IA Scholar Query: A Simplified Stabilizer ZX-calculus.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgSat, 03 Dec 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Quantum computation on a 19-qubit wide 2d nearest neighbour qubit array
https://scholar.archive.org/work/qwur4ba465fjhaaubhh54rux3i
In this paper, we explore the relationship between the width of a qubit lattice constrained in one dimension and physical thresholds for scalable, fault-tolerant quantum computation. To circumvent the traditionally low thresholds of small fixed-width arrays, we deliberately engineer an error bias at the lowest level of encoding using the surface code. We then address this engineered bias at a higher level of encoding using a lattice-surgery surface code bus that exploits this bias, or a repetition code to make logical qubits with unbiased errors out of biased surface code qubits. Arbitrarily low error rates can then be reached by further concatenating with other codes, such as Steane [[7,1,3]] code and the [[15,7,3]] CSS code. This enables a scalable fixed-width quantum computing architecture on a square qubit lattice that is only 19 qubits wide, given physical qubits with an error rate of 8.0× 10^-4. This potentially eases engineering issues in systems with fine qubit pitches, such as quantum dots in silicon or gallium arsenide.Alexis Shaw, Michael Bremner, Alexandru Paler, Daniel Herr, Simon J. Devittwork_qwur4ba465fjhaaubhh54rux3iSat, 03 Dec 2022 00:00:00 GMTPromotion strategy for online healthcare platform during the COVID-19 pandemic: Evidence from Spring Rain Doctor in China
https://scholar.archive.org/work/nljjzybmqraqldef6t5jo6yeda
IntroductionOnline healthcare platform (OHP) is a new form of medical treatment that solves the problems of an unbalanced distribution of medical resources in China. Especially during the COVID-19 pandemic, OHP has greatly reduced the medical pressure of the hospital and the risk of cross-infection.MethodsBased on self-determination theory (SDT) (Ryan and Deci, 2000), privacy calculus theory (PCT) (Culnan, 1999) and perceived value theory (PVT) (Choi, 2004), this study uses evolutionary game theory to analyze behavioral strategies and their dynamic evolution in the promotion of OHP. Moreover, we conduct numerical simulations with the help of program compilation.ResultsThe results demonstrate that (1) both the qualification inspection of doctors and the investment in information protection influence doctors' participation in and patients' usage of OHP; (2) both the initial probabilities of doctor participation and patient usage influence the multi-game results; (3) the trend of doctors joining OHP is affected by registration cost, time cost, and reputation loss; and (4) the trend of patients using online healthcare is mainly decided by the cost.ConclusionThis study takes the Spring Rain Doctor as an example to verify the game results. To further popularize online medical treatment among patients, the platform should attach importance to the inspection of doctors and the protection of privacy information and strengthen its publicity in remote places.Lanting Zhang, Dan Lv, Weijia Li, Zeyu Xingwork_nljjzybmqraqldef6t5jo6yedaWed, 30 Nov 2022 00:00:00 GMTScattering theory for Dirac fields near an extreme Kerr–de Sitter black hole
https://scholar.archive.org/work/ai5ey5tmzreqrp7rbpqttkqdi4
In this paper, we construct a scattering theory for classical massive Dirac fields near the "double" horizon of an extreme Kerr-de Sitter blackhole. Our main tool is the existence of a conjugate operator in the sense of Mourre theory. Additionally, despite the fact that effects of the rotation are "amplified" near the double horizon, we show that one can still reduce our study to a 1-dimensional problem through an appropriate decomposition of the Hilbert space. Résumé. -Dans cet article, nous développons une théorie de la diffusion pour des champs de Dirac massifs en métrique Kerr-de Sitter extrême, dans la région située entre l'horizon (double) du trou noir et l'horizon cosmologique. L'outil principal de la construction est l'existence d'un opérateur conjugué au sens de la théorie de Mourre. Par ailleurs, bien que les effets de la rotation soient amplifiées au voisinage de l'horizon double, nous montrons qu'il est néanmoins possible de se ramener à un problème de diffusion unidimensionnelle moyennant une décomposition ad-hoc de l'espace de Hilbert.Jack A. Borthwickwork_ai5ey5tmzreqrp7rbpqttkqdi4Mon, 28 Nov 2022 00:00:00 GMTActive volume: An architecture for efficient fault-tolerant quantum computers with limited non-local connections
https://scholar.archive.org/work/bn5ufifdg5gedaernazflyc56y
