Holographic Complexity of Einstein-Maxwell-Dilaton Gravity

We study the holographic complexity of Einstein-Maxwell-Dilaton gravity using the recently proposed "complexity = volume" and "complexity = action" dualities. The model we consider has a ground state that is represented in the bulk via a so-called hyperscaling violating geometry. We calculate the action growth of the Wheeler-DeWitt patch of the corresponding black hole solution at non-zero temperature and find that, in the presence of violations of hyperscaling, there is a parametric enhancement of the action growth rate. We partially match this behavior to simple tensor network models which can capture aspects of hyperscaling violation. We also exhibit the switchback effect in complexity growth using shockwave geometries and comment on a subtlety of our action calculations when the metric is discontinuous at a null surface.Comment: 30 pages; v2: Fixed a technical error. Corrected result no longer has a logarithmic divergence in the action growth rate associated with the singularity. Conjectured complexity growth rate now also matches better with tensor network model

Assessing Parents On Factors Impacting Primary Students’ Continuance Intention to Use Tencent Class Platform in Chongqing City, China

Purpose: This research investigates parents on the factors influencing students' continuance intention of the Tencent Class platform among parents in a primary school located in Chongqing city, China. The conceptual framework encompasses perceived responsiveness, information quality, self-efficacy, service quality, satisfaction, trust, and continuance intention. Research design, data, and methodology: The target population comprises 500 parents of students in Grade 1-3 attending Shuren Primary School in China who have utilized the Tencent Class Platform. A quantitative research approach was employed, utilizing a questionnaire. The sampling techniques employed in this study encompass judgmental, convenience, and snowball sampling. To ensure the validity and reliability of the instrument, a pilot test was conducted involving a sample of 50 participants, and the item-objective congruence (IOC) index and Cronbach's alpha were utilized for the validity and reliability testing, respectively. The data obtained were analyzed using confirmatory factor analysis (CFA) and structural equation modeling (SEM). Results: Perceived responsiveness and information quality significantly impact self-efficacy. Self-efficacy, service quality and information quality significantly impact satisfaction. Satisfaction significantly impacts continuance intention through trust. Conclusions: This study lies in its potential to inform educational practices, platform development, policy-making, and academic discussions, ultimately benefiting parents, educators, platform developers, policy-makers, and researchers in the field of e-learning in primary education

RECOVERY AND RECONSTRUCTION IN QUANTUM SYSTEMS

Quantum systems are prone to noises. Accordingly, many techniques are developed tocancel the action of a quantum operation, or to protect the quantum information against the noises. In this dissertation, I discuss two such schemes, namely the recovery channel and the quantum error correction, and various scenarios in which they are applied. The first scenario is the perfect recovery in the Gaussian fermionic systems. When therelative entropy between two states remains unchanged under a channel, the perfect recovery can be achieved. It is realized by the Petz recovery map. We study the Petz recovery map in the case where the quantum channel and input states are fermionic and Gaussian. Gaussian states are convenient because they are totally determined by their covariance matrix and because they form a closed set under so-called Gaussian channels. Using a Grassmann representation of fermionic Gaussian maps, we show that the Petz recovery map is also Gaussian and determine it explicitly in terms of the covariance matrix of the reference state and the data of the channel. As a by-product, we obtain a formula for the fidelity between two fermionic Gaussian states. This scenario is based on the work [1]. The second scenario is the approximate recovery in the context of quantum field theory.When perfect recovery is not achievable, the existence of a universal approximate recovery channel is proven. The approximation is in the sense that the fidelity between the recovered state and the original state is lower bounded by the change of the relative entropy under the quantum channel. This result is a generalization of previous results that applied to type-I von Neumann algebras in [2]. To deal with quantum field theory, the type of the von Neumann algebras is not restrained here. This induces qualitatively new features and requires extra proving techniques. This results hinge on the construction of certain analytic vectors and computations/estimations of their Araki-Masuda Lp norms. This part is based on the work [3]. The third scenario is applying quantum error correction codes on tensor networks on hyperbolicplanes. This kind of model is proposed to be toy models of the AdS/CFT duality, thus also dubbed holographic tensor networks. In the case when the network consists of a single type of tensor that also acts as an erasure correction code, we show that it cannot be both locally contractible and sustain power-law correlation functions. Motivated by this no-go theorem, and the desirability of local contractibility, we provide guidelines for constructing networks consisting of multiple types of tensors which are efficiently contractible variational ansatze, manifestly (approximate) quantum error correction codes, and can support power-law correlation functions. An explicit construction of such networks is also provided. It approximates the holographic HaPPY pentagon code when variational parameters are taken to be small. This part is based on the work [4]. Supplementary materials and technical details are collected in the appendices

