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

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

Development of a prediction model for postoperative pneumonia A multicentre prospective observational study

BACKGROUND Postoperative pneumonia is associated with increased morbidity, mortality and costs. Prediction models of pneumonia that are currently available are based on retrospectively collected data and administrative coding systems. OBJECTIVE To identify independent variables associated with the occurrence of postoperative pneumonia. DESIGN A prospective observational study of a multicentre cohort (Prospective Evaluation of a RIsk Score for postoperative pulmonary COmPlications in Europe database). SETTING Sixty-three hospitals in Europe. PATIENTS Patients undergoing surgery under general and/or regional anaesthesia during a 7-day recruitment period. MAIN OUTCOME MEASURE The primary outcome was postoperative pneumonia. Definition: the need for treatment with antibiotics for a respiratory infection and at least one of the following criteria: new or changed sputum; new or changed lung opacities on a clinically indicated chest radiograph; temperature more than 38.3 degrees C; leucocyte count more than 12 000 mu l(-1). RESULTS Postoperative pneumonia occurred in 120 out of 5094 patients (2.4%). Eighty-two of the 120 (68.3%) patients with pneumonia required ICU admission, compared with 399 of the 4974 (8.0%) without pneumonia (P < 0.001). We identified five variables independently associated with postoperative pneumonia: functional status [odds ratio (OR) 2.28, 95% confidence interval (CI) 1.58 to 3.12], pre-operative SpO(2) values while breathing room air (OR 0.83, 95% CI 0.78 to 0.84), intra-operative colloid administration (OR 2.97, 95% CI 1.94 to 3.99), intra-operative blood transfusion (OR 2.19, 95% CI 1.41 to 4.71) and surgical site (open upper abdominal surgery OR 3.98, 95% CI 2.19 to 7.59). The model had good discrimination (c-statistic 0.89) and calibration (Hosmer-Lemeshow P = 0.572). CONCLUSION We identified five variables independently associated with postoperative pneumonia. The model performed well and after external validation may be used for risk stratification and management of patients at risk of postoperative pneumonia