Quantum state characterization with deep neural networks

In this licentiate thesis, I explain some of the interdisciplinary topics connecting machine learning to quantum physics. The thesis is based on the two appended papers, where deep neural networks were used for the characterization of quantum systems. I discuss the connections between parameter estimation, inverse problems and machine learning to put the results of the appended papers in perspective. In these papers, we have shown how to incorporate prior knowledge of quantum physics and noise models in generative adversarial neural networks. This thesis further discusses how automatic differentiation techniques allow training such custom neural-network-based methods to characterize quantum systems or learn their description. In the appended papers, we have demonstrated that the neural-network approach could learn a quantum state description from an order of magnitude fewer data points and faster than an iterative maximum-likelihood estimation technique. The goal of the thesis is to bring such tools and techniques from machine learning to the physicist’s arsenal and to explore the intersection between quantum physics and machine learning

Virtual excitations in the ultra-strongly-coupled spin-boson model: physical results from unphysical modes

Here we show how, in the ultra-strongly-coupled spin-boson model, apparently unphysical "Matsubara modes" are required not only to regulate detailed balance, but also to arrive at a correct and physical description of the non-perturbative dynamics and steady-state. In particular, in the zero-temperature limit, we show that neglecting the Matsubara modes results in an erroneous emission of virtual photons from the collective ground state. To explore this difficult-to-model regime we start by using a non-perturbative hierarchical equations of motion (HEOM) approach, based on a partial fitting of the bath correlation-function which takes into account the infinite sum of Matsubara frequencies using only a biexponential function. We compare the HEOM method to both a pseudo-mode model, and the reaction coordinate (RC) mapping, which help explain the nature of the aberrations observed when Matsubara frequencies are neglected. For the pseudo-mode method we present a general proof of validity, which allows for negative Matsubara-contributions to the decomposition of the bath correlation functions to be described by zero-frequency Matsubara-modes with non-Hermitian coupling to the system. The latter obey a non-Hermitian pseudo-Schr\"odinger equation, ultimately justifying why superficially unphysical modes can give rise to physical system behavior.Comment: 21 page

Implicit differentiation of variational quantum algorithms

Several quantities important in condensed matter physics, quantum information, and quantum chemistry, as well as quantities required in meta-optimization of machine learning algorithms, can be expressed as gradients of implicitly defined functions of the parameters characterizing the system. Here, we show how to leverage implicit differentiation for gradient computation through variational quantum algorithms and explore applications in condensed matter physics, quantum machine learning, and quantum information. A function defined implicitly as the solution of a quantum algorithm, e.g., a variationally obtained ground- or steady-state, can be automatically differentiated using implicit differentiation while being agnostic to how the solution is computed. We apply this notion to the evaluation of physical quantities in condensed matter physics such as generalized susceptibilities studied through a variational quantum algorithm. Moreover, we develop two additional applications of implicit differentiation -- hyperparameter optimization in a quantum machine learning algorithm, and the variational construction of entangled quantum states based on a gradient-based maximization of a geometric measure of entanglement. Our work ties together several types of gradient calculations that can be computed using variational quantum circuits in a general way without relying on tedious analytic derivations, or approximate finite-difference methods.Comment: 13 pages, 8 figures. The code and data for the article is available at https://github.com/quantshah/quantum-implicit-differentiatio

Gradient-Descent Quantum Process Tomography by Learning Kraus Operators

We perform quantum process tomography (QPT) for both discrete- and continuous-variable quantum systems by learning a process representation using Kraus operators. The Kraus form ensures that the reconstructed process is completely positive. To make the process trace preserving, we use a constrained gradient-descent (GD) approach on the so-called Stiefel manifold during optimization to obtain the Kraus operators. Our ansatz uses a few Kraus operators to avoid direct estimation of large process matrices, e.g., the Choi matrix, for low-rank quantum processes. The GD-QPT matches the performance of both compressed-sensing (CS) and projected least-squares (PLS) QPT in benchmarks with two-qubit random processes, but shines by combining the best features of these two methods. Similar to CS (but unlike PLS), GD-QPT can reconstruct a process from just a small number of random measurements, and similar to PLS (but unlike CS) it also works for larger system sizes, up to at least five qubits. We envisage that the data-driven approach of GD-QPT can become a practical tool that greatly reduces the cost and computational effort for QPT in intermediate-scale quantum systems