Quantum Lego and XP Stabilizer Codes

We apply the recent graphical framework of ''quantum lego'' to XP stabilizer codes where the stabilizer group is generally non-abelian. We show that the idea of operator matching continues to hold for such codes and is sufficient for generating all their XP symmetries provided the resulting code is XP. We provide an efficient classical algorithm for tracking these symmetries under tensor contraction or conjoining. This constitutes a partial extension of the algorithm implied by Gottesman-Knill theorem beyond Pauli stabilizer states and Clifford operations. Because conjoining transformations generate quantum operations that are universal, the XP symmetries obtained from these algorithms do not uniquely identify the resulting tensors in general. Using this extended framework, we provide a novel XP stabilizer code with higher distance and a $[[8,1,2]]$ code with fault-tolerant $T$ gate. For XP regular codes, we also construct a tensor-network-based the maximum likelihood decoder for any i.i.d. single qubit error channel.Comment: 18 pages, 6 figure

Clifford operations and homological codes for rotors and oscillators

We develop quantum information processing primitives for the planar rotor, the state space of a particle on a circle. By interpreting rotor wavefunctions as periodically identified wavefunctions of a harmonic oscillator, we determine the group of bosonic Gaussian operations inherited by the rotor. This $n$-rotor Clifford group, $\text{U}(1)^{n(n+1)/2} \rtimes \text{GL}_n(\mathbb{Z})$, is represented by continuous $\text{U}(1)$ gates generated by polynomials quadratic in angular momenta, as well as discrete $\text{GL}_n(\mathbb Z)$ momentum sign-flip and sum gates. We classify homological rotor error-correcting codes [arXiv:2303.13723] and various rotor states based on equivalence under Clifford operations. Reversing direction, we map homological rotor codes and rotor Clifford operations back into oscillators by interpreting occupation-number states as rotor states of non-negative angular momentum. This yields new multimode homological bosonic codes protecting against dephasing and changes in occupation number, along with their corresponding encoding and decoding circuits. In particular, we show how to non-destructively measure the oscillator phase using conditional occupation-number addition and post selection. We also outline several rotor and oscillator varieties of the GKP-stabilizer codes [arXiv:1903.12615].Comment: 26 pages, 5 figure

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

Adaptive Model Prediction Control-Based Multi-Terrain Trajectory Tracking Framework for Mobile Spherical Robots

Owing to uncertainties in both kinematics and dynamics, the current trajectory tracking framework for mobile robots like spherical robots cannot function effectively on multiple terrains, especially uneven and unknown ones. Since this is a prerequisite for robots to execute tasks in the wild, we enhance our previous hierarchical trajectory tracking framework to handle this issue. First, a modified adaptive RBF neural network (RBFNN) is proposed to represent all uncertainties in kinodynamics. Then the Lyapunov function is utilized to design its adaptive law, and a variable step-size algorithm is employed in the weights update procedure to accelerate convergence and improve stability. Hence, a new adaptive model prediction control-based instruction planner (VAN-MPC) is proposed. Without modifying the bottom controllers, we finally develop the multi-terrain trajectory tracking framework by employing the new instruction planner VAN-MPC. The practical experiments demonstrate its effectiveness and robustness.Comment: 10 pages, 20 figures. This work has been submitted to the IEEE Transactions on Industrial Electronics for possible publicatio

Black-Box Dissector: Towards Erasing-based Hard-Label Model Stealing Attack

Previous studies have verified that the functionality of black-box models can be stolen with full probability outputs. However, under the more practical hard-label setting, we observe that existing methods suffer from catastrophic performance degradation. We argue this is due to the lack of rich information in the probability prediction and the overfitting caused by hard labels. To this end, we propose a novel hard-label model stealing method termed \emph{black-box dissector}, which consists of two erasing-based modules. One is a CAM-driven erasing strategy that is designed to increase the information capacity hidden in hard labels from the victim model. The other is a random-erasing-based self-knowledge distillation module that utilizes soft labels from the substitute model to mitigate overfitting. Extensive experiments on four widely-used datasets consistently demonstrate that our method outperforms state-of-the-art methods, with an improvement of at most $8.27\%$. We also validate the effectiveness and practical potential of our method on real-world APIs and defense methods. Furthermore, our method promotes other downstream tasks, \emph{i.e.}, transfer adversarial attacks