By leveraging the Variational Quantum Eigensolver (VQE), the ``quantum equation of motion" (qEOM) method established itself as a promising tool for quantum chemistry on near term quantum computers, and has been used extensively to estimate molecular excited states. Here, we explore a novel application of this method, employing it to compute thermal averages of quantum systems, specifically molecules like ethylene and butadiene. A drawback of qEOM is that it requires measuring the expectation values of a large number of observables on the ground state of the system, and the number of necessary measurements can become a bottleneck of the method. In this work we focus on measurements through informationally complete positive operator-valued measures (IC-POVMs) to achieve a reduction in the measurements overheads. We show with numerical simulations that the qEOM combined with IC-POVM measurements ensures a satisfactory accuracy in the reconstruction of the thermal state with a reasonable number of shots.
Many prominent quantum computing algorithms with applications in fields such as chemistry and materials science require a large number of measurements, which represents an important roadblock for future real-world use cases. We introduce a novel approach to tackle this problem through an adaptive measurement scheme. We present an algorithm that optimizes informationally complete positive operator-valued measurements (POVMs) on the fly in order to minimize the statistical fluctuations in the estimation of relevant cost functions. We show its advantage by improving the efficiency of the variatio…
We construct an informationally complete set of mutually unbiased - like bases for N ququarts. These bases are used in an explicit tomographic protocol which performance is analyzed by estimating quadratic errors and compared to other reconstruction schemes.
We address the problem of properly quantifying information in quantum theory. Brukner and Zeilinger proposed the concept of an operationally invariant measure based on measurement statistics. Their measure of information is calculated with probabilities generated in a complete set of mutually complementary observations. This approach was later criticized for several reasons. We show that some critical points can be overcome by means of natural extension or reformulation of the Brukner-Zeilinger approach. In particular, this approach is connected with symmetric informationally complete measurem…
Near-optimal pure state estimation with adaptive Fisher-symmetric measurements
Instituto Milenio de Investigación en Óptica, Universidad de Concepción（孔塞普西翁大学米利尼奥光学研究所）；Facultad de Ciencias Físicas y Matemáticas, Departamento de Física, Universidad de Concepción（孔塞普西翁大学物理与数学科学学院物理系）；ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（巴塞罗那科学技术研究所光子科学研究所）
Identifying and calibrating quantitative dynamical models for physical quantum systems is important for a variety of applications. Here we present a closed-loop Bayesian learning algorithm for estimating multiple unknown parameters in a dynamical model, using optimised experimental "probe" controls and measurement. The estimation algorithm is based on a Bayesian particle filter, and is designed to autonomously choose informationally-optimised probe experiments with which to compare to model predictions. We demonstrate the performance of the algorithm in both simulated calibration tasks and in …
Interaction of molecules with light may lead to electronic transitions and simultaneous vibrational excitations. Franck-Condon factors (FCFs) play an important role in quantifying the intensities of such vibronic transitions occurring during molecular photo-excitations. In this article, we describe a general method for estimating FCFs using a quantum information processor. The method involves the application of a translation operator followed by the measurement of certain projections. We also illustrate the method by experimentally estimating FCFs with the help of a three-qubit NMR quantum inf…
When an informationally complete measurement is not available, the reconstruction of the density operator that describes the state of a quantum system can be accomplish, in a reliable way, by adopting the maximum entropy principle (MaxEnt principle), as an additional criterion, to obtain the least biased estimation. In this paper, we study the performance of the MaxEnt method for quantum state estimation when there is prior information about symmetries of the unknown state. We explicitly describe how to work with this method in the most general case, and present an algorithm that allows to imp…
We address the characterization of molecular nanomagnets at the quantum level and analyze the performance of local measurements in estimating the physical parameters in their spin Hamiltonians. To this aim, we compute key quantities in quantum estimation theory, such as the classical and the quantum Fisher information, in the prototypical case of an heterometallic antiferromagnetic ring. We show that local measurements, performed only on a portion of the molecule, allow a precise estimate of the parameters related to both magnetic defects and avoided level crossings.
Obtaining precise estimates of quantum observables is a crucial step of variational quantum algorithms. We consider the problem of estimating expectation values of molecular Hamiltonians, obtained on states prepared on a quantum computer. We propose a novel estimator for this task, which is locally optimised with knowledge of the Hamiltonian and a classical approximation to the underlying quantum state. Our estimator is based on the concept of classical shadows of a quantum state, and has the important property of not adding to the circuit depth for the state preparation. We test its performan…
Modeling chemical reactions and complicated molecular systems has been proposed as the `killer application' of a future quantum computer. Accurate calculations of derivatives of molecular eigenenergies are essential towards this end, allowing for geometry optimization, transition state searches, predictions of the response to an applied electric or magnetic field, and molecular dynamics simulations. In this work, we survey methods to calculate energy derivatives, and present two new methods: one based on quantum phase estimation, the other on a low-order response approximation. We calculate as…
We present a simple $^1$H NMR approach for characterizing intermediate to fast regime molecular motions using $^1$H time-domain NMR at low magnetic field. The method is based on a Goldmann Shen dipolar filter (DF) followed by a Mixed Magic Sandwich Echo (MSE). The dipolar filter suppresses the signals arising from molecular segments presenting sub kHz mobility, so only signals from mobile segments are detected. Thus, the temperature dependence of the signal intensities directly evidences the onset of molecular motions with rates higher than kHz. The DF-MSE signal intensity is described by an a…
Machine Learning of Quantum Entanglement from Noisy Measurements
Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Torun（托伦尼古拉·哥白尼大学物理、天文学与信息学学院物理研究所）；Faculty of Cybernetics, Military University of Technology（军事技术大学网络学系）
We derive the stochastic Schrödinger equation for the system wave vector and use it to describe the excitation energy transfer dynamics in molecular aggregates. We suggest a quantum-measurement based method of estimating the excitation transfer time. Adequacy of the proposed approach is demonstrated by performing calculations on a model system. The theory is then applied to study the excitation transfer dynamics in a photosynthetic pigment-protein Fenna-Matthews-Olson (FMO) aggregate using both the Debye spectral density and the spectral density obtained from earlier molecular dynamics simulat…
Understanding heat transport is relevant to develop efficient strategies for thermal management in microelectronics for instance, as well as for fundamental science purposes. However, measuring temperatures in nanostructured environments and in cryogenic conditions remains a challenging task, that requires both high sentitivity and a non-invasive approach. Here we present a portable nanothermometer based on a molecular two-level quantum system that operates in the 3 - 30 K temperature range, with excellent temperature and spatial resolutions on the order of mK and $μ$m, respectively. We valida…
Indian Institute of Technology Madras（印度理工学院马德拉斯分校）
Quantum state tomography aims to estimate the state of a quantum mechanical system which is described by a trace one, Hermitian positive semidefinite complex matrix, given a set of measurements of the state. Existing works focus on estimating the density matrix that represents the state, using a compressive sensing approach, with only fewer measurements than that required for a tomographically complete set, with the assumption that the true state has a low rank. One very popular method to estimate the state is the use of the Singular Value Thresholding (SVT) algorithm. In this work, we present…