Classification and reconstruction of optical quantum states with deep neural networks

We apply deep-neural-network-based techniques to quantum state classification and reconstruction. We demonstrate high classification accuracies and reconstruction fidelities, even in the presence of noise and with little data. Using optical quantum states as examples, we first demonstrate how convolutional neural networks (CNNs) can successfully classify several types of states distorted by, e.g., additive Gaussian noise or photon loss. We further show that a CNN trained on noisy inputs can learn to identify the most important regions in the data, which potentially can reduce the cost of tomography by guiding adaptive data collection. Secondly, we demonstrate reconstruction of quantum-state density matrices using neural networks that incorporate quantum-physics knowledge. The knowledge is implemented as custom neural-network layers that convert outputs from standard feedforward neural networks to valid descriptions of quantum states. Any standard feed-forward neural-network architecture can be adapted for quantum state tomography (QST) with our method. We present further demonstrations of our proposed [arXiv:2008.03240] QST technique with conditional generative adversarial networks (QST-CGAN). We motivate our choice of a learnable loss function within an adversarial framework by demonstrating that the QST-CGAN outperforms, across a range of scenarios, generative networks trained with standard loss functions. For pure states with additive or convolutional Gaussian noise, the QST-CGAN is able to adapt to the noise and reconstruct the underlying state. The QST-CGAN reconstructs states using up to two orders of magnitude fewer iterative steps than a standard iterative maximum likelihood (iMLE) method. Further, the QST-CGAN can reconstruct both pure and mixed states from two orders of magnitude fewer randomly chosen data points than iMLE.Comment: 40 pages, 20 figures, 5 tables, code will be available at https://github.com/quantshah/qst-n

Assessing Water Consumption of Major Crops in the Command Area of Malwah Distributary, Shaheed Benazirabad, Sindh.

Soil and water are vital natural resources on which agriculture sector growth and village livelihood depend and having the proper knowledge of the Soil, Plant, and water relationship are extremely important to achieve sustainable agricultural productivity. Pakistan has entered the 21st century with the rising challenge to meet food and fiber requirements for its population for domestic consumption and export. Without having appropriate knowledge about the intense water need of plants, most of the agricultural land in Pakistan is still being irrigated by conventional methods, which in turn produces so many problems and reduces the agricultural productivity putting extra stress on the country’s economy, so to avoid these issues, it is extremely necessary to provide the required quantity of water to plant, which will only be possible by consideration and accurate estimation of Evapotranspiration of plant so to enhance awareness and practice of water-saving agriculture in Pakistan to increase the agricultural commodities. In this study, estimation of Actual Evapotranspiration ( ETa ) of Malwah Distributary located in Shaheed Benazirbad, Sindh was selected from Command area of Rohri Canal, ET of four different crops; Cotton, Fallow, Rice and Sugarcane for the period of Rabi 2019-2020 and Kharif 2020 was estimated by using satellite-based evapotranspiration mapping tool namely METRIC REFLUX. The actual ET for each season was obtained using the Reference ET fraction (ETrf) of satellite data and reference ET(ETr) obtained from the literature. The classified crop mask was obtained using maximum likelihood classification on bands 8,4, and 3 of sentinel-2 images of the year 2020. The overall accuracy obtained is 93% with a kappa coefficient 0.921841. The average Actual Evapotranspiration of different crops namely, banana, cotton, rice, and sugarcane were found to be 1527.2 mm, 536.6 mm, 386.80 mm, and 814.02 m

