Quantum algorithms for approximate function loading

Loading classical data into quantum computers represents an essential stage in many relevant quantum algorithms, especially in the field of quantum machine learning. Therefore, the inefficiency of this loading process means a major bottleneck for the application of these algorithms. Here, we introduce two approximate quantum-state preparation methods inspired by the Grover-Rudolph algorithm, which partially solve the problem of loading real functions. Indeed, by allowing for an infidelity $\epsilon$ and under certain smoothness conditions, we prove that the complexity of Grover-Rudolph algorithm can be reduced from $\mathcal{O}(2^{n})$ to $\mathcal{O}(2^{k_0(\epsilon)})$, with $n$ the number of qubits and $k_0(\epsilon)$ asymptotically independent of $n$. This leads to a dramatic reduction in the number of required two-qubit gates. Aroused by this result, we also propose a variational algorithm capable of loading functions beyond the aforementioned smoothness conditions. Our variational ansatz is explicitly tailored to the landscape of the function, leading to a quasi-optimized number of hyperparameters. This allows us to achieve high fidelity in the loaded state with high speed convergence for the studied examples

The Cost of Emulating a Small Quantum Annealing Problem in the Circuit-Model

Demonstrations of quantum advantage for certain sampling problems has generated considerable excitement for quantum computing and has further spurred the development of circuit-model quantum computers, which represent quantum programs as a sequence of quantum gates acting on a finite number of qubits. Amongst this excitement, analog quantum computation has become less prominent, with the expectation that circuit-model quantum computers will eventually be sufficient for emulating analog quantum computation and thus rendering analog quantum computation obsolete. In this work we explore the basic requirements for emulating a specific analog quantum computation in the circuit model: the preparation of a biased superposition of degenerate ground states of an Ising Hamiltonian using an adiabatic evolution. We show that the overhead of emulation is substantial even for this simple problem. This supports using analog quantum computation for solving time-dependent Hamiltonian dynamics in the short and mid-term, assuming analog errors can be made low enough and coherence times long enough to solve problems of practical interest

Efficient amplitude encoding of polynomial functions into quantum computers

Loading functions into quantum computers represents an essential step in several quantum algorithms, such as in the resolution of partial derivative equations. Therefore, the inefficiency of this process leads to a major bottleneck for the application of these algorithms. Here, we present and compare two efficient methods for the amplitude encoding of real polynomial functions. The first one relies on the matrix product state representation, where we study and benchmark the approximations of the target state when the bond dimension is assumed to be small. The second algorithm combines two subroutines, initially we encode the linear function into the quantum registers with a swallow sequence of multi-controlled gates that loads its Hadamard-Walsh series expansion, followed by the inverse discrete Hadamard-Walsh transform. Then, we use this construction as a building block to achieve a $\mathcal{O}(n)$ block encoding of the amplitudes corresponding to the linear function and apply the quantum singular value transformation that implements the corresponding polynomial transformation to the block encoding of the amplitudes. Additionally, we explore how truncating the Hadamard-Walsh series of the linear function affects the final fidelity of the target state, reporting high fidelities with small resources

Estimación de la humedad de tapones de corcho mediante medida de la resistencia electrica

En este trabajo se exponen los resultados obtenidos en el Departamento de Productos Forestales del CIFOR-INIA sobre la relación entre la resistencia eléctrica y el contenido de humedad de los tapones de corcho. Estos resultados muestran que los medidores de humedad utilizados habitualmente en la industria pueden alcanzar una precisión elevada, siempre y cuando se tenga en cuenta la influencia de los distintos factores que afectan a la relación resistencia eléctrica-humedad: tipo de tapón, dirección de la medida, temperatura del material. Además, se han obtenido los modelos matemáticos que permiten la calibración de cualquier aparato de este tipo de manera rápida y sencill

Towards Prediction of Financial Crashes with a D-Wave Quantum Computer

Prediction of financial crashes in a complex financial network is known to be an NP-hard problem, i.e., a problem which cannot be solved efficiently with a classical computer. We experimentally explore a novel approach to this problem by using a D-Wave quantum computer to obtain financial equilibrium more efficiently. To be specific, the equilibrium condition of a nonlinear financial model is embedded into a higher-order unconstrained binary optimization (HUBO) problem, which is then transformed to a spin-$1/2$ Hamiltonian with at most two-qubit interactions. The problem is thus equivalent to finding the ground state of an interacting spin Hamiltonian, which can be approximated with a quantum annealer. Our experiment paves the way to study quantitative macroeconomics, enlarging the number of problems that can be handled by current quantum computers

