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Quantum inverse problem (QIP) is the problem of estimating an unknown quantum system from a set of measurements, whereas the classical counterpart is the inverse problem of estimating a distribution from a set of observations. In this paper, we present a neural-network-based method for QIPs, which has been widely explored for its classical counterpart. The proposed method utilizes the quantumness of the QIPs and takes advantage of the computational power of neural networks to achieve remarkable efficiency for the quantum state estimation. We test the method on the problem of maximum entropy estimation of an unknown state ρ from partial information both numerically and experimentally. Our method yields high fidelity, efficiency and robustness for both numerical experiments and quantum optical experiments.

A bstract The computation of the parton distribution functions (PDF) or distribution amplitudes (DA) of hadrons from first principles lattice QCD constitutes a central open problem in high energy nuclear physics. In this study, we present and evaluate the efficiency of several numerical methods, well established in the study of inverse problems, to reconstruct the full x -dependence of PDFs. Our starting point are the so called Ioffe time PDFs, which are accessible from Euclidean time simulations in conjunction with a matching procedure. Using realistic mock data tests, we find that the ill-posed incomplete Fourier transform underlying the reconstruction requires careful regularization, for which both the Bayesian approach as well as neural networks are efficient and flexible choices.

A bstract This work employs the spectral reconstruction approach of ref. [ 1 ] to determine an inclusive rate in the 1 + 1 dimensional O(3) non-linear σ -model, analogous to the QCD part of e + e − → hadrons. The Euclidean two-point correlation function of the conserved current j is computed using Monte Carlo lattice field theory simulations for a variety of spacetime volumes and lattice spacings. The spectral density of this correlator is related to the inclusive rate for j → X in which all final states produced by the external current are summed. The ill-posed inverse problem of determining the spectral density from the correlation function is made tractable through the determination of smeared spectral densities in which the desired density is convolved with a set of known smearing kernels of finite width ϵ . The smooth energy dependence of the underlying spectral density enables a controlled ϵ → 0 extrapolation in the inelastic region, yielding the real-time inclusive rate without reference to individual finite-volume energies or matrix elements. Systematic uncertainties due to cutoff effects and residual finite-volume effects are estimated and taken into account in the final error budget. After taking the continuum limit, the results are consistent with the known analytic rate to within the combined statistical and systematic errors. Above energies where 20-particle states contribute, the overall precision is sufficient to discern the four-particle contribution to the spectral density.

A bstract We extend the boundary-to-bound (B2B) correspondence to incorporate radiative as well as conservative radiation-reaction effects. We start by deriving a map between the total change in observables due to gravitational wave emission during hyperbolic-like motion and in one period of an elliptic-like orbit, which is valid in the adiabatic expansion for non-spinning as well as aligned-spin configurations. We also discuss the inverse problem of extracting the associated fluxes from scattering data. Afterwards we demonstrate, to all orders in the Post-Minkowskian expansion, the link between the radiated energy and the ultraviolet pole in the radial action in dimensional regularization due to tail effects. This implies, as expected, that the B2B correspondence for the conservative sector remains unchanged for local-in-time radiation-reaction tail effects with generic orbits. As a side product, this allows us to read off the energy flux from the associated pole in the tail Hamiltonian. We show that the B2B map also holds for non-local-in-time terms, but only in the large-eccentricity limit. Remarkably, we find that all of the trademark logarithmic contributions to the radial action map unscathed between generic unbound and bound motion. However, unlike logarithms, other terms due to non-local effects do not transition smoothly to quasi-circular orbits. We conclude with a discussion on these non-local pieces. Several checks of the B2B dictionary are displayed using state-of-the-art knowledge in Post-Newtonian/Minkowskian theory.

A bstract In recent years, several pulsar timing array collaborations have reported first hints for a stochastic gravitational wave background at nano-Hertz frequencies. Here we elaborate on the possibility that this signal comes from new physics that leads to the generation of a primordial stochastic gravitational wave background. We propose a set of simple but concrete models that can serve as benchmarks for gravitational waves sourced by cosmological phase transitions, domain wall networks, cosmic strings, axion dynamics, or large scalar fluctuations. These models are then confronted with pulsar timing data and with cosmological constraints. With only a limited number of free parameters per model, we are able to identify viable regions of parameter space and also make predictions for future astrophysical and laboratory tests that can help with model identification and discrimination.

