Automated detection of symmetry-protected subspaces in quantum simulations

The analysis of symmetry in quantum systems is of utmost theoretical importance, useful in a variety of applications and experimental settings, and is difficult to accomplish in general. Symmetries imply conservation laws, which partition Hilbert space into invariant subspaces of the time-evolution operator, each of which is demarcated according to its conserved quantity. We show that, starting from a chosen basis, any invariant, symmetry-protected subspaces which are diagonal in that basis are discoverable using transitive closure on graphs representing state-to-state transitions under $k$-local unitary operations. Importantly, the discovery of these subspaces relies neither upon the explicit identification of a symmetry operator or its eigenvalues nor upon the construction of matrices of the full Hilbert space dimension. We introduce two classical algorithms, which efficiently compute and elucidate features of these subspaces. The first algorithm explores the entire symmetry-protected subspace of an initial state in time complexity linear to the size of the subspace by closing local basis state-to-basis state transitions. The second algorithm determines, with bounded error, if a given measurement outcome of a dynamically-generated state is within the symmetry-protected subspace of the state in which the dynamical system is initialized. We demonstrate the applicability of these algorithms by performing post-selection on data generated from emulated noisy quantum simulations of three different dynamical systems: the Heisenberg-XXX model and the $T_6$ and $F_4$ quantum cellular automata. Due to their efficient computability and indifference to identifying the underlying symmetry, these algorithms lend themselves to the post-selection of quantum computer data, optimized classical simulation of quantum systems, and the discovery of previously hidden symmetries in quantum mechanical systems.Comment: 23 pages, 7 figures, 4 appendice

Blending of PLA and TPU in a Single Screw Extruder to Create 3D Printing Filament

3D printing has become of interest to the plastics industry to mainstream manufacturing because it can significantly increase the speed and reduce the cost of part production compared to traditional manufacturing methods for small production runs in the plastics industry. Poly lactic acid (PLA) is a hard, strong thermoplastic material that is processed in several different ways, including extrusion for 3D printing filament. Given its rigid nature, adding thermoplastic polyurethane (TPU), which is highly elastic, will improve filament flexibility while maintaining the desirable physical properties from PLA in a blended filament despite the two being immiscible with each other. Initial blending of the two materials was performed on a single screw Yellow Jacket extruder. PLA and TPU were blended in the following ratios: 100% PLA/0% TPU, 90% PLA/10% TPU, 70% PLA/30% TPU, 50% PLA/50% TPU, 30% PLA/70% TPU, 10% PLA/90% TPU, and 0% PLA/100% TPU by weight. Extrusion process parameters were adjusted until consistent filament diameters were achieved. The filaments were then analyzed by TGA and DSC for thermal properties and tensile testing for mechanical properties. The blend ratio by weight of 70% PLA/30% TPU and 50% PLA/50% TPU were found to have the most uniform diameters compared to the other ratios. The thermal analysis from TGA and DSC showed little thermal degradation after processing and the mechanical testing showed promising results for use as 3D printing filament

Proposed manufacturing facility for nylon 6,6

The purpose of this project was to design an economically viable process that produces 85 million pounds of nylon 6,6 annually. This process would be carried out in a new plant that would be built in the Calvert City, Kentucky area. The full capacity fiber design achieves this production goal and produces nylon 6,6 with a number average molecular weight of 2635 amu and an average degree of polymerization of 23.3 monomers per molecule.The production of nylon 6,6 fibers was determined to be more economically attractive than granular nylon 6,6 due to its much larger net present value (NPV) of approximately $174 million compared to the granular NPV of negative$190 million. The production of nylon 6,6 fibers had a discount cash flow rate of return (DCFROR) of 243% and a discounted payback period of only 6 months. The production of nylon 6,6 fibers is still economically attractive and physically feasible under turndown conditions with an NPV of approximately $98 million, a DCFROR of 145$1.59 per pound as opposed to the $1.51 per pound that full scale production costs. It is recommended that the design to produce nylon 6,6 fiber is carried forward to the detailed design stage and operated at full capacity.The reaction was simulated in Polymath using two key assumptions. The reaction was carried out at 72.5 psig and 622 degrees F while the vapor pressure of water under these conditions was greater than 1400 psig. This discrepancy in reactor pressure and vapor pressure led to the assumption that the water produced by the condensation polymerization reaction and the water introduced by the feed stream instantly vaporizes and it is vented from the reactor. HMDA is significantly less volatile than water and was assumed to be non-volatile under reaction conditions. The 72.5 psig reaction pressure was chosen to help justify this assumption without impacting capital costs significantly. Further investigation into these two assumptions and the effects of deviations from the simulation model are recommended

Calculating the expected value function of a two-stage stochastic optimization program with a quantum algorithm