In existing general-purpose architectures for surface-code-based fault-tolerant quantum computers, the cost of a quantum computation is determined by the circuit volume, i.e., the number of qubits multiplied by the number of non-Clifford gates. We introduce an architecture using non-2D-local connections in which the cost does not scale with the number of qubits, and instead only with the number of logical operations. Each logical operation has an associated active volume, such that the cost of a quantum computation can be quantified as a sum of active volumes of all operations. For quantum computations with thousands of logical qubits, the active volume can be orders of magnitude lower than the circuit volume. Importantly, the architecture does not require all-to-all connectivity between N logical qubits. Instead, each logical qubit is connected to O(log N) other sites. As an example, we show that, using the same number of logical qubits, a 2048-bit factoring algorithm can be executed 44 times faster than on a general-purpose architecture without non-local connections. With photonic qubits, long-range connections are available and we show how photonic components can be used to construct a fusion-based active-volume quantum computer.Daniel Litinski, Naomi Nickersonwork_bn5ufifdg5gedaernazflyc56yMon, 28 Nov 2022 00:00:00 GMTA new and asymptotically optimally contracting coupling for the random walk Metropolis
https://scholar.archive.org/work/mruxqdwmmvbdjopifypyxdkkke
The reflection-maximal coupling of the random walk Metropolis (RWM) algorithm was recently proposed for use within unbiased MCMC. Numerically, when the target is spherical this coupling has been shown to perform well even in high dimensions. We derive high-dimensional ODE limits for Gaussian targets, which confirm this behaviour in the spherical case. However, we then extend our theory to the elliptical case and find that as the dimension increases the reflection coupling performs increasingly poorly relative to the mixing of the underlying RWM chains. To overcome this obstacle, we introduce gradient common random number (GCRN) couplings, which leverage gradient information. We show that the behaviour of GCRN couplings does not break down with the ellipticity or dimension. Moreover, we show that GCRN couplings are asymptotically optimal for contraction, in a sense which we make precise, and scale in proportion to the mixing of the underling RWM chains. Numerically, we apply GCRN couplings for convergence and bias quantification, and demonstrate that our theoretical findings extend beyond the Gaussian case.Tamás P. Papp, Chris Sherlockwork_mruxqdwmmvbdjopifypyxdkkkeTue, 22 Nov 2022 00:00:00 GMTEstimates of the Kobayashi metric and Gromov hyperbolicity on convex domains of finite type
https://scholar.archive.org/work/tnon6fwk7rhrbcwbi3lt4xen3a
In this paper we give an local estimate for the Kobayashi distance on a bounded convex domain of finite type, which relates to a local pseudodistance near the boundary. The estimate is precise up to a bounded additive term. Also we conclude that the domain equipped with the Kobayashi distance is Gromov hyperbolic which gives another proof of the result of Zimmer.Hongyu Wangwork_tnon6fwk7rhrbcwbi3lt4xen3aSat, 19 Nov 2022 00:00:00 GMTOptimal PID Controllers for AVR Systems Using Hybrid Simulated Annealing and Gorilla Troops Optimization
https://scholar.archive.org/work/hl6hiun3vzhjthgofpnaktoj7u
In the literature, all investigations dealing with regulator design in the AVR loop observe the AVR system as a single input single output (SISO) system, where the input is the generator reference voltage, while the output is the generator voltage. Besides, the regulator parameters are determined by analyzing the terminal generator voltage response for a step change from zero to the rated value of the generator voltage reference. Unlike literature approaches, in this study, tuning of the AVR controllers is conducted while modeling the AVR system as a double input single output (DISO) system, where the inputs are the setpoint of the generator voltage and the step disturbance on the excitation voltage, while the output is the generator voltage. The transfer functions of the generator voltage dependence on the generator voltage reference value and the excitation voltage change were derived in the developed DISO-AVR model. A novel objective function for estimating DISO-AVR regulator parameters is proposed. Also, a novel metaheuristic algorithm named hybrid simulated annealing and gorilla troops optimization is employed to solve the optimization problem. Many literature approaches are compared using different regulator structures and practical limitations. Furthermore, the experimental results of 120 MVA synchronous generators in HPP Piva (Montenegro) are presented to show the drawbacks of the literature approaches that observe generator setpoint voltage change from zero to the rated value. Based on the presented results, the proposed procedure is efficient and strongly applicable in practice.Sultan Alghamdi, Hatem F. Sindi, Muhyaddin Rawa, Abdullah A. Alhussainy, Martin Calasan, Mihailo Micev, Ziad M. Ali, Shady H. E. Abdel Aleemwork_hl6hiun3vzhjthgofpnaktoj7uFri, 18 Nov 2022 00:00:00 GMTCategorical lifting of the Jones polynomial: a survey
