Quantum state tomography of molecules by ultrafast diffraction

AbstractUltrafast electron diffraction and time-resolved serial crystallography are the basis of the ongoing revolution in capturing at the atomic level of detail the structural dynamics of molecules. However, most experiments capture only the probability density of the nuclear wavepackets to determine the time-dependent molecular structures, while the full quantum state has not been accessed. Here, we introduce a framework for the preparation and ultrafast coherent diffraction from rotational wave packets of molecules, and we establish a new variant of quantum state tomography for ultrafast electron diffraction to characterize the molecular quantum states. The ability to reconstruct the density matrix, which encodes the amplitude and phase of the wavepacket, for molecules of arbitrary degrees of freedom, will enable the reconstruction of a quantum molecular movie from experimental x-ray or electron diffraction data.

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Molecular Tomography of the Quantum State by Time-Resolved Electron Diffraction

Physics Research International ◽

10.1155/2013/236743 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 5

Author(s):

A. A. Ischenko

Keyword(s):

Electron Diffraction ◽

Density Matrix ◽

Probability Density ◽

Wigner Function ◽

Quantum State ◽

Joint Probability ◽

Diffraction Method ◽

Boltzmann Distribution ◽

Electron Diffraction Data ◽

Time Resolved

A procedure is described that can be used to reconstruct the quantum state of a molecular ensemble from time-dependent internuclear probability density functions determined by time-resolved electron diffraction. The procedure makes use of established techniques for evaluating the density matrix and the phase-space joint probability density, that is, the Wigner function. A novel expression for describing electron diffraction intensities in terms of the Wigner function is presented. An approximate variant of the method, neglecting the off-diagonal elements of the density matrix, was tested by analyzing gas electron diffraction data for N2 in a Boltzmann distribution and TRED data obtained from the 193 nm photodissociation of CS2 to carbon monosulfide, CS, at 20, 40, and 120 ns after irradiation. The coherent changes in the nuclear subsystem by time-resolved electron diffraction method determine the fundamental transition from the standard kinetics to the dynamics of the phase trajectory of the molecule and the tomography of molecular quantum state.

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Adaptive quantum state tomography with neural networks

npj Quantum Information ◽

10.1038/s41534-021-00436-9 ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Yihui Quek ◽

Stanislav Fort ◽

Hui Khoon Ng

Keyword(s):

Machine Learning ◽

Quantum State ◽

The State ◽

Learning To Learn ◽

Seamless Integration ◽

Quantum State Tomography ◽

Flexible Machine ◽

Meta Learning ◽

Long Time ◽

State Tomography

AbstractCurrent algorithms for quantum state tomography (QST) are costly both on the experimental front, requiring measurement of many copies of the state, and on the classical computational front, needing a long time to analyze the gathered data. Here, we introduce neural adaptive quantum state tomography (NAQT), a fast, flexible machine-learning-based algorithm for QST that adapts measurements and provides orders of magnitude faster processing while retaining state-of-the-art reconstruction accuracy. As in other adaptive QST schemes, measurement adaptation makes use of the information gathered from previous measured copies of the state to perform a targeted sensing of the next copy, maximizing the information gathered from that next copy. Our NAQT approach allows for a rapid and seamless integration of measurement adaptation and statistical inference, using a neural-network replacement of the standard Bayes’ update, to obtain the best estimate of the state. Our algorithm, which falls into the machine learning subfield of “meta-learning” (in effect “learning to learn” about quantum states), does not require any ansatz about the form of the state to be estimated. Despite this generality, it can be retrained within hours on a single laptop for a two-qubit situation, which suggests a feasible time-cost when extended to larger systems and potential speed-ups if provided with additional structure, such as a state ansatz.

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