Stochastic optimization problems are powerful models for the operation of systems under uncertainty and are in general computationally intensive to solve. Two-stage stochastic optimization is one such problem, where the objective function involves calculating the expected cost of future decisions to inform the best decision in the present. In general, even approximating this expectation value is a #P-Hard problem. We provide a quantum algorithm to estimate the expected value function in a two-stage stochastic optimization problem in time complexity largely independent from the complexity of the random variable. Our algorithm works in two steps: (1) By representing the random variable in a register of qubits and using this register as control logic for a cost Hamiltonian acting on the primary system of qubits, we use the quantum alternating operator ansatz (QAOA) with operator angles following an annealing schedule to converge to the minimal decision for each scenario in parallel. (2) We then use Quantum Amplitude Estimation (QAE) to approximate the expected value function of the per-scenario optimized wavefunction. We show that the annealing time of the procedure in (1) is independent of the number of scenarios in the probability distribution. Additionally, estimation error in QAE converges inverse-linear in the number of "repetitions" of the algorithm, as opposed to converging as the inverse of the square root in traditional Monte Carlo sampling. Because both QAOA and QAE are expected to have polynomial advantage over their classical computing counterparts, we expect our algorithm to have polynomial advantage over classical methods to compute the expected value function. We implement our algorithms for a simple optimization problem inspired by operating the power grid with renewable generation and uncertainty in the weather, and give numerical evidence to support our arguments.Comment: 20 pages, 5 figure

2007-2008 Philharmonia Season Program Spring

Philharmonia No. 4 February 16, 2008 at 7:30 PM and February 17, 2008 at 4:00 PM Jon Robertson, guest conductor ; Daniela Shtereva, violin Academic Festival Overture in C Minor, op. 80 / Johaness Brahms -- Violin Concerto in D Major, op. 35 / Pyotr Ilyich Tchaikovsky -- Symphony No. 8 in G Major, op. 88 / Antonín Dvořák Philharmonia No. 5 2007 Concerto Competition Winner\u27s Concert March 29, 2008 at 7:30 PM and March 30, 2008 at 4:00 PM Albert-George Schram, conductor and music director ; Caleb Jones, cello Symphonic Metamorphoses on Themes by Carl Maria von Weber / Paul Hindemith -- Cello Concerto in A Minor, op. 129 / Robert Schumann -- Pétrouchka: Burlesque in Four Scenes (1947 version) / Igor Stravinskyhttps://spiral.lynn.edu/conservatory_philharmonia/1029/thumbnail.jp

Understanding the different challenges facing students in transitioning to university particularly with a focus on ethnicity

A positive and successful transition into University is crucial if students are to stay the course in higher education and experience successful outcomes. However, challenges exist in ensuring a connected transition from secondary and further education to higher education that is inclusive and supports the diversity in our current undergraduate student body. We set out to explore the diverse experiences that first year students report about their recent transition to a post-1992 University. We were particularly interested in how these experiences and challenges differed by ethnicity. This is incredibly important given the disparity, recognised in the sector, in the attainment of Black and Minority Ethnic (BME) students compared to their White counterparts and particularly pertinent that this trend reverses attainment patterns in secondary education. This paper summarises some of our key findings in determining the challenges facing students from different backgrounds in their transition to university. It argues that Universities will have to change their transition and wider offer to ensure that diverse students feel welcomed and develop a sense belonging in Higher Education in order for them to achieve successful outcomes

The Effect of Value-Focused Discussions on Scientists' Ethical Decision Making

Many scientists view science as value-free, despite the fact that both epistemic and non-epistemic values structure scientific inquiry. Current ethics training usually focuses on transmitting knowledge about high-level ethical concepts or rules and is widely regarded as ineffective. We argue that ethics training will be more effective at improving ethical decision making if it focuses on connecting values to science. We pull from philosophy and psychology to define ethical decision making using the Four Component Model. This model states that in order to make an ethical decision someone must consider four components: moral sensitivity, moral reasoning, moral motivation, and moral implementation. We formed a moderated fellowship of fourteen science faculty from different disciplines who met for ten sessions over the course of a year, where they discussed the values embedded in different scientific norms. We then conducted interviews before and after the year-long fellowship that involved guided reflection of scenarios where there was some kind of ethical misconduct where the scientific practice required value judgements (e.g using unpublished data in their own work). We looked at how the fellowship affected the scientists' ability to recognize ethical dimensions regarding the scenarios. We found that this fellowship improved moral sensitivity, but their moral reasoning does not improve. We outlined our approach on how to look at scientists' ethical decision making and made recommendations on how to improve our approach. This work can inform future ethical training to align better with what scientists value and introduce useful concepts from philosophy and psychology to education research in physics