https://scholar.archive.org/work/pk3vtvcwvrgrvmky7lw37i4yqu
This is a brief review of the categorification of the Jones polynomial and its significance and ramifications in geometry, algebra, and low-dimensional topology.Mikhail Khovanov, Robert Lipshitzwork_pk3vtvcwvrgrvmky7lw37i4yquTue, 15 Nov 2022 00:00:00 GMTNew examples of W^* and C^*-superrigid groups
https://scholar.archive.org/work/ghuxivymvbcwbcjb533ku2ss4u
A group G is called W^*-superrigid (resp. C^*-superrigid) if it is completely recognizable from its von Neumann algebra L(G) (resp. reduced C^*-algebra C_r^*(G)). Developing new technical aspects in Popa's deformation/rigidity theory we introduce several new classes of W^*-superrigid groups which appear as direct products, semidirect products with non-amenable core and iterations of amalgamated free products and HNN-extensions. As a byproduct we obtain new rigidity results in C^*-algebra theory including additional examples of C^*-superrigid groups and explicit computations of symmetries of reduced group C^*-algebras.Ionut Chifan, Alec Diaz-Arias, Daniel Drimbework_ghuxivymvbcwbcjb533ku2ss4uWed, 09 Nov 2022 00:00:00 GMTCompatibility of Cyclic Causal Structures with Spacetime in General Theories with Free Interventions
https://scholar.archive.org/work/kogsjffevzculpddynbqgswpgm
By relating and ordering events, causality constitutes a pivotal feature of our world. However, we distinguish between information-theoretic causality, covering operational information processing, and relativistic causality, limiting signalling to the future. In this work, we improve on various results on the connection between both notions, as studied by V. Vilasini and R. Colbeck in arXiv:2206.12887 and arXiv:2203.11245, in particular regarding cyclicity. In the first part, we take an information-theoretic point of view, reviewing cyclic and fine-tuned causal models. Using interventions and affects relations to generically model signalling in these graphs, we study the properties of affects relations and establish new ways to use them to characterize causal structures. Focusing on higher-order (HO) affects relations, we can use knowledge of the absence of affects relations for causal inference. Further, we demonstrate a complete and constructive way to detect causal loops from a set of affects relations. In the second part, we embed causal structures into a generic partially ordered spacetime. Building on the results of arXiv:2206.12887, we propose additional stability conditions on the spacetime embedding and find that this can rule out a class of operationally detectable loops, that cannot be ruled out by the principle of no-signalling (outside the relativistic future) alone. We then propose a number of order-theoretic properties that we conjecture to hold in Minkowski spacetime with d ≥ 2 spatial dimensions. This would imply that in contrast to our result for generic spacetimes, in that Minkowski case, the no-signalling principle is indeed sufficient for ruling out this class of loops. Finally, we deduce novel restrictions for compatibility for certain HO affects relations.Maarten Grothuswork_kogsjffevzculpddynbqgswpgmMon, 07 Nov 2022 00:00:00 GMTStage structured prey-predator model incorporating mortal peril consequential to inefficiency and habitat complexity in juvenile hunting
https://scholar.archive.org/work/2fndtf4pcjhdfbrv4sdunsl65a
Dynamic exploration for a predator-prey biosystem of two species with ratio-dependent functional response together with the capability for predation by both juvenile and adult stage of the predator is carried out; coupled with incentive from all the natural documentation acquainting habitat complexity as an armour for the prey and also as a factor effectuating mortality of only the juvenile predators, attributable to their inefficiency. So as to avoid extinction of either of the species and to preserve the food chain of the ecological system, the results pertaining to the existence and stability of all the equilibrium points of the biosystem along with permanence, transcritical and Hopf bifurcation have been thoroughly studied. Excessive