Exploring entanglement phenomena with near-term quantum computers

A methodology to explore quantum entanglement phenomena on near-term quantum computers is presented. The method combines two prominent Noisy Intermediate-Scale Quantum (NISQ) algorithms, the variational quantum eigensolver (VQE) and pairwise tomography, to extract pairwise quantum properties from quantum many-body systems. VQE prepares a parametrized quantum circuit and optimizes it to represent the ground state of the system under study. Pairwise tomography provides an exponential decrease in the required measurements to construct two-qubit reduced density matrices. Two pairwise quantities, mutual information and concurrence, are used to construct complex network representations of the system. Then, network properties can be used to analyze the entanglement structures. Three quantum spin chains are explored: the Ising model, the spin-1/2 XX model and the XXZ model. The methodology is benchmarked with known results and new results for the XXZ model are presented. Applications for the study of fundamental physics are explored. More specifically, emergent space from quantum entanglement is studied. Mutual information between parts of a redundancy-constrained system is used to define a metric that is then embedded into a smooth manifold embedded in Rᴰ. Effects of entanglement perturbations on the geometry of the embedding are studied.Tässä Pro Gradussa esitetään metodologia, jonka avulla voidaan tutkia kvanttilomittumisilmiöitä lähitulevaisuuden kvanttitietokoneilla. Tämä metodi yhdistää kaksi merkittävää kvanttialgoritmia, jotka ovat Variaationaalinen KvanttiOminaisarvoLaskija (VKOL) (eng. Variational Quantum Eigensolver (VQE)) ja parittainen kvanttitilatomografia (eng. pairwise quantum state tomography). Nämä algoritmit on suunniteltu lähitulevaisuuden meluisille keskikokoisille kvattitietokoneille (MEKEKVA (eng. noisy intermediate-scale quantum (NISQ)) sopiviksi. VKOL valmistaa parametrisoidun kvanttipiirin, jonka se optimoi edustamaan tutkittavana olevan systeemin perustilaa. Parittainen kvanttitilatomografia laskee exponentiaalisesti tarvittavien mittausten määrää, jotta systeemin perustilasta saadaan rakennettua redusoidut tiheysmatriisit kaikille kahden kubitin pareille. Näistä redusoiduista tiheysmatriiseista voidaan laskea parittaisia ominaisuuksia systeemin perustilalle. Kahta parittaista ominaisuutta, yhteistä informaatiota (eng. mutual information) ja konkurrensia (eng. concurrence), käytetään muodostamaan systeemille kompleksiset verkostoesitykset. Näiden verkostojen ominaisuuksilla voidaan sitten analysoida kvanttilomittumisrakenteita. Kolmea kvanttispiniketjua tutkitaan: Ising mallia, spin-1/2 XX mallia sekä XXZ mallia. Tässä tutkielmassa esitetyn metodin suorituskykyä testataan vertaamalla saatuja tuloksia jo tunnettuihin tuloksiin. Sen lisäksi, myös uusia tuloksia esitetään XXZ mallille. Metodin käyttökohteita fundamentaalisen fysiikan tutkimuksessa tutkitaan myös. Tutkimuksen kohteena on emergentin avaruuden syntyminen kvanttilomittumisesta. Redundanssirajoitettujen (eng. redundancy-constrained) systeemien välistä yhteistä informaatiota käytetään luomaan metriikka, joka upotetaan sileään monistoon, joka on upotettuna Rᴰ:hen. Kvanttilomittumisen häiriöiden vaikutusta upotuksen geometriaan tutkitaan

Mitigating the measurement overhead of ADAPT-VQE with optimised informationally complete generalised measurements

ADAPT-VQE stands out as a robust algorithm for constructing compact ans\"atze for molecular simulation. It enables to significantly reduce the circuit depth with respect to other methods, such as UCCSD, while achieving higher accuracy and not suffering from so-called barren plateaus that hinder the variational optimisation of many hardware-efficient ans\"atze. In its standard implementation, however, it introduces a considerable measurement overhead in the form of gradient evaluations trough estimations of many commutator operators. In this work, we mitigate this measurement overhead by exploiting a recently introduced method for energy evaluation relying on Adaptive Informationally complete generalised Measurements (AIM). Besides offering an efficient way to measure the energy itself, Informationally Complete (IC) measurement data can be reused to estimate all the commutators of the operators in the operator pool of ADAPT-VQE, using only classically efficient post-processing. We present the AIM-ADAPT-VQE scheme in detail, and investigate its performance with several H4 Hamiltonians and operator pools. Our numerical simulations indicate that the measurement data obtained to evaluate the energy can be reused to implement ADAPT-VQE with no additional measurement overhead for the systems considered here. In addition, we show that, if the energy is measured within chemical precision, the CNOT count in the resulting circuits is close to the ideal one. With scarce measurement data, AIM-ADAPT-VQE still converges to the ground state with high probability, albeit with an increased circuit depth in some cases

How can talent remain within the business? : A qualitative study on employee retention activities and strategies within the retail sector

Since the retail industry has been drastically affected due to the growth of online shopping, companies have become more aware of higher competition in their current physical stores. Since there is still demand for companies to have physical stores, they have to understand the values those remaining physical stores possess and understand the undergoing changes in the sector. The change has created a value of digitalization and as it looks the digital environment remains cheaper than labour work in stores which in turn creates a certain attraction of lowering cost and maximizing profit. But statistics have shown that retail suffers low retention rates, and it relates to costs of recruiting, education, loss of sales, service quality and much more. It has become more important due to the high turnover cost to retain employees, and especially those who are “talented” and to attract those employees has become more important. Our research is based on different literature which revolves around the fields of employee retention factors and retention strategies within the retail industry. There is a high academic attention towards retention strategies in general, but far less attention is paid towards the retail industry. We chose a manager approach toward investigating our research questions, since the majority of earlier studies have based their research from employees' perspectives toward why they leave their jobs, or why they stay. Our thesis answers the research question of “What strategies or activities are made by managers in order to retain talented employees within the Swedish retail sector?”. In order to find an answer to our research question, we conducted a qualitative study which involved interviewing managers within the Swedish retail industry. Through thematic analysis we discussed different key takeaways from our empirical findings, which we compared to our theoretical framework, in order to later conclude our discussion into our conclusion chapter. Our findings show how different retention factors, namely: Social support, development opportunities, autonomy, compensation and work life balance are being implemented in practice within different organizations. While our thesis provides answers on how retention factors are being implemented within the Swedish retail sector, it is necessary to research the subject further in order to gain more detailed insights on the implementation of the retention methods and strategies used, as well as gaining an employee perspective on how the effectiveness of each method and strategy are being perceived