Impact of estimation techniques on regression analysis: an application to survey data on child nutritional status in five African countries

This paper illustrates the impact of ignoring survey design and hierarchical structure of survey data when fitting regression models. Data on child nutritional status from Ghana, Malawi, Tanzania, Zambia, and Zimbabwe are analysed using four techniques: ordinary least squares; weighted regression using standard statistical software; regression using specialist software that accounts for the survey design; and multilevel modelling. The impact of ignoring survey design on logistic and linear regression models is examined. The results show bias in estimates averaging between five and 17 per cent in linear models and between five and 22 per cent in logistic regression models. The standard errors are also under-estimated by up to 49 per cent in some countries. Socio-economic variables and service utilisation variables are poorly estimated when the survey design is ignored

Exploiting symmetries in nuclear Hamiltonians for ground state preparation

The Lipkin and Agassi models are simplified nuclear models that provide natural test beds for quantum simulation methods. Prior work has investigated the suitability of the Variational Quantum Eigensolver (VQE) to find the ground state of these models. There is a growing awareness that if VQE is to prove viable, we will need problem inspired ans\"{a}tze that take into account the symmetry properties of the problem and use clever initialization strategies. Here, by focusing on the Lipkin and Agassi models, we investigate how to do this in the context of nuclear physics ground state problems. We further use our observations to discus the potential of new classical, but quantum-inspired, approaches to learning ground states in nuclear problems.Comment: 7 pages, 4 figure

Using Action-congruent Language Facilitates the Motor Response during Action Observation: A Combined Transcranial Magnetic Stimulation and Eye-tracking Study.

There is evidence that action observation (AO) and the processing of action-related words are associated with increased activity in cortical motor regions. Research has examined the effects of AO and action verb processing on activity in the motor system independently. The aim of this experiment was to investigate, for the first time, the modulation of corticospinal excitability and visual attention during the concurrent processing of action verbs and AO stimuli. Twenty participants took part in an integrated transcranial magnetic stimulation and eye-tracking protocol. Single-pulse transcranial magnetic stimulation was delivered to the hand representation of the left motor cortex during (i) observation of a static hand, (ii) AO of a hand squeezing a sponge, (iii) AO of the same action with an audio recording of the word "squeeze," and (iv) AO of the same action with an audio recording of the word "green". Motor evoked potentials were recorded from the abductor pollicis brevis and abductor digiti minimi muscles of the right hand. Eye gaze was recorded throughout the four conditions as a proxy for visual attention. Interviews were conducted to discuss participants' preferences and imagery use for each condition. The AO and action verb condition resulted in significantly increased motor evoked potential amplitudes in the abductor pollicis brevis; participants also made significantly more fixations on the sponge and reported wanting to move their hand. The inclusion of auditory action verbs, alongside AO stimuli, in movement simulation interventions could have implications for the delivery of AO interventions for motor (re)learning

Classical surrogate simulation of quantum systems with LOWESA

We introduce LOWESA as a classical algorithm for faithfully simulating quantum systems via a classically constructed surrogate expectation landscape. After an initial overhead to build the surrogate landscape, one can rapidly study entire families of Hamiltonians, initial states and target observables. As a case study, we simulate the 127-qubit transverse-field Ising quantum system on a heavy-hexagon lattice with up to 20 Trotter steps which was recently presented in Nature 618, 500-505 (2023). Specifically, we approximately reconstruct (in minutes to hours on a laptop) the entire expectation landscape spanned by the heavy-hex Ising model. The expectation of a given observable can then be evaluated at different parameter values, i.e. with different onsite magnetic fields and coupling strengths, in fractions of a second on a laptop. This highlights that LOWESA can attain state-of-the-art performance in quantum simulation tasks, with the potential to become the algorithm of choice for scanning a wide range of systems quickly.Comment: 13 pages, 6 figure

On nonlinear transformations in quantum computation

While quantum computers are naturally well-suited to implementing linear operations, it is less clear how to implement nonlinear operations on quantum computers. However, nonlinear subroutines may prove key to a range of applications of quantum computing from solving nonlinear equations to data processing and quantum machine learning. Here we develop a series of basic subroutines for implementing nonlinear transformations of input quantum states. Our algorithms are framed around the concept of a weighted state, a mathematical entity describing the output of an operational procedure involving both quantum circuits and classical post-processing.Comment: 10 pages, 9 figures in the main text. 14 pages, 6 figures in the Appendice

QSlack: A slack-variable approach for variational quantum semi-definite programming

Solving optimization problems is a key task for which quantum computers could possibly provide a speedup over the best known classical algorithms. Particular classes of optimization problems including semi-definite programming (SDP) and linear programming (LP) have wide applicability in many domains of computer science, engineering, mathematics, and physics. Here we focus on semi-definite and linear programs for which the dimensions of the variables involved are exponentially large, so that standard classical SDP and LP solvers are not helpful for such large-scale problems. We propose the QSlack and CSlack methods for estimating their optimal values, respectively, which work by 1) introducing slack variables to transform inequality constraints to equality constraints, 2) transforming a constrained optimization to an unconstrained one via the penalty method, and 3) replacing the optimizations over all possible non-negative variables by optimizations over parameterized quantum states and parameterized probability distributions. Under the assumption that the SDP and LP inputs are efficiently measurable observables, it follows that all terms in the resulting objective functions are efficiently estimable by either a quantum computer in the SDP case or a quantum or probabilistic computer in the LP case. Furthermore, by making use of SDP and LP duality theory, we prove that these methods provide a theoretical guarantee that, if one could find global optima of the objective functions, then the resulting values sandwich the true optimal values from both above and below. Finally, we showcase the QSlack and CSlack methods on a variety of example optimization problems and discuss details of our implementation, as well as the resulting performance. We find that our implementations of both the primal and dual for these problems approach the ground truth, typically achieving errors of order $10^{-2}$.Comment: 66 pages, 11 figure