predation by juveniles exhibits destabilization of the biosystem through supercritical Hopf bifurcation; likewise, minimal inefficiency of juveniles and habitat complexity spawns extinction and fluctuation of each species, contrarily an abundance of them decimates the predator species. The obtained results and the dependence of the biosystem on some vital parameters are corroborated from a biological viewpoint, through numerical simulation, for implementation of the system in real-life scenario. Interestingly, an illustration reveals an intriguing limit cycle between the proposed system's trivial and axial equilibriums of the proposed system along with the co-existing periodic point for specific parametric values of inefficiency of juvenile predators.Debasish Bhattacharjee, Tapasvini Roy, Santanu Acharjee, Tarini Kumar Duttawork_2fndtf4pcjhdfbrv4sdunsl65aMon, 31 Oct 2022 00:00:00 GMTLQR Active Control of Fractional-Order Pantograph-Catenary System Based on Feedback Linearization
https://scholar.archive.org/work/hqcwfxq2nbddddcmiep5ns37mi
Fractional-order calculus has exclusive advantages in modeling the viscoelastic components with obvious fractional-order characteristics such as air springs and metal rubbers in the pantograph structure. In this paper, the air spring is tested, and fractional-order calculus is applied to the modeling of pantograph-catenary system of the high-speed train. The parameter identification method of fractional-order derivative is analytically derived. The traditional lumped mass model is improved and a coupling two-degree-of-freedom model of the fractional-order pantograph-catenary system is established. The fractional-order derivative term in the pantograph-catenary model is approximately calculated by the Oustaloup filter algorithm. Taking the time-varying nature into consideration, the catenary is treated as an extended variable to obtain an augmented model. On this basis, the system is linearized based on differential geometry theory, and an LQR controller is designed to control the pantograph-catenary system. The feedback linearized LQR control and PID control are used to control the same type of traditional pantograph, and the results are compared. Meanwhile, the control effects of feedback linearized LQR control under different pantograph parameters and at different train speeds are analyzed. The results show that the feedback linearized LQR control can present a much better control performance than PID control, and the pantograph-catenary contact force and pantograph head vibration amplitude are both reduced obviously. Even at different train speeds or under different pantograph parameters, it can also effectively reduce these control indexes and provide more robust control performance. These results help to put forward new control ideas and theoretical basis for the vibration control of the pantograph-catenary or similar dynamical system.Beining Wang, Shaofang Wen, Yongjun Shen, Haijun Renwork_hqcwfxq2nbddddcmiep5ns37miFri, 21 Oct 2022 00:00:00 GMTQuantifying the performance of bidirectional quantum teleportation
https://scholar.archive.org/work/s2dobun3jng5jmq3lsthmr6swi
Bidirectional teleportation is a fundamental protocol for exchanging quantum information between two parties by means of a shared resource state and local operations and classical communication (LOCC). Here we develop two seemingly different ways of quantifying the simulation error of unideal bidirectional teleportation by means of the normalized diamond distance and the channel infidelity, and we prove that they are equivalent. By relaxing the set of operations allowed from LOCC to those that completely preserve the positivity of the partial transpose, we obtain semi-definite programming lower bounds on the simulation error of unideal bidirectional teleportation. We evaluate these bounds for several key examples: when there is no resource state at all and for isotropic and Werner states, in each case finding an analytical solution. The first aforementioned example establishes a benchmark for classical versus quantum bidirectional teleportation. Another example consists of a resource state resulting from the action of a generalized amplitude damping channel on two Bell states, for which we find an analytical expression for the simulation error. We then evaluate the performance of some schemes for bidirectional teleportation due to Kiktenko et al. and find that they are suboptimal and do not go beyond the aforementioned classical limit. We offer a scheme alternative to theirs that is provably optimal. Finally, we generalize the whole development to the setting of bidirectional controlled teleportation, in which there is an additional assisting party who helps with the exchange of quantum information, and we establish semi-definite programming lower bounds on the simulation error for this task. More generally, we provide semi-definite programming lower bounds on the performance of bipartite and multipartite channel simulation using a shared resource state and LOCC.Aliza U. Siddiqui, Mark M. Wildework_s2dobun3jng5jmq3lsthmr6swiWed, 19 Oct 2022 00:00:00 GMTPhysics of Soil and Other Natural Porous Media
