New Algorithm and Phase Diagram of Noncommutative Phi**4 on the Fuzzy Sphere

We propose a new algorithm for simulating noncommutative phi-four theory on the fuzzy sphere based on, i) coupling the scalar field to a U(1) gauge field, in such a way that in the commutative limit N\longrightarrow \infty, the two modes decouple and we are left with pure scalar phi-four on the sphere, and ii) diagonalizing the scalar field by means of a U(N) unitary matrix, and then integrating out the unitary group from the partition function. The number of degrees of freedom in the scalar sector reduces, therefore, from N^2 to the N eigenvalues of the scalar field, whereas the dynamics of the U(1) gauge field, is given by D=3 Yang-Mills matrix model with a Myers term. As an application, the phase diagram, including the triple point, of noncommutative phi-four theory on the fuzzy sphere, is reconstructed with small values of N up to N=10, and large numbers of statistics.Comment: 29 pages,9 figures, 4 tables, v2: new section added in which we compare briefly between the different algorithms,30 pages, v3:two figures added, one equation added, various comments added throughout the article, typos corrected, writing style improved, 33 page

Including parameter dependence in the data and covariance for cosmological inference

The final step of most large-scale structure analyses involves the comparison of power spectra or correlation functions to theoretical models. It is clear that the theoretical models have parameter dependence, but frequently the measurements and the covariance matrix depend upon some of the parameters as well. We show that a very simple interpolation scheme from an unstructured mesh allows for an efficient way to include this parameter dependence self-consistently in the analysis at modest computational expense. We describe two schemes for covariance matrices. The scheme which uses the geometric structure of such matrices performs roughly twice as well as the simplest scheme, though both perform very well.Comment: 17 pages, 4 figures, matches version published in JCA

Option Pricing using Quantum Computers

We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we cover include vanilla options, multi-asset options and path-dependent options such as barrier options. We put an emphasis on the implementation of the quantum circuits required to build the input states and operators needed by amplitude estimation to price the different option types. Additionally, we show simulation results to highlight how the circuits that we implement price the different option contracts. Finally, we examine the performance of option pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. We employ a simple, yet effective, error mitigation scheme that allows us to significantly reduce the errors arising from noisy two-qubit gates.Comment: Fixed a typo. This article has been accepted in Quantu