A bstract We study the “inverse problem” in the context of the Standard Model Effective Field Theory (SMEFT): how and to what extend can one reconstruct the UV theory, given the measured values of the operator coefficients in the IR? The main obstacle of this problem is the degeneracies in the space of coefficients: a given SMEFT truncated at a finite dimension can be mapped to infinitely many UV theories. We discuss these degeneracies at the dimension-8 level, and show that positivity bounds play a crucial role in the inverse problem. In particular, the degeneracies either vanish or become significantly limited for SMEFTs that live on or close to the positivity bounds. The UV particles of these SMEFTs, and their properties such as spin, charge, other quantum numbers, and interactions with the SM particles, can often be uniquely determined, assuming dimension-8 coefficients are measured. The allowed region for SMEFTs, which forms a convex cone, can be systematically constructed by enumerating its generators. We show that a geometric notion, extremality, conveniently connects the positivity problem with the inverse problem. We discuss the implications of a SMEFT living on an extremal ray, on a k -face, and on the vertex of the positive cone. We also show that the information of the dimension-8 coefficients can be used to set exclusion limits on all individual UV states that interact with the SM, independent of specific model assumptions. Our results indicate that the dimension-8 operators encode much more information about the UV than one would naively expect, which can be used to reverse engineer the UV physics from the SMEFT.

A bstract We present a global analysis program for the generalized parton distributions (GPDs) based on conformal moment expansion. We apply the strategy of universal moment parameterization to fit both the collinear parton distribution functions (PDFs) from phenomenology and generalized form factors from lattice calculations, and show that the parameterization is flexible enough to accommodate these constraints. In addition, we can also fit direct lattice calculations of GPDs from large-momentum effective theory. In this work we focus on the analysis of t -dependent PDFs which correspond to GPDs in the ξ → 0 limit. The strategy also applies to the ξ ≠ 0 region with extra parameters, and therefore can be fitted to experimental observables in the future. With a demonstrative example of fitted GPDs, we exhibit the quark transverse angular momentum densities of the proton as well as the impact parameter space distributions of quarks in both unpolarized and transversely polarized protons.

A bstract We investigate the problem of bulk metric reconstruction in holography by leveraging the inverse scattering framework applied to boundary two-point correlation functions. We generalize our previous work of scalar field and show that reconstruction can be achieved using a single operator rather than a pair. We also apply this method into reconstruction of static homogeneous anisotropic black holes and the reconstruction using correlation function of gauge field. In addition, we analyze the method’s robustness under measurement noise and propose filtering strategies to improve reconstruction accuracy. This work advances data-driven bulk reconstruction by providing a concrete, experimentally viable pathway to recover spacetime geometry from field-theoretic observables.

A bstract We discuss a method to construct hadronic scattering and decay amplitudes from Euclidean correlators, by combining the approach of a regulated inverse Laplace transform with the work of Maiani and Testa [1]. Revisiting the original result of ref. [1], we observe that the key observation, i.e. that only threshold scattering information can be extracted at large separations, can be understood by interpreting the correlator as a spectral function, ρ ( ω ), convoluted with the Euclidean kernel, e −ωt , which is sharply peaked at threshold. We therefore consider a modification in which a smooth step function, equal to one above a target energy, is inserted in the spectral decomposition. This can be achieved either through Backus-Gilbert-like methods or more directly using the variational approach. The result is a shifted resolution function, such that the large t limit projects onto scattering or decay amplitudes above threshold. The utility of this method is highlighted through large t expansions of both three- and four-point functions that include leading terms proportional to the real and imaginary parts (separately) of the target observable. This work also presents new results relevant for the un-modified correlator at threshold, including expressions for extracting the Nπ scattering length from four-point functions and a new strategy to organize the large t expansion that exhibits better convergence than the expansion in powers of 1/ t .

In this paper we show that any static and spherically symmetric anisotropic solution of the Einstein field equations can be thought as a system sourced by certain deformed isotropic system in the context of Minimal Geometric Deformation-decoupling approach. To be more precise, we developed a mechanism to obtain an isotropic solution from any anisotropic solution of the Einstein field equations. As an example, we implement the method to obtain the sources of a simple static anisotropic and spherically symmetric traversable wormhole.