Quantum approximated cloning-assisted density matrix exponentiation

Classical information loading is an essential task for many processing quantum algorithms, constituting a cornerstone in the field of quantum machine learning. In particular, the embedding techniques based on Hamiltonian simulation techniques enable the loading of matrices into quantum computers. A representative example of these methods is the Lloyd-Mohseni-Rebentrost protocol, which efficiently implements matrix exponentiation when multiple copies of a quantum state are available. However, this is a quite ideal set up, and in a realistic scenario, the copies are limited and the non-cloning theorem prevents from producing more exact copies in order to increase the accuracy of the protocol. Here, we propose a method to circumvent this limitation by introducing imperfect quantum copies that significantly enhance the performance of previous proposals

The influence of the moisture content on the electrical resistance of two types of cork stoppers

The relationship between the log of the electrical resistance (ER; measured using pin electrodes) and the moisture content (MC) have not been reported in any form of cork. That is important for the cork stoppers industry because it should help in the design and verification of more precise devices for measuring cork moisture content. In this study, using linear regression techniques, different regression models of the type log(Log(R) + 1) = axh + b were derived to describe the relationship ERMC, that was measured using pin electrodes on two types of cork stoppers [natural (N) and agglomerate(AG)]. The results obtained show that in the models proposed, the moisture content of AG cork stoppers can be estimated with an error of ± 0.3%, while that of N stoppers can be estimated with an error of 0.5%. Neither the geographical origin of the N corks nor the surface treatment to which the AG corks were subjected significantly affected the proposed models. Therefore, the moisture content of cork stoppers could be measured at the industrial scale using electrical resistancetype moisture meter

A Discrete Choice Experiment to assess patients’ preferences for HIV treatment in the rural population in Colombia

"Aim: To elicit patients’ preferences for HIV treatment of the rural population in Colombia. Methods: A discrete choice experiment (DCE), conducted in a HIV clinic in Bogotá, was used to examine the trade-off between five HIV treatment attributes: effect on life expectancy, effect on physical activity, risk of moderate side-effects, accessibility to clinic, and economic costs to access controls. Attributes selection was based on literature review, expert consultation and a focus group with six patients. An efficient experimental design was used to define two versions of the questionnaire with each of 12 choice sets and a dominance task was added to check reliability. A mixed logit model was then used to analyse the data and sub-group analyses were conducted on the basis of age, gender, education, and sexual preference. Results: A total of 129 HIV patients were included for analysis. For all treatment attributes, significant differences between at least two levels were observed, meaning that all attributes were significant predictors of choice. Patients valued the effect on physical activity (conditional relative importance of 27.5%) and the effect on life expectancy (26.0%) the most. Sub-group analyses regard age and education showed significant differences: younger patients and high educated patients valued the effect on physical activity the most important, whereas older patients mostly valued the effect on life expectancy and low educated patients mostly valued the accessibility to clinic. Limitations: One potential limitation is selection bias, as only patients from one HIV clinic were reached. Additionally, questionnaires were partly administered in the waiting rooms, which potentially led to noise in the data. Conclusions: This study suggests that all HIV treatment characteristics included in this DCE were important and that HIV patients from rural Colombia valued short-term efficacy (i.e. effect on physical activity) and long-term efficacy (i.e. effect on life expectancy) the most. © 2020, © 2020 The Author(s). Published by Informa UK Limited, trading as Taylor and Francis Group.

A Discrete Choice Experiment to assess patients’ preferences for HIV treatment in the urban population in Colombia

Aim: This study aimed to assess patients' preferences for HIV treatment in an urban Colombian population. Methods: A Discrete Choice Experiment (DCE) was conducted. Urban Colombian HIV patients were asked to repetitively choose between two hypothetical treatments that differ in regard to five attributes 'effect on life expectancy', 'effect on physical activity', 'risk of moderate side effects, 'accessibility to clinic' and 'economic cost to access controls'. Twelve choice sets were made using an efficient design. A Mixed Logit Panel Model was used for the analysis and subgroup analyses were performed according to age, gender, education level and sexual preference. Results: A total of 224 HIV patients were included. All attributes were significant, indicating that there were differences between at least two levels of each attribute. Patients preferred to be able to perform all physical activity without difficulty, to have large positive effects on life expectancy, to travel less than 2 h, to have lower risk of side-effects and to have subsidized travel costs. The attributes 'effect on physical activity' and 'effects on life expectancy' were deemed the most important. Sub-analyses showed that higher educated patients placed more importance on the large positive effects of HIV treatment, and a more negative preference for subsidized travel cost (5% level). Limitations: A potential limitation is selection bias as it is difficult to make a systematic urban/rural division of respondents. Additional, questionnaires were partly administered in the waiting rooms, which potentially led to some noise in the data. Conclusions: Findings suggests that short-term efficacy (i.e. effect on physical activity) and long-term efficacy (i.e. effect on life expectancy) are the most important treatment characteristics for HIV urban patients in Colombia. Preference data could provide relevant information for clinical and policy decision-making to optimize HIV care