We solve a multi-period portfolio optimization problem using D-Wave Systems' quantum annealer. We derive a formulation of the problem, discuss several possible integer encoding schemes, and present numerical examples that show high success rates. The formulation incorporates transaction costs (including permanent and temporary market impact), and, significantly, the solution does not require the inversion of a covariance matrix. The discrete multi-period portfolio optimization problem we solve is significantly harder than the continuous variable problem. We present insight into how results may be improved using suitable software enhancements, and why current quantum annealing technology limits the size of problem that can be successfully solved today. The formulation presented is specifically designed to be scalable, with the expectation that as quantum annealing technology improves, larger problems will be solvable using the same techniques.Comment: 7 pages; expanded and update

Abstract-We solve a multi-period portfolio optimization problem using D-Wave Systems' quantum annealer. We derive a formulation of the problem, discuss several possible integer encoding schemes, and present numerical examples that show high success rates. The formulation incorporates transaction costs (including permanent and temporary market impact), and, significantly, the solution does not require the inversion of a covariance matrix. The discrete multiperiod portfolio optimization problem we solve is significantly harder than the continuous variable problem. We present insight into how results may be improved using suitable software enhancements and why current quantum annealing technology limits the size of problem that can be successfully solved today. The formulation presented is specifically designed to be scalable, with the expectation that as quantum annealing technology improves, larger problems will be solvable using the same techniques.

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Modeling of a clinical lab carbon footprint is performed in this study from the aspects of electricity, water, gas consumption and waste production from lab instruments. These environmental impact indicators can be expressed in the form of the CO 2 equivalent. For each type of clinical test, the corresponding consumption of energy resources and the production of plastics and papers are taken into consideration. In addition, the basic lab infrastructures such as heating, ventilation, air-conditioning (HVAC) systems, lights, and computers also contribute to the environmental impact. Human comfort is to be taken into account when optimizing the operation of lab instruments, and is related to the operation of HVAC and lighting systems. The detailed modeling takes into consideration the types of clinical tests, operating times, and instrument specifications. Two ways of disposing waste are classified. Moreover, the indoor environment is modeled. A case study of the Biochrom 30+ amino acid analyzer physiological system in Alder Hey Children's Hospital is carried out, and the methods of mitigating the overall environmental impacts are discussed. Furthermore, the influence of climate on the results is investigated by using the climate data in Liverpool and Athens in October.