Financial derivatives are contracts that can have a complex payoff dependent upon underlying benchmark assets. In this work, we present quantum algorithm for the Monte Carlo pricing of financial derivatives. We show how relevant probability distributions be prepared in superposition, functions implemented via circuits, and price extracted measurements. amplitude estimation applied to achieve quadratic speedup number steps required obtain an estimate with high confidence. This work provides...

A key result of isotropic loop quantum cosmology is the existence a bounce which occurs when energy density matter field approaches universal maximum close to Planck density. Though has been exhibited in various models, due severe computational challenges, some important questions have so far remained unaddressed. These include demonstration for widely spread states, its detailed properties states probes regions volume and reliability continuum effective spacetime description general. In...

A device called a 'Gaussian Boson Sampler' has initially been proposed as near-term demonstration of classically intractable quantum computation. As recently shown, it can also be used to decide whether two graphs are isomorphic. Based on these results we construct feature map and graph similarity measure or 'graph kernel' using samples from the device. We show that kernel performs well compared standard kernels typical benchmark datasets, provide theoretical motivation for this success,...

Observational missions have provided us with a reliable model of the evolution universe starting from last scattering surface all way to future infinity.Furthermore given specific inflation, using quantum field theory on curved space-times this history can be pushed back in time epoch when space-time curvature was some 10 62 times that at horizon solar mass black hole!However, extend further Planck regime requires input gravity.An important aspect is choice background geometry and Heisenberg...

In recent years, numerical simulations with Gaussian initial states have demonstrated the existence of a quantum bounce in loop cosmology various models.A key issue pertaining to robustness and associated physics is understand evolution for more general which may depart significantly from Gaussianity no well defined peakedness properties.The analysis such states, including squeezed highly non-Gaussian has been computationally challenging until now.In this manuscript, we overcome these...

We introduce new and simple algorithms for the calculation of number perfect matchings complex weighted, undirected graphs with without loops. Our compact formulas hafnian loop n × matrices run in O ( 3 2 /2 ) time, are embarrassingly parallelizable and, to best our knowledge, fastest exact compute these quantities. Despite highly optimized algorithm, numerical benchmarks on Titan supercomputer up size 56 indicate that one would require 288,000 CPUs this machine about 6 weeks a 100 matrix.

Gupt et al., (2019). The Walrus: a library for the calculation of hafnians, Hermite polynomials and Gaussian boson sampling. Journal Open Source Software, 4(44), 1705, https://doi.org/10.21105/joss.01705

Certain anomalies in the CMB bring out a tension between six-parameter flat $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model and data. We revisit PLANCK analysis with loop quantum cosmology (LQC) predictions show that LQC alleviates both large-scale power anomaly lensing amplitude. These differences arise because, LQC, primordial spectrum is scale dependent for small $k$, specific suppression. conclude prediction of larger optical depth suppression $B$-mode polarization on large scales.

A characteristic feature of loop quantization the isotropic and Bianchi-I spacetimes is existence universal bounds on energy density expansion shear scalars, independent matter content. We investigate properties these physical quantities in Bianchi-II Bianchi-IX spacetimes, which have been recently quantized using connection operator approach. Using effective Hamiltonian approach, we show that for spacetime, scalars turn out to be bounded, albeit not by values. In when approach classical...

Due to non-perturbative quantum gravitational effects, the classical big bang singularity is replaced by a bounce of mean scale factor in loop quantization Bianchi-I spacetime. An important issue understand various differences physical properties spacetime across bounce. We investigate this context geometrical structures, identified Kasner exponents metric, which arise on approach theory. Using effective description model cosmology with dust, radiation and stiff matter, we find that as...

We investigate the pre-inflationary dynamics of inflation with Starobinsky potential, favored by recent data from Planck mission, using techniques developed to study cosmological perturbations on quantum spacetimes in framework loop cosmology. find that for a large part initial data, compatible observations occurs. There exists subset this leads gravity signatures are potentially observable. Interestingly, despite different inflationary dynamics, these corrections powerspectra similar those...

Penrose proposed that the big bang singularity should be constrained by requiring Weyl curvature vanishes there. The idea behind this past hypothesis is attractive because it constrains initial conditions for universe in geometric terms and not confined to a specific early paradigm. However, precise statement of Penrose's tied classical space-times furthermore restricts only gravitational degrees freedom. These are encapsulated tensor modes commonly used cosmological perturbation theory....

