Extremal RN/CFT in Both Hands Revisited

We study RN/CFT correspondence for four dimensional extremal Reissner-Nordstrom black hole. We uplift the 4d RN black hole to a 5d rotating black hole and make a geometric regularization of the 5d space-time. Both hands central charges are obtained correctly at the same time by Brown-Henneaux technique.Comment: 10 pages, no figur

Anatomy of Geodesic Witten Diagrams

We revisit the so-called "Geodesic Witten Diagrams" (GWDs) \cite{ScalarGWD}, proposed to be the holographic dual configuration of scalar conformal partial waves, from the perspectives of CFT operator product expansions. To this end, we explicitly consider three point GWDs which are natural building blocks of all possible four point GWDs, discuss their gluing procedure through integration over spectral parameter, and this leads us to a direct identification with the integral representation of CFT conformal partial waves. As a main application of this general construction, we consider the holographic dual of the conformal partial waves for external primary operators with spins. Moreover, we consider the closely related "split representation" for the bulk to bulk spinning propagator, to demonstrate how ordinary scalar Witten diagram with arbitrary spin exchange, can be systematically decomposed into scalar GWDs. We also discuss how to generalize to spinning cases.Comment: 40 pages, 4 figures, v2: typos corrected, references added, Appendix E and a Mellin space discussion added, v3: typos correcte

Towards Spinning Mellin Amplitudes

We construct the Mellin representation of four point conformal correlation function with external primary operators with arbitrary integer spacetime spins, and obtain a natural proposal for spinning Mellin amplitudes. By restricting to the exchange of symmetric traceless primaries, we generalize the Mellin transform for scalar case to introduce discrete Mellin variables for incorporating spin degrees of freedom. Based on the structures about spinning three and four point Witten diagrams, we also obtain a generalization of the Mack polynomial which can be regarded as a natural kinematical polynomial basis for computing spinning Mellin amplitudes using different choices of interaction vertices.Comment: 32 pages, 2 figures, v2: typos corrected, clarification added, references updated, to appear in NP

Qubit-oscillator concatenated codes: decoding formalism & code comparison

Concatenating bosonic error-correcting codes with qubit codes can substantially boost the error-correcting power of the original qubit codes. It is not clear how to concatenate optimally, given there are several bosonic codes and concatenation schemes to choose from, including the recently discovered GKP-stabilizer codes [arXiv:1903.12615] that allow protection of a logical bosonic mode from fluctuations of the mode's conjugate variables. We develop efficient maximum-likelihood decoders for and analyze the performance of three different concatenations of codes taken from the following set: qubit stabilizer codes, analog/Gaussian stabilizer codes, GKP codes, and GKP-stabilizer codes. We benchmark decoder performance against additive Gaussian white noise, corroborating our numerics with analytical calculations. We observe that the concatenation involving GKP-stabilizer codes outperforms the more conventional concatenation of a qubit stabilizer code with a GKP code in some cases. We also propose a GKP-stabilizer code that suppresses fluctuations in both conjugate variables and that can be initialized using only controlled-SUM and Hadamard gates, and formulate qudit versions of GKP-stabilizer codes.Comment: 17 pages, 5 figure

