Exponential Qubit Reduction in Optimization for Financial Transaction Settlement

We extend the qubit-efficient encoding presented in [Tan et al., Quantum 5, 454 (2021)] and apply it to instances of the financial transaction settlement problem constructed from data provided by a regulated financial exchange. Our methods are directly applicable to any QUBO problem with linear inequality constraints. Our extension of previously proposed methods consists of a simplification in varying the number of qubits used to encode correlations as well as a new class of variational circuits which incorporate symmetries, thereby reducing sampling overhead, improving numerical stability and recovering the expression of the cost objective as a Hermitian observable. We also propose optimality-preserving methods to reduce variance in real-world data and substitute continuous slack variables. We benchmark our methods against standard QAOA for problems consisting of 16 transactions and obtain competitive results. Our newly proposed variational ansatz performs best overall. We demonstrate tackling problems with 128 transactions on real quantum hardware, exceeding previous results bounded by NISQ hardware by almost two orders of magnitude.Comment: 16 pages, 8 figure

Location Dependent Dirichlet Processes

Dirichlet processes (DP) are widely applied in Bayesian nonparametric modeling. However, in their basic form they do not directly integrate dependency information among data arising from space and time. In this paper, we propose location dependent Dirichlet processes (LDDP) which incorporate nonparametric Gaussian processes in the DP modeling framework to model such dependencies. We develop the LDDP in the context of mixture modeling, and develop a mean field variational inference algorithm for this mixture model. The effectiveness of the proposed modeling framework is shown on an image segmentation task

Patient experiences of receiving arthroscopic surgery or personalised hip therapy for femoroacetabular impingement in the context of the UK fashion study:a qualitative study

UK FASHIoN was a multicentre randomised controlled trial comparing hip arthroscopic surgery (HA) with personalised hip therapy (PHT, physiotherapist-led conservative care), for patients with hip pain attributed to femoroacetabular impingement (FAI) syndrome. Our aim was to describe the treatment and trial participation experiences of patients, to contextualise the trial results and offer further information to assist treatment decision-making in FAI. We conducted in-depth semi-structured telephone interviews with a purposive sample of trial participants from each of the trial arms. They were interviewed after they received treatment and completed their first year of trial participation. Thematic analysis and constant comparison analytical approaches were used to identify themes of patient treatment experiences during the trial. Forty trial participants were interviewed in this qualitative study. Their baseline characteristics were similar to those in the main trial sample. On average, their hip-related quality of life (iHOT-33 scores) at 12 months follow-up were lower than average for all trial participants, indicating poorer hip-related quality of life as a consequence of theoretical sampling. Patient experiences occurred in five patient groups: those who felt their symptoms improved with hip arthroscopy, or with personal hip therapy, patients who felt their hip symptoms did not change with PHT but did not want HA, patients who decided to change from PHT to HA and a group who experienced serious complications after HA. Interviewees mostly described a trouble-free, enriching and altruistic trial participation experience, although most participants expected more clinical follow-up at the end of the trial. Both HA and PHT were experienced as beneficial by participants in the trial. Treatment success appeared to depend partly on patients' prior own expectations as well as their outcomes, and future research is needed to explore this further. Findings from this study can be combined with the primary results to inform future FAI patients

Thermodynamics of a Trapped Bose-Fermi Mixture

By using the Hartree-Fock-Bogoliubov equations within the Popov approximation, we investigate the thermodynamic properties of a dilute binary Bose-Fermi mixture confined in an isotropic harmonic trap. For mixtures with an attractive Bose-Fermi interaction we find a sizable enhancement of the condensate fraction and of the critical temperature of Bose-Einstein condensation with respect to the predictions for a pure interacting Bose gas. Conversely, the influence of the repulsive Bose-Fermi interaction is less pronounced. The possible relevance of our results in current experiments on trapped $^{87}{\rm Rb}-^{40}${\rm K} mixtures is discussed.Comment: 5 pages + 4 figures; minor changes, final version to appear in Phys. Rev. A; the extension work on the finite-temperature low-lying excitations can be found in cond-mat/030763

Density profiles and density oscillations of an interacting three-component normal Fermi gas

We use a semiclassical approximation to investigate density variations and dipole oscillations of an interacting three-component normal Fermi gas in a harmonic trap. We consider both attractive and repulsive interactions between different pairs of fermions and study the effect of population imbalance on densities. We find that the density profiles significantly deviate from those of non-interacting profiles and extremely sensitive to interactions and population imbalance. Unlike for a two-component Fermi system, we find density imbalance even for balanced populations. For some range of parameters, one component completely repels from the trap center giving rise a donut shape density profile. Further, we find that the in-phase dipole oscillation frequency is consistent with Kohn's theorem and other two dipole mode frequencies are strongly effected by the interactions and the number of atoms in the harmonic trap.Comment: Total seven pages with five figures. Published versio