The effective description of loop quantum cosmology (LQC) has proved to be a convenient platform study phenomenological implications the bounce that resolves classical big bang singularity. Originally, this was derived using Gaussian states with small dispersions. In paper we present generalization incorporate large Specifically, derive generalized Friedmann and Raychaudhuri equations propose Hamiltonian which are being used in an ongoing consequences broad class geometries. We also discuss...

While the standard, six-parameter, spatially flat $\Lambda$CDM model has been highly successful, certain anomalies in cosmic microwave background bring out a tension between this and observations. The statistical significance of any one anomaly is small. However, taken together, presence two or more them imply that according to standard inflationary theories we live quite an exceptional universe. We revisit analysis PLANCK collaboration using loop quantum cosmology, where unforeseen...

Solving the electronic structure problem of molecules and solids to high accuracy is a major challenge in quantum chemistry condensed matter physics. The rapid emergence development computers offer promising route systematically tackle this problem. Recent work by [Huggins , ] proposed hybrid quantum-classical Monte Carlo (QC-QMC) algorithm using Clifford shadows determine ground state Fermionic Hamiltonian. This approach displayed inherent noise resilience potential for improved compared...

We investigate the ϕ2 inflationary model in Bianchi-I spacetime using effective description of loop quantum cosmology to understand issues resolution initial singularity, isotropization, effect anisotropies on amount inflation, and phase-space attractors presence non-perturbative gravitational modifications. A comparative analysis with classical theory by including more general conditions than ones previously considered latter is also performed. show that, general, singularity replaced a...

The goal of this paper is to probe phenomenological implications large fluctuations quantum geometry in the Planck era, using cosmology early universe. For background (Friedmann, Lemaître, Robertson, Walker) \emph{quantum} geometry, we allow `widely spread' states which \emph{relative} dispersions are as $168\%$ regime. By introducing suitable methods overcome ensuing conceptual and computational issues, calculate power spectrum $P_{\mathcal{R}}(k)$ spectral index $n_s(k)$ primordial...

The existence of a quantum bounce in isotropic spacetimes is key result loop cosmology (LQC), which has been demonstrated to arise all the models studied so far. In most models, using numerical simulations involving states are sharply peaked and at volumes much larger than Planck volume. An important issue confirm for have wide spread, or closer Numerical with such demand large computational domains, making them very expensive practically infeasible techniques implemented To overcome these...

Understanding transitions between different vacua of a multiverse allowing eternal inflation is an open problem whose resolution important to gain insights on the global structure spacetime as well measure. In classical theory, from anti--de Sitter de are forbidden due big-crunch singularity. this paper, we consider toy landscape potentials: double and triple potential vacua, in effective dynamics loop quantum cosmology for $k=\ensuremath{-}1$ FRW model. We show that nonperturbative gravity...

Recent cosmic microwave background (CMB) observations put strong constraints on the spatial curvature via estimation of parameter $\Omega_k$ assuming an almost scale invariant primordial power spectrum. We study evolution geometry and gauge-invariant scalar perturbations in inflationary closed FLRW model calculate find that dynamics is modified due to presence curvature, leading corrections nearly spectrum at end inflation. When evolved surface last scattering, resulting temperature...

Solving the electronic structure problem of molecules and solids to high accuracy is a major challenge in quantum chemistry condensed matter physics. The rapid emergence development computers offer promising route systematically tackle this problem. Recent work by Huggins et al.[1] proposed hybrid quantum-classical Monte Carlo (QC-QMC) algorithm using Clifford shadows determine ground state Fermionic Hamiltonian. This approach displayed inherent noise resilience potential for improved...

In a recent paper [1], we studied the evolution of background geometry and scalar perturbations in an inflationary, spatially closed Friedmann-Lemaȋtre-Robertson-Walker (FLRW) model having constant positive spatial curvature topology S3. Due to curvature, early phase slow-roll inflation is modified, leading suppression power spectrum at large angular scales. this paper, extend analysis include tensor perturbations. We find that, similarly perturbations, also shows for long wavelength modes....