A framework for engineering quantum likelihood functions for expectation estimation

We develop a framework for characterizing and analyzing engineered likelihood functions (ELFs), which play an important role in the task of estimating the expectation values of quantum observables. These ELFs are obtained by choosing tunable parameters in a parametrized quantum circuit that minimize the expected posterior variance of an estimated parameter. We derive analytical expressions for the likelihood functions arising from certain classes of quantum circuits and use these expressions to pick optimal ELF tunable parameters. Finally, we show applications of ELFs in the Bayesian inference framework.Comment: 52 page

Entanglement Scaling in Quantum Advantage Benchmarks

A contemporary technological milestone is to build a quantum device performing a computational task beyond the capability of any classical computer, an achievement known as quantum adversarial advantage. In what ways can the entanglement realized in such a demonstration be quantified? Inspired by the area law of tensor networks, we derive an upper bound for the minimum random circuit depth needed to generate the maximal bipartite entanglement correlations between all problem variables (qubits). This bound is (i) lattice geometry dependent and (ii) makes explicit a nuance implicit in other proposals with physical consequence. The hardware itself should be able to support super-logarithmic ebits of entanglement across some poly($n$) number of qubit-bipartitions, otherwise the quantum state itself will not possess volumetric entanglement scaling and full-lattice-range correlations. Hence, as we present a connection between quantum advantage protocols and quantum entanglement, the entanglement implicitly generated by such protocols can be tested separately to further ascertain the validity of any quantum advantage claim.Comment: updates and improvements from the review process; 8 pages; 3 figure

Measurement of the charged pion mass using X-ray spectroscopy of exotic atoms

The $5g-4f$ transitions in pionic nitrogen and muonic oxygen were measured simultaneously by using a gaseous nitrogen-oxygen mixture at 1.4\,bar. Due to the precise knowledge of the muon mass the muonic line provides the energy calibration for the pionic transition. A value of (139.57077\,$\pm$\,0.00018)\,MeV/c$^{2}$ ($\pm$\,1.3ppm) is derived for the mass of the negatively charged pion, which is 4.2ppm larger than the present world average

Fluorescence Tomography Characterization for Sub-Surface Imaging with Protoporphyrin IX

Optical imaging of fluorescent objects embedded in a tissue simulating medium was characterized using non-contact based approaches to fluorescence remittance imaging (FRI) and sub-surface fluorescence diffuse optical tomography (FDOT). Using Protoporphyrin IX as a fluorescent agent, experiments were performed on tissue phantoms comprised of typical in-vivo tumor to normal tissue contrast ratios, ranging from 3.5:1 up to 10:1. It was found that tomographic imaging was able to recover interior inclusions with high contrast relative to the background; however, simple planar fluorescence imaging provided a superior contrast to noise ratio. Overall, FRI performed optimally when the object was located on or close to the surface and, perhaps most importantly, FDOT was able to recover specific depth information about the location of embedded regions. The results indicate that an optimal system for localizing embedded fluorescent regions should combine fluorescence reflectance imaging for high sensitivity and sub-surface tomography for depth detection, thereby allowing more accurate localization in all three directions within the tissue

Hadronic shift in pionic hydrogen

The hadronic shift in pionic hydrogen has been redetermined to be $\epsilon_{1s}=7.086\,\pm\,0.007(stat)\,\pm\,0.006(sys)$\,eV by X-ray spectroscopy of ground state transitions applying various energy calibration schemes. The experiment was performed at the high-intensity low-energy pion beam of the Paul Scherrer Institut by using the cyclotron trap and an ultimate-resolution Bragg spectrometer with bent crystals.Comment: 10 pages, 6 figure