QUANTUM SIMULATION OF BOSONIC SYSTEM AND APPLICATION OF MACHINE LEARNING

First, we introduce the notion of "generalized bosons," whose exchange statistics resemble those of bosons, but the local bosonic commutator $[a_i,a_i^{\dagger}]=1$ is replaced by an arbitrary single-mode operator that is diagonal in the generalized Fock basis. Examples of generalized bosons include boson pairs and spins. We consider the analogue of the boson sampling task for these particles and observe that its output probabilities are still given by permanents, so the results regarding the difficulty of sampling carry over directly. Finally, we propose implementations of generalized boson sampling in circuit-QED and ion-trap platforms. In the rest of the thesis, we move on to different topics. Firstly, we incorporate machine learning techniques in quantum information. We use machine learning to classify rational two-dimensional conformal field theories (CFTs). We first use the energy spectra of these minimal models to train a supervised learning algorithm. In contrast to conventional methods that are typically qualitative and involve system size scaling, our method quantifies the similarity of the spectrum of a system at a fixed size to candidate CFTs. Such an approach allows us to correctly predict the nature and value of critical points of several strongly correlated spin models using only their energy spectra. Our results are also relevant for the ground-state entanglement Hamiltonian of certain topological phases of matter described by CFTs. Remarkably, we achieve high prediction accuracy by only using the lowest few Rényi entropies as the input. Finally, using autoencoders, an unsupervised learning algorithm, we find a hidden variable that has a direct correlation with the central charge and discuss prospects for using machine learning to investigate other conformal field theories, including higher-dimensional ones. Next, we demonstrate how machine learning techniques, especially unsupervised learning algorithms, can be used to study Symmetry-Protected Topological (SPT) phases of matter. SPT phases are short-range entangled phases of matter with a non-local order parameter that are preserved under a local symmetry group. Here, we use an unsupervised learning algorithm, namely diffusion maps, to differentiate between symmetry-broken phases and topologically ordered phases and between non-trivial topological phases in different classes. Specifically, we show that phase transitions associated with these phases can be detected in various bosonic and fermionic models in one dimension, including the interacting SSH model, the AKLT model and its variants, and weakly interacting fermionic models. Our approach provides a cost-effective computational method for detecting topological phase transitions associated with SPT systems, which can also be applied to experimental data obtained from quantum simulators

Qubit-Oscillator Concatenated Codes: Decoding Formalism and Code Comparison

Concatenating bosonic error-correcting codes with qubit codes can substantially boost the error-correcting power of the original qubit codes. It is not clear how to concatenate optimally, given that there are several bosonic codes and concatenation schemes to choose from, including the recently discovered Gottesman-Kitaev-Preskill (GKP) – stabilizer codes [Phys. Rev. Lett. 125, 080503 (2020)] that allow protection of a logical bosonic mode from fluctuations of the conjugate variables of the mode. We develop efficient maximum-likelihood decoders for and analyze the performance of three different concatenations of codes taken from the following set: qubit stabilizer codes, analog or Gaussian stabilizer codes, GKP codes, and GKP-stabilizer codes. We benchmark decoder performance against additive Gaussian white noise, corroborating our numerics with analytical calculations. We observe that the concatenation involving GKP-stabilizer codes outperforms the more conventional concatenation of a qubit stabilizer code with a GKP code in some cases. We also propose a GKP-stabilizer code that suppresses fluctuations in both conjugate variables without extra quadrature squeezing and formulate qudit versions of GKP-stabilizer codes

Decoding conformal field theories: From supervised to unsupervised learning

We use machine learning to classify rational two-dimensional conformal field theories (CFTs). We first use the energy spectra of these minimal models to train a supervised learning algorithm. In contrast to conventional methods that are typically qualitative and also involve system size scaling, our method quantifies the similarity of the spectrum of a system at a fixed size to candidate CFTs. Such an approach allows us to correctly predict the nature and the value of critical points of several strongly correlated spin models using only their energy spectra. Our results are also relevant for the ground-state entanglement Hamiltonian of certain topological phases of matter, described by CFTs. Remarkably, we achieve high prediction accuracy by only using the lowest few Réyni entropies as the input. Finally, using autoencoders, an unsupervised learning algorithm, we find a hidden variable that has a direct correlation with the central charge and discuss prospects for using machine learning to investigate other conformal field theories, including higher-dimensional ones

Path sampling of recurrent neural networks by incorporating known physics

Recurrent neural networks have seen widespread use in modeling dynamical systems in varied domains such as weather prediction, text prediction and several others. Often one wishes to supplement the experimentally observed dynamics with prior knowledge or intuition about the system. While the recurrent nature of these networks allows them to model arbitrarily long memories in the time series used in training, it makes it harder to impose prior knowledge or intuition through generic constraints. In this work, we present a path sampling approach based on principle of Maximum Caliber that allows us to include generic thermodynamic or kinetic constraints into recurrent neural networks. We show the method here for a widely used type of recurrent neural network known as long short-term memory network in the context of supplementing time series collected from different application domains. These include classical Molecular Dynamics of a protein and Monte Carlo simulations of an open quantum system continuously losing photons to the environment and displaying Rabi oscillations. Our method can be easily generalized to other generative artificial intelligence models and to generic time series in different areas of physical and social sciences, where one wishes to supplement limited data with intuition or theory based corrections.Comment: Added results for open quantum system with dissipative photon dynamic