11839•Apr 26, 2019•0 citations

Semiclassical approach to fidelity amplitude

García-Mata, I., Vallejos, R.O., Wisniacki, D.A.

The fidelity amplitude (FA) is a quantity of paramount importance in echo-type experiments. We use semiclassical theory to study the average FA for quantum chaotic systems under external perturbation. We explain analytically two extreme cases: the random dynamics limit-attained approximately by strongly chaotic systems-and the random perturbation limit, which shows a Lyapunov decay. Numerical simulations help us to bridge the gap between both the extreme cases. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

•Jan 1, 2011•7 citations

Numerical strategies for quantum tomography: Alternatives to full optimization

Max S. Kaznady, Daniel F. V. James

We examine a variety of strategies for numerical quantum-state estimation from data of the sort commonly measured in experiments involving quantum-state tomography. We find that, in some important circumstances, an elaborate and time-consuming numerical optimization to obtain the optimum density matrix corresponding to a given data set is not necessary and that cruder, faster numerical techniques may well be sufficient; in other words, ``the best'' is the enemy of ``good enough.''

Physical Review A•Feb 9, 2009•61 citations
© 2014 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. Standard tomographic analyses ignore model uncertainty. It is assumed that a given model generated the data and the task is to estimate the quantum state, or a subset of parameters within that model. Here we apply a model averaging technique to mitigate the risk of overconfident estimates of model parameters in two examples: (1) selecting the rank of the state in tomography and (2) selecting the model for the fidelity decay curve in randomized benchmarking.
© 2017 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. We introduce a fast and accurate heuristic for adaptive tomography that addresses many of the limitations of prior methods. Previous approaches were either too computationally intensive or tailored to handle special cases such as single qubits or pure states. By contrast, our approach combines the efficiency of online optimization with generally applicable and well-motivated data-processing techniques. We numerically demonstrate these advantages in several scenarios including mixed states, higher-dimensional systems, and restricted measurements.
Quantum state tomography is currently the standard tool for verifying that a state prepared in the lab is close to an ideal target state, but up to now there have been no rigorous methods for evaluating the precision of the state preparation in tomographic experiments. We propose a new estimator for quantum state tomography, and prove that the (always physical) estimates will be close to the true prepared state with a high probability. We derive an explicit formula for evaluating how high the probability is for an arbitrary finite-dimensional system and explicitly give the one- and two-qubit cases as examples. This formula applies for any informationally complete sets of measurements, arbitrary finite number of data sets, and general loss functions including the infidelity, the Hilbert-Schmidt, and the trace distances. Using the formula, we can evaluate not only the difference between the estimated and prepared states, but also the difference between the prepared and target states. This is the first result directly applicable to the problem of evaluating the precision of estimation and preparation in quantum tomographic experiments.
In this paper, we study extended linear regression approaches for quantum state tomography based on regularization techniques. For unknown quantum states represented by density matrices, performing measurements under certain basis yields random outcomes, from which a classical linear regression model can be established. First of all, for complete or over-complete measurement bases, we show that the empirical data can be utilized for the construction of a weighted least squares estimate (LSE) for quantum tomography. Taking into consideration the trace-one condition, a constrained weighted LSE can be explicitly computed, being the optimal unbiased estimation among all linear estimators. Next, for general measurement bases, we show that ℓ2\ell_2ℓ2​-regularization with proper regularization gain provides even lower mean-square error under a cost in bias. The regularization parameter is tuned by two estimators in terms of a risk characterization. Finally, a concise and unified formula is established for the regularization parameter with complete measurement basis under an equivalent regression model, which proves that the proposed tuning estimators are asymptotically optimal as the number of samples grows to infinity under the risk metric. Additionally, numerical examples are provided to validate the established results.
The fidelity amplitude (FA) is a quantity of paramount importance in echo-type experiments. We use semiclassical theory to study the average FA for quantum chaotic systems under external perturbation. We explain analytically two extreme cases: the random dynamics limit-attained approximately by strongly chaotic systems-and the random perturbation limit, which shows a Lyapunov decay. Numerical simulations help us to bridge the gap between both the extreme cases. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
We examine a variety of strategies for numerical quantum-state estimation from data of the sort commonly measured in experiments involving quantum-state tomography. We find that, in some important circumstances, an elaborate and time-consuming numerical optimization to obtain the optimum density matrix corresponding to a given data set is not necessary and that cruder, faster numerical techniques may well be sufficient; in other words, ``the best'' is the enemy of ``good enough.''