First observation of two hyperfine transitions in antiprotonic He-3

We report on the first experimental results for microwave spectroscopy of the hyperfine structure of antiprotonic He-3. Due to the helium nuclear spin, antiprotonic He-3 has a more complex hyperfine structure than antiprotonic He-4 which has already been studied before. Thus a comparison between theoretical calculations and the experimental results will provide a more stringent test of the three-body quantum electrodynamics (QED) theory. Two out of four super-super-hyperfine (SSHF) transition lines of the (n,L)=(36,34) state were observed. The measured frequencies of the individual transitions are 11.12559(14) GHz and 11.15839(18) GHz, less than 1 MHz higher than the current theoretical values, but still within their estimated errors. Although the experimental uncertainty for the difference of these frequencies is still very large as compared to that of theory, its measured value agrees with theoretical calculations. This difference is crucial to be determined because it is proportional to the magnetic moment of the antiproton.Comment: 8 pages, 6 figures, just published (online so far) in Physics Letters

Infinets: The parallel syntax for non-wellfounded proof-theory

Logics based on the µ-calculus are used to model induc-tive and coinductive reasoning and to verify reactive systems. A well-structured proof-theory is needed in order to apply such logics to the study of programming languages with (co)inductive data types and automated (co)inductive theorem proving. While traditional proof system suffers some defects, non-wellfounded (or infinitary) and circular proofs have been recognized as a valuable alternative, and significant progress have been made in this direction in recent years. Such proofs are non-wellfounded sequent derivations together with a global validity condition expressed in terms of progressing threads. The present paper investigates a discrepancy found in such proof systems , between the sequential nature of sequent proofs and the parallel structure of threads: various proof attempts may have the exact threading structure while differing in the order of inference rules applications. The paper introduces infinets, that are proof-nets for non-wellfounded proofs in the setting of multiplicative linear logic with least and greatest fixed-points (µMLL ∞) and study their correctness and sequentialization. Inductive and coinductive reasoning is pervasive in computer science to specify and reason about infinite data as well as reactive properties. Developing appropriate proof systems amenable to automated reasoning over (co)inductive statements is therefore important for designing programs as well as for analyzing computational systems. Various logical settings have been introduced to reason about such inductive and coinductive statements, both at the level of the logical languages modelling (co)induction (such as Martin Löf's inductive predicates or fixed-point logics, also known as µ-calculi) and at the level of the proof-theoretical framework considered (finite proofs with explicit (co)induction rulesà la Park [23] or infinite, non-wellfounded proofs with fixed-point unfold-ings) [6-8, 4, 1, 2]. Moreover, such proof systems have been considered over classical logic [6, 8], intuitionistic logic [9], linear-time or branching-time temporal logic [19, 18, 25, 26, 13-15] or linear logic [24, 16, 4, 3, 14]

Low specificity of determine HIV1/2 RDT using whole blood in south west Tanzania

Objective: To evaluate the diagnostic performance of two rapid detection tests (RDTs) for HIV 1/2 in plasma and in whole blood samples. Methods: More than 15,000 study subjects above the age of two years participated in two rounds of a cohort study to determine the prevalence of HIV. HIV testing was performed using the Determine HIV 1/2 test (Abbott) in the first (2006/2007) and the HIV 1/2 STAT-PAK Dipstick Assay (Chembio) in the second round (2007/2008) of the survey. Positive results were classified into faint and strong bands depending on the visual appearance of the test strip and confirmed by ELISA and Western blot. Results: The sensitivity and specificity of the Determine RDT were 100% (95% confidence interval = 86.8 to 100%) and 96.8% (95.9 to 97.6%) in whole blood and 100% (99.7 to 100%) and 97.9% (97.6 to 98.1%) in plasma respectively. Specificity was highly dependent on the tested sample type: when using whole blood, 67.1% of positive results were false positive, as opposed to 17.4% in plasma. Test strips with only faint positive bands were more often false positive than strips showing strong bands and were more common in whole blood than in plasma. Evaluation of the STAT-PAK RDT in plasma during the second year resulted in a sensitivity of 99.7% (99.1 to 99.9%) and a specificity of 99.3% (99.1 to 99.4%) with 6.9% of the positive results being false. Conclusions: Our study shows that the Determine HIV 1/2 strip test with its high sensitivity is an excellent tool to screen for HIV infection, but that – at least in our setting – it can not be recommended as a confirmatory test in VCT campaigns where whole blood is used