https://scholar.archive.org/work/dfvi25xojberllleyi3ubvrtom
The purpose of this monograph is to review the early theoretical basis of what is known today as soil physics and to serve as a textbook for intermediate porous media physics or transport in porous media graduate courses.Tairone Paiva Leãowork_dfvi25xojberllleyi3ubvrtomMon, 17 Oct 2022 00:00:00 GMTBeyond the classical Cauchy-Born rule
https://scholar.archive.org/work/n5lyonaz5zav7kcnab7x32kmey
Physically motivated variational problems involving non-convex energies are often formulated in a discrete setting and contain boundary conditions. The long-range interactions in such problems, combined with constraints imposed by lattice discreteness, can give rise to the phenomenon of geometric frustration even in a one-dimensional setting. While non-convexity entails the formation of microstructures, incompatibility between interactions operating at different scales can produce nontrivial mixing effects which are exacerbated in the case of incommensuration between the optimal microstructures and the scale of the underlying lattice. Unraveling the intricacies of the underlying interplay between non-convexity, non-locality and discreteness, represents the main goal of this study. While in general one cannot expect that ground states in such problems possess global properties, such as periodicity, in some cases the appropriately defined global solutions exist, and are sufficient to describe the corresponding continuum (homogenized) limits. We interpret those cases as complying with a Generalized Cauchy-Born (GCB) rule, and present a new class of problems with geometrical frustration which comply with GCB rule in one range of (loading) parameters while being strictly outside this class in a complementary range. A general approach to problems with such mixed behavior is developed.Andrea Braides, Andrea Causin, Margherita Solci, Lev Truskinovskywork_n5lyonaz5zav7kcnab7x32kmeySat, 15 Oct 2022 00:00:00 GMTElliptic homogenization from qualitative to quantitative
https://scholar.archive.org/work/j3yhf4hy2rc23ft45zz23auali
We give a self-contained introduction of the theory of elliptic homogenization for random coefficient fields, starting from classical qualitative homogenization. Our exposition of the quantitative theory is greatly compressed and much more readable compared to what has appeared previously. Our presentation also contains new results, such as optimal estimates (both in terms of stochastic moments and scaling of the error) for coefficient fields which are local functions of Gaussian random fields.Scott Armstrong, Tuomo Kuusiwork_j3yhf4hy2rc23ft45zz23aualiWed, 12 Oct 2022 00:00:00 GMTK-theory and index theory on manifolds with a proper Lie group action
https://scholar.archive.org/work/3logxmpg7bcotcz4nkbjgyjsua
The paper is devoted to the index theory of orbital and transverse elliptic operators on manifolds with a proper Lie group action. It corrects errors of my previous paper (published in JNCG in 2016) on transverse operators and contains new results. The two index theories, orbital and transverse, are very much intertwined and interdependent, and are treated together. The theory of orbital operators is developed from the basic definitions to the final index theorem. The KK-theoretic proofs of index theorems for elliptic, t-elliptic and orbital elliptic operators are given in sections 9, 10, 11. Throughout the paper, we use a simpler method in constructing pseudo-differential operators.Gennadi Kasparovwork_3logxmpg7bcotcz4nkbjgyjsuaWed, 05 Oct 2022 00:00:00 GMTDetection and Evaluation of Clusters within Sequential Data
https://scholar.archive.org/work/bue3nywa3nbqffglua55yjgbd4
