Holographic Quantum Circuits from Splitting/Joining Local Quenches

We study three different types of local quenches (local operator, splitting and joining) in both the free fermion and holographic CFTs in two dimensions. We show that the computation of a quantity called entanglement density, provides a systematic method to capture essential properties of local quenches. This allows us to clearly understand the differences between the free and holographic CFTs as well as the distinctions between three local quenches. We also analyze holographic geometries of splitting/joining local quenches using the AdS/BCFT prescription. We show that they are essentially described by time evolutions of boundary surfaces in the bulk AdS. We find that the logarithmic time evolution of entanglement entropy arises from the region behind the Poincare horizon as well as the evolutions of boundary surfaces. In the CFT side, our analysis of entanglement density suggests such a logarithmic growth is due to initial non-local quantum entanglement just after the quench. Finally, by combining our results, we propose a new class of gravity duals, which are analogous to quantum circuits or tensor networks such as MERA, based on the AdS/BCFT construction.Comment: 59 pages, 28 figures; v2: explanations added, minor corrections; v3: eq.(4.25), eq.(4.26) and related contents correcte

世界の終わりを越える量子重力

京都大学新制・課程博士博士(理学)甲第24403号理博第4902号新制||理||1700(附属図書館)京都大学大学院理学研究科物理学・宇宙物理学専攻(主査)教授 高柳 匡, 教授 杉本 茂樹, 教授 橋本 幸士学位規則第4条第1項該当Doctor of ScienceKyoto UniversityDFA

Improving the Improved Training of Wasserstein GANs: A Consistency Term and Its Dual Effect

Despite being impactful on a variety of problems and applications, the generative adversarial nets (GANs) are remarkably difficult to train. This issue is formally analyzed by \cite{arjovsky2017towards}, who also propose an alternative direction to avoid the caveats in the minmax two-player training of GANs. The corresponding algorithm, called Wasserstein GAN (WGAN), hinges on the 1-Lipschitz continuity of the discriminator. In this paper, we propose a novel approach to enforcing the Lipschitz continuity in the training procedure of WGANs. Our approach seamlessly connects WGAN with one of the recent semi-supervised learning methods. As a result, it gives rise to not only better photo-realistic samples than the previous methods but also state-of-the-art semi-supervised learning results. In particular, our approach gives rise to the inception score of more than 5.0 with only 1,000 CIFAR-10 images and is the first that exceeds the accuracy of 90% on the CIFAR-10 dataset using only 4,000 labeled images, to the best of our knowledge.Comment: Accepted as a conference paper in International Conference on Learning Representation(ICLR). Xiang Wei and Boqing Gong contributed equally in this wor

Counting atypical black hole microstates from entanglement wedges

Disentangled black hole microstates are atypical states in holographic CFTs whose gravity duals do not have smooth horizons. If there exist sufficiently many disentangled microstates to account for the entire Bekenstein-Hawking entropy, then any black hole microstate can be written as a superposition of states without smooth horizons. We show that there exist sufficiently many disentangled microstates to account for almost the entire Bekenstein-Hawking entropy of a large AdS black hole at the semiclassical limit $G_N\rightarrow 0$. In addition, we also argue that in generic quantum many-body systems with short-ranged interactions, there exist sufficiently many area law states in the microcanonical subspace to account for almost the entire thermodynamic entropy in the standard thermodynamic limit. Area law states are atypical since a typical state should contain volume law entanglement. Furthermore, we also present an explicit way to construct such a set of area law states, and argue that the same construction may also be used to construct disentangled states.Comment: 29 pages plus appendix, 3 figure

Double Local Quenches in 2D CFTs and Gravitational Force

In this work we extensively study the dynamics of excited states created by instantaneous local quenches at two different points, i.e., double local quenches. We focus on setups in two dimensional holographic and free Dirac fermion CFTs. We calculate the energy stress tensor and entanglement entropy for double joining and splitting local quenches. In the splitting local quenches we find an interesting oscillating behaviors. Finally, we study the energy stress tensor in double operator local quenches. In all these examples, we find that, in general, there are non-trivial interactions between the two local quenches. Especially, in holographic CFTs, the differences of the above quantities between the double local quench and the simple sum of two local quenches tend to be negative. We interpret this behavior as merely due to gravitational force in their gravity duals.Comment: 80pages, 50figures; v2: minor corrections, v3: explanations added in section 7, minor correction

Improving the Improved Training of Wasserstein GANs: A Consistency Term and Its Dual Effect

Despite being impactful on a variety of problems and applications, the generative adversarial nets (GANs) are remarkably difficult to train. This issue is formally analyzed by \cite{arjovsky2017towards}, who also propose an alternative direction to avoid the caveats in the minmax two-player training of GANs. The corresponding algorithm, called Wasserstein GAN (WGAN), hinges on the 1-Lipschitz continuity of the discriminator. In this paper, we propose a novel approach to enforcing the Lipschitz continuity in the training procedure of WGANs. Our approach seamlessly connects WGAN with one of the recent semi-supervised learning methods. As a result, it gives rise to not only better photo-realistic samples than the previous methods but also state-of-the-art semi-supervised learning results. In particular, our approach gives rise to the inception score of more than 5.0 with only 1,000 CIFAR-10 images and is the first that exceeds the accuracy of 90% on the CIFAR-10 dataset using only 4,000 labeled images, to the best of our knowledge.Comment: Accepted as a conference paper in International Conference on Learning Representation(ICLR). Xiang Wei and Boqing Gong contributed equally in this wor

Efficient Simulation of Low Temperature Physics in One-Dimensional Gapless Systems

We discuss the computational efficiency of the finite temperature simulation with the minimally entangled typical thermal states (METTS). To argue that METTS can be efficiently represented as matrix product states, we present an analytic upper bound for the average entanglement Renyi entropy of METTS for Renyi index $0<q\leq 1$. In particular, for 1D gapless systems described by CFTs, the upper bound scales as $\mathcal{O}(c N^0 \log \beta)$ where $c$ is the central charge and $N$ is the system size. Furthermore, we numerically find that the average Renyi entropy exhibits a universal behavior characterized by the central charge and is roughly given by half of the analytic upper bound. Based on these results, we show that METTS provide a significant speedup compared to employing the purification method to analyze thermal equilibrium states at low temperatures in 1D gapless systems.Comment: 6 pages, revte

SVD Entanglement Entropy

In this paper, we introduce a new quantity called SVD entanglement entropy. This is a generalization of entanglement entropy in that it depends on two different states, as in pre- and post-selection processes. This SVD entanglement entropy takes non-negative real values and is bounded by the logarithm of the Hilbert space dimensions. The SVD entanglement entropy can be interpreted as the average number of Bell pairs distillable from intermediates states. We observe that the SVD entanglement entropy gets enhanced when the two states are in the different quantum phases in an explicit example of the transverse-field Ising model. Moreover, we calculate the R{\'e}nyi SVD entropy in various field theories and examine holographic calculations using the AdS/CFT correspondence.Comment: 42 pages, 23 figure

Entanglement entropy in holographic moving mirror and Page curve

We calculate the time evolution of entanglement entropy in two dimensional conformal field theory with a moving mirror. For a setup modeling Hawking radiation, we obtain a linear growth of entanglement entropy and show that this can be interpreted as the production of entangled pairs. For a setup, which mimics black hole formation and evaporation, we find that the evolution follows the ideal Page curve. We perform these computations by constructing the gravity dual of the moving mirror model via holography. We also argue that our holographic setup provides a concrete model to derive the Page curve for black hole radiation in the strong coupling regime of gravity.Comment: 8 pages, 7 figures, v2: references adde