Quantum State Tomography with Conditional Generative Adversarial Networks

Quantum state tomography (QST) is a challenging task in intermediate-scale quantum devices. Here, we apply conditional generative adversarial networks (CGANs) to QST. In the CGAN framework, two duelling neural networks, a generator and a discriminator, learn multi-modal models from data. We augment a CGAN with custom neural-network layers that enable conversion of output from any standard neural network into a physical density matrix. To reconstruct the density matrix, the generator and discriminator networks train each other on data using standard gradient-based methods. We demonstrate that our QST-CGAN reconstructs optical quantum states with high fidelity orders of magnitude faster, and from less data, than a standard maximum-likelihood method. We also show that the QST-CGAN can reconstruct a quantum state in a single evaluation of the generator network if it has been pre-trained on similar quantum states.Comment: 5 pages, 5 figures, code will be available at https://github.com/quantshah/qst-cgan; v2: minor updates; see also the companion paper arXiv:2012.0218

Prevalence of exclusive breastfeeding and associated factors among mothers in rural Bangladesh: a cross-sectional study

This article was published in International Breastfeeding Journal [© 2014 BioMed Central Ltd.] and the definite version is available at: https://internationalbreastfeedingjournal.biomedcentral.com/articles/10.1186/1746-4358-9-7Background: Exclusive breastfeeding (EBF) means that the infant receives only breast milk for the first six months of life after birth. In Bangladesh, the prevalence of EBF remained largely unchanged for nearly two decades and was 43% in 2007. However, in 2011, a prevalence of 64% was reported, an increase by 21 percentage points. The reasons for this large change remain speculative at this point. Thus to investigate the issue further, this study was conducted. The objective was to assess the prevalence of EBF and associated factors among mothers having children aged 0-6 months in rural Bangladesh. Methods: A cross-sectional study was conducted in Mirzapur Upazilla (sub district) among 121 mothers of infants aged 0-6 months. Eligible mothers were identified and randomly selected using the demographic surveillance system's computerized database that is updated weekly. A semi-structured questionnaire was used for interviews that inquired information on socio-demographic characteristics, obstetric, health service, breastfeeding related factors (initiation of breastfeeding, prelacteal feeding and colostrum feeding) and economic factors. EBF prevalence was calculated using 24 hour recall method. In multivariate analysis, a logistic regression model was developed using stepwise modeling to analyze the factors associated with EBF. Results: The prevalence of EBF in the last 24 hours preceding the survey was 36%. Bivariate and multivariate analysis revealed no significant association between EBF and its possible predictors at 0.05 level of alpha. However, there was some evidence of an association between EBF and having a caesarean delivery (OR = 0.47, 95% CI: 0.21, 1.06). In multivariate analysis, type of delivery: caesarean (AOR = 0.45, 95% CI: 0.19, 1.03) and wealth quintile: richer (AOR = 2.40, 95% CI: 0.94, 6.16) also showed some evidence of an association with EBF. Conclusion: The prevalence of EBF in Mirzapur (36%) is lower than the national figure (64%). Prelacteal feeding was not uncommon. These findings suggest that there is a need for breastfeeding support provided by health services. Hence, promotion of EBF during the first six months of life needs to be addressed and future breastfeeding promotion programmes should give special attention to those women who are not practicing EBF.Publishe

Outcome of Percutaneous Ultrasound Guided Aspiration versus Open Surgical Drainage of Psoas Muscle Abscess

Objective: To compare the outcome of percutaneous ultrasound guided aspiration V/S open surgical drainage for psoas muscle abscess. Methodology: This comparative study was conducted in department of general surgery at Liaquat medical university hospital Hyderabad/Jamshoro, from June 2017 to November 2017. Diagnosed Patients of psoas muscle abscess size more than 5cm, between 18 to 60 years of age and either of gender were included. Patients were randomly divided into two groups, A and B by odd and even method, patients in group A abscess was aspirated by percutaneous ultrasound guided aspiration and patients in group B was underwent open surgical drainage, all the data were entered in the pre designed performa and analyzed into SPSS V:16.0 Results: A total of 58 patients of Psoas muscle abscess were selected, the mean age of study subjects of group A was 38.5+10.5 and group B was 36.5+12.7 (p-673). Early post-operative pain relief was assessed among patients of group A as compared to group B. As per outcome resolution of abscess cavity was significantly high among patients of group B (p-0.004), while post-operative Hospital stay was significantly lower in group A (p-0.002). Conclusion: Both techniques has their own benefits like percutaneous aspiration has shorter duration of hospital stay while in complete resolution of abscess cavity was found in open surgical drainage group of patients