Motivated by theoretical advancements in dimensionality reduction techniques we use a recent model, called Block Markov Chains, to conduct a practical study of clustering in real-world sequential data. Clustering algorithms for Block Markov Chains possess theoretical optimality guarantees and can be deployed in sparse data regimes. Despite these favorable theoretical properties, a thorough evaluation of these algorithms in realistic settings has been lacking. We address this issue and investigate the suitability of these clustering algorithms in exploratory data analysis of real-world sequential data. In particular, our sequential data is derived from human DNA, written text, animal movement data and financial markets. In order to evaluate the determined clusters, and the associated Block Markov Chain model, we further develop a set of evaluation tools. These tools include benchmarking, spectral noise analysis and statistical model selection tools. An efficient implementation of the clustering algorithm and the new evaluation tools is made available together with this paper. Practical challenges associated to real-world data are encountered and discussed. It is ultimately found that the Block Markov Chain model assumption, together with the tools developed here, can indeed produce meaningful insights in exploratory data analyses despite the complexity and sparsity of real-world data.Alexander Van Werde, Albert Senen-Cerda, Gianluca Kosmella, Jaron Sanderswork_bue3nywa3nbqffglua55yjgbd4Tue, 04 Oct 2022 00:00:00 GMTCompleteness of the ZX-calculus
https://scholar.archive.org/work/caqlai75azdvbjbhld26lrmvuq
The ZX-calculus is an intuitive but also mathematically strict graphical language for quantum computing, which is especially powerful for the framework of quantum circuits. Completeness of the ZX-calculus means any equality of matrices with size powers of n can be derived purely diagrammatically. In this thesis, we give the first complete axiomatisation the ZX-calculus for the overall pure qubit quantum mechanics, via a translation from the completeness result of another graphical language for quantum computing – the ZW-calculus. This paves the way for automated pictorial quantum computing, with the aid of some software like Quantomatic. Based on this universal completeness, we directly obtain a complete axiomatisation of the ZX-calculus for the Clifford+T quantum mechanics, which is approximatively universal for quantum computing, by restricting the ring of complex numbers to its subring corresponding to the Clifford+T fragment resting on the completeness theorem of the ZW-calculus for arbitrary commutative ring. Furthermore, we prove the completeness of the ZX-calculus (with just 9 rules) for 2-qubit Clifford+T circuits by verifying the complete set of 17 circuit relations in diagrammatic rewriting. In addition to completeness results within the qubit related formalism, we extend the completeness of the ZX-calculus for qubit stabilizer quantum mechanics to the qutrit stabilizer system. Finally, we show with some examples the application of the ZX-calculus to the proof of generalised supplementarity, the representation of entanglement classification and Toffoli gate, as well as equivalence-checking for the UMA gate.Quanlong Wangwork_caqlai75azdvbjbhld26lrmvuqThu, 29 Sep 2022 00:00:00 GMTUnique Games hardness of Quantum Max-Cut, and a conjectured vector-valued Borell's inequality
https://scholar.archive.org/work/skytuoytojh4tku23vzh2smgum
The Gaussian noise stability of a function f:ℝ^n →{-1, 1} is the expected value of f(x) · f(y) over ρ-correlated Gaussian random variables x and y. Borell's inequality states that for -1 ≤ρ≤ 0, this is minimized by the halfspace f(x) = sign(x_1). In this work, we generalize this result to hold for functions f:ℝ^n → S^k-1 which output k-dimensional unit vectors. Our main conjecture, which we call the vector-valued Borell's inequality, asserts that the expected value of ⟨ f(x), f(y)⟩ is minimized by the function f(x) = x_≤ k / ‖ x_≤ k‖, where x_≤ k = (x_1, ..., x_k). We give several pieces of evidence in favor of this conjecture, including a proof that it does indeed hold in the special case of n = k. As an application of this conjecture, we show that it implies several hardness of approximation results for a special case of the local Hamiltonian problem related to the anti-ferromagnetic Heisenberg model known as Quantum Max-Cut. This can be viewed as a natural quantum analogue of the classical Max-Cut problem and has been proposed as a useful testbed for developing algorithms. We show the following, assuming our conjecture: (1) The integrality gap of the basic SDP is 0.498, matching an existing rounding algorithm. Combined with existing results, this shows that the basic SDP does not achieve the optimal approximation ratio. (2) It is Unique Games-hard (UG-hard) to compute a (0.956+ε)-approximation to the value of the best product state, matching an existing approximation algorithm. (3) It is UG-hard to compute a (0.956+ε)-approximation to the value of the best (possibly entangled) state.Yeongwoo Hwang, Joe Neeman, Ojas Parekh, Kevin Thompson, John Wrightwork_skytuoytojh4tku23vzh2smgumWed, 28 Sep 2022 00:00:00 GMT