Variational theory of two-fluid hydrodynamic modes at unitarity

We present the results of a variational calculation of the frequencies of the low-lying Landau two-fluid hydrodynamic modes in a trapped Fermi superfluid gas at unitarity. Landau's two-fluid hydrodynamics is expected to be the correct theory of Fermi superfluids at finite temperatures close to unitarity, where strong interactions give rise to collisional hydrodynamics. Two-fluid hydrodynamics predicts the existence of in-phase modes in which the superfluid and normal fluid components oscillate together, as well as out-of-phase modes where the two components move against each other. We prove that at unitarity, the dipole and breathing in-phase modes are locally isentropic. Their frequencies are independent of temperature and are the same above and below the superfluid transition. The out-of-phase modes, in contrast, are strongly dependent on temperature and hence, can be used to test the thermodynamic properties and superfluid density of a Fermi gas at unitarity. We give numerical results for the frequencies of these new modes as function of temperature in an isotropic trap at unitarity.Comment: 16 pages; 5 figure

TULIP: a randomised controlled trial of surgical versus non-surgical treatment of lateral compression injuries of the pelvis with complete sacral fractures (LC1) in the non-fragility fracture patient-a feasibility study protocol

Introduction Lateral compression type 1 (LC1) pelvic fractures are the most common type of pelvic fracture. The majority of LC1 fractures are considered stable. Fractures where a complete sacral fracture is present increases the degree of potential instability and have the potential to displace over time. Non-operative management of these unstable fractures may involve restricted weight bearing and significant rehabilitation. Frequent monitoring with X-rays is also necessary for displacement of the fracture. Operative stabilisation of these fractures may be appropriate to prevent displacement of the fracture. This may allow patients to mobilise pain-free, quicker. Methods and analysis The study is a feasibility study to inform the design of a full definitive randomised controlled trial to guide the most appropriate management of these injuries. Participants will be recruited from major trauma centres and randomly allocated to either operative or non-operative management of their injuries. A variety of outcome instruments, measuring health-related quality of life, functional outcome and pain, will be completed at several time points up to 12 months post injury. Qualitative interviews will be undertaken with participants to explore their views of the treatments under investigation and trial processes. Eligibility and recruitment to the study will be analysed to inform the feasibility of a definitive trial. Completion rates of the measurement instruments will be assessed, as well as their sensitivity to change and the presence of floor or ceiling effects in this population, to inform the choice of the primary outcome for a definitive trial. Ethics and dissemination Ethical approval for the study was given by the South West—Central Bristol NHS Research Ethics Committee on 2nd July 2018 (Ref; 18/SW/0135). The study will be reported in relevant specialist journals and through presentation at specialist conferences. Trial registration number ISRCTN1064995

C-axis Raman spectra of a normal plane-chain bilayer cuprate and the pseudogap

We investigate the Raman spectra in the geometry where both incident and scattered photon polarizations are parallel to the $\hat{z}$-direction, for a plane-chain bilayer coupled via a single-particle tunneling $t_\perp$. The Raman vertex is derived in the tight-binding limit and in the absence of Coulomb screening, the Raman intensity can be separated into intraband ($\propto t_\perp^4$) and interband ($\propto t_\perp^2$) transitions. In the small-$t_\perp$ limit, the interband part dominates and a pseudogap will appear as it does in the conductivity. Coulomb interactions bring in a two-particle coupling and result in the breakdown of intra- and interband separation. Nevertheless, when $t_\perp$ is small, the Coulomb screening ($\propto t_\perp^4$) has little effect on the intensity to which the unscreened interband transitions contribute most. In general, the total Raman spectra are strongly dependent on the magnitude of $t_\perp$.Comment: 23 pages, 6 figures, submitted to Phys. Rev.

Fe XVII X-ray Line Ratios for Accurate Astrophysical Plasma Diagnostics

New laboratory measurements using an Electron Beam Ion Trap (EBIT) and an x-ray microcalorimeter are presented for the n=3 to n=2 Fe XVII emission lines in the 15 {\AA} to 17 {\AA} range, along with new theoretical predictions for a variety of electron energy distributions. This work improves upon our earlier work on these lines by providing measurements at more electron impact energies (seven values from 846 to 1185 eV), performing an in situ determination of the x-ray window transmission, taking steps to minimize the ion impurity concentrations, correcting the electron energies for space charge shifts, and estimating the residual electron energy uncertainties. The results for the 3C/3D and 3s/3C line ratios are generally in agreement with the closest theory to within 10%, and in agreement with previous measurements from an independent group to within 20%. Better consistency between the two experimental groups is obtained at the lowest electron energies by using theory to interpolate, taking into account the significantly different electron energy distributions. Evidence for resonance collision effects in the spectra is discussed. Renormalized values for the absolute cross sections of the 3C and 3D lines are obtained by combining previously published results, and shown to be in agreement with the predictions of converged R-matrix theory. This work establishes consistency between results from independent laboratories and improves the reliability of these lines for astrophysical diagnostics. Factors that should be taken into account for accurate diagnostics are discussed, including electron energy distribution, polarization, absorption/scattering, and line blends.Comment: 29 pages, including 7 figure

Finite temperature effects on the collapse of trapped Bose-Fermi mixtures

By using the self-consistent Hartree-Fock-Bogoliubov-Popov theory, we present a detailed study of the mean-field stability of spherically trapped Bose-Fermi mixtures at finite temperature. We find that, by increasing the temperature, the critical particle number of bosons (or fermions) and the critical attractive Bose-Fermi scattering length increase, leading to a significant stabilization of the mixture.Comment: 5 pages, 4 figures; minor changes, proof version, to appear in Phys. Rev. A (Nov. 1, 2003