Permutationally invariant state reconstruction

@article{Moroder2012PermutationallyIS,
  title={Permutationally invariant state reconstruction},
  author={Tobias Moroder and Philipp Hyllus and G{\'e}za T{\'o}th and Christian Schwemmer and Alexander Niggebaum and Stefanie Gaile and Otfried G{\"u}hne and Harald Weinfurter},
  journal={New Journal of Physics},
  year={2012},
  volume={14}
}
Feasible tomography schemes for large particle numbers must possess, besides an appropriate data acquisition protocol, an efficient way to reconstruct the density operator from the observed finite data set. Since state reconstruction typically requires the solution of a nonlinear large-scale optimization problem, this is a major challenge in the design of scalable tomography schemes. Here we present an efficient state reconstruction scheme for permutationally invariant quantum state tomography… 

A scalable maximum likelihood method for quantum state tomography

The principle of maximum likelihood reconstruction has proven to yield satisfactory results in the context of quantum state tomography for many-body systems of moderate system sizes. Until recently,

Fast quantum state reconstruction via accelerated non-convex programming

TLDR
The proposed quantum state reconstruction method, called Momentum-Inspired Factored Gradient Descent (MiFGD), converges provably close to the true density matrix at an accelerated linear rate, in the absence of experimental and statistical noise, and under common assumptions.

Reconstructing quantum states with generative models

TLDR
The key insight is to reduce state tomography to an unsupervised learning problem of the statistics of an informationally complete quantum measurement, which constitutes a modern machine learning approach to the validation of complex quantum devices.

Efficiently reconstructing compound objects by quantum imaging with higher-order correlation functions

TLDR
A method to reduce the number of parameters required and identify an optimal degree of photon correlation for imaging is demonstrated, resulting in super-resolving reconstruction of grey compound transmission objects.

Quantum tomography : asymptotic theory and statistical methodology

Recent experimental progress in the preparation and control of quantum systems has brought to light the importance of Quantum State Tomography (QST) in validating the results. In this thesis we

Experimental quantum tomography assisted by multiply symmetric states in higher dimensions

High-dimensional quantum information processing has become a mature field of research with several different approaches being adopted for the encoding of $D$-dimensional quantum systems. Such

Practical and Reliable Error Bars in Quantum Tomography.

TLDR
This work proposes a practical yet robust method for obtaining error bars by introducing a novel representation of the output of the tomography procedure, the quantum error bars, and presents an algorithm for computing this representation and provides ready-to-use software.

Neural-network quantum state tomography in a two-qubit experiment

We study the performance of efficient quantum state tomography methods based on neural network quantum states using measured data from a two-photon experiment. Machine learning inspired variational

Adaptive quantum tomography of high-dimensional bipartite systems

TLDR
A novel tomographic protocol specially designed for the reconstruction of high-dimensional quantum states that shows qualitative improvement in infidelity scaling with the number of measurements and is fast enough to allow for complete state tomography of states with dimensionality up to 36.

Density matrix reconstruction using non-negative matrix product states

Quantum state tomography is a key technique for quantum information processing, but is chal-lenging due to the exponential growth of its complexity with the system size. In this work, we propose an
...

References

SHOWING 1-10 OF 75 REFERENCES

Scalable reconstruction of density matrices.

TLDR
A scalable method to reconstruct mixed states that are well approximated by matrix product operator operators, based on a constructive proof that generic matrix product operators are fully determined by their local reductions.

Efficient quantum state tomography.

TLDR
Two tomography schemes that scale much more favourably than direct tomography with system size are presented, one of them requires unitary operations on a constant number of subsystems, whereas the other requires only local measurements together with more elaborate post-processing.

Information criteria for efficient quantum state estimation

Recently several more efficient versions of quantum state tomography have been proposed, with the purpose of making tomography feasible even for many-qubit states. The number of state parameters to

Maximum-likelihood methods in quantum mechanics

Maximum Likelihood estimation is a versatile tool covering wide range of applications, but its benefits are apparent particularly in the quantum domain. For a given set of measurements, the most

Optimal Experiment Design for Quantum State and Process Tomography and Hamiltonian Parameter Estimation

A number of problems in quantum state and system identification are addressed. Specifically, it is shown that the maximum likelihood estimation (MLE) approach, already known to apply to quantum state

Reliable quantum state tomography.

TLDR
This work shows that quantum state tomography, together with an appropriate data analysis procedure, yields reliable and tight error bounds, specified in terms of confidence regions-a concept originating from classical statistics.

Quantum state tomography via compressed sensing.

TLDR
These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems, and are able to reconstruct an unknown density matrix of dimension d and rank r using O(rdlog²d) measurement settings, compared to standard methods that require d² settings.

Permutationally invariant quantum tomography.

We present a scalable method for the tomography of large multiqubit quantum registers. It acquires information about the permutationally invariant part of the density operator, which is a good

Quantum tomography via compressed sensing: error bounds, sample complexity and efficient estimators

TLDR
This paper shows how to certify the accuracy of a low-rank estimate using direct fidelity estimation, and describes a method for compressed quantum process tomography that works for processes with small Kraus rank and requires only Pauli eigenstate preparations and Pauli measurements.

Practical characterization of quantum devices without tomography.

TLDR
It is demonstrated that fidelity can be estimated from a number of simple experiments that is independent of the system size, removing an important roadblock for the experimental study of larger quantum information processing units.
...