Coarse-Grained Picture for Controlling Complex Quantum Systems

We propose a coarse-grained picture to control ``complex'' quantum dynamics, i.e., multi-level-multi-level transition with a random interaction. Assuming that optimally controlled dynamics can be described as a Rabi-like oscillation between an initial and final state, we derive an analytic optimal field as a solution to optimal control theory. For random matrix systems, we numerically confirm that the analytic optimal field steers an initial state to a target state which both contains many eigenstates.Comment: jpsj2.cls, 2 pages, 3 figure files; appear in J. Phys. Soc. Jpn. Vol.73, No.11 (Nov. 15, 2004

Effects of nonlinear sweep in the Landau-Zener-Stueckelberg effect

We study the Landau-Zener-Stueckelberg (LZS) effect for a two-level system with a time-dependent nonlinear bias field (the sweep function) W(t). Our main concern is to investigate the influence of the nonlinearity of W(t) on the probability P to remain in the initial state. The dimensionless quantity epsilon = pi Delta ^2/(2 hbar v) depends on the coupling Delta of both levels and on the sweep rate v. For fast sweep rates, i.e., epsilon << l and monotonic, analytic sweep functions linearizable in the vicinity of the resonance we find the transition probability 1-P ~= epsilon (1+a), where a>0 is the correction to the LSZ result due to the nonlinearity of the sweep. Further increase of the sweep rate with nonlinearity fixed brings the system into the nonlinear-sweep regime characterized by 1-P ~= epsilon ^gamma with gamma neq 1 depending on the type of sweep function. In case of slow sweep rates, i.e., epsilon >>1 an interesting interference phenomenon occurs. For analytic W(t) the probability P=P_0 e^-eta is determined by the singularities of sqrt{Delta ^2+W^2(t)} in the upper complex plane of t. If W(t) is close to linear, there is only one singularity, that leads to the LZS result P=e^-epsilon with important corrections to the exponent due to nonlinearity. However, for, e.g., W(t) ~ t^3 there is a pair of singularities in the upper complex plane. Interference of their contributions leads to oscillations of the prefactor P_0 that depends on the sweep rate through epsilon and turns to zero at some epsilon. Measurements of the oscillation period and of the exponential factor would allow to determine Delta, independently.Comment: 11 PR pages, 12 figures. To be published in PR

Polarizations and Nullcone of Representations of Reductive Groups

The paper starts with the following simple observation. Let V be a representation of a reductive group G, and let f_1,f_2,...,f_n be homogeneous invariant functions. Then the polarizations of f_1,f_2,...,f_n define the nullcone of k 0} h(t) x = 0 for all x in L. This is then applied to many examples. A surprising result is about the group SL(2,C) where almost all representations V have the property that all linear subspaces of the nullcone are annihilated. Again, this has interesting applications to the invariants on several copies. Another result concerns the n-qubits which appear in quantum computing. This is the representation of a product of n copies of $SL_2$ on the n-fold tensor product C^2 otimes C^2 otimes ... otimes C^2. Here we show just the opposite, namely that the polarizations never define the nullcone of several copies if n <= 3. (An earlier version of this paper, distributed in 2002, was split into two parts; the first part with the title ``On the nullcone of representations of reductive groups'' is published in Pacific J. Math. {bf 224} (2006), 119--140.

Evaluation of OpenAI Codex for HPC Parallel Programming Models Kernel Generation

We evaluate AI-assisted generative capabilities on fundamental numerical kernels in high-performance computing (HPC), including AXPY, GEMV, GEMM, SpMV, Jacobi Stencil, and CG. We test the generated kernel codes for a variety of language-supported programming models, including (1) C++ (e.g., OpenMP [including offload], OpenACC, Kokkos, SyCL, CUDA, and HIP), (2) Fortran (e.g., OpenMP [including offload] and OpenACC), (3) Python (e.g., numba, Numba, cuPy, and pyCUDA), and (4) Julia (e.g., Threads, CUDA.jl, AMDGPU.jl, and KernelAbstractions.jl). We use the GitHub Copilot capabilities powered by OpenAI Codex available in Visual Studio Code as of April 2023 to generate a vast amount of implementations given simple + + prompt variants. To quantify and compare the results, we propose a proficiency metric around the initial 10 suggestions given for each prompt. Results suggest that the OpenAI Codex outputs for C++ correlate with the adoption and maturity of programming models. For example, OpenMP and CUDA score really high, whereas HIP is still lacking. We found that prompts from either a targeted language such as Fortran or the more general-purpose Python can benefit from adding code keywords, while Julia prompts perform acceptably well for its mature programming models (e.g., Threads and CUDA.jl). We expect for these benchmarks to provide a point of reference for each programming model's community. Overall, understanding the convergence of large language models, AI, and HPC is crucial due to its rapidly evolving nature and how it is redefining human-computer interactions.Comment: Accepted at the Sixteenth International Workshop on Parallel Programming Models and Systems Software for High-End Computing (P2S2), 2023 to be held in conjunction with ICPP 2023: The 52nd International Conference on Parallel Processing. 10 pages, 6 figures, 5 table

Transient response of a quantum wave to an instantaneous potential step switching

The transient response of a stationary state of a quantum particle in a step potential to an instantaneous change in the step height (a simplified model for a sudden bias switch in an electronic semiconductor device) is solved exactly by means of a semianalytical expression. The characteristic times for the transient process up to the new stationary state are identified. A comparison is made between the exact results and an approximate method.Comment: 8 pages, 8 figures, Revtex

Comparing Llama-2 and GPT-3 LLMs for HPC kernels generation

We evaluate the use of the open-source Llama-2 model for generating well-known, high-performance computing kernels (e.g., AXPY, GEMV, GEMM) on different parallel programming models and languages (e.g., C++: OpenMP, OpenMP Offload, OpenACC, CUDA, HIP; Fortran: OpenMP, OpenMP Offload, OpenACC; Python: numpy, Numba, pyCUDA, cuPy; and Julia: Threads, CUDA.jl, AMDGPU.jl). We built upon our previous work that is based on the OpenAI Codex, which is a descendant of GPT-3, to generate similar kernels with simple prompts via GitHub Copilot. Our goal is to compare the accuracy of Llama-2 and our original GPT-3 baseline by using a similar metric. Llama-2 has a simplified model that shows competitive or even superior accuracy. We also report on the differences between these foundational large language models as generative AI continues to redefine human-computer interactions. Overall, Copilot generates codes that are more reliable but less optimized, whereas codes generated by Llama-2 are less reliable but more optimized when correct.Comment: Accepted at LCPC 2023, The 36th International Workshop on Languages and Compilers for Parallel Computing http://www.lcpcworkshop.org/LCPC23/ . 13 pages, 5 figures, 1 tabl

Size-controlled quantum dots reveal the impact of intraband transitions on high-order harmonic generation in solids

Since the discovery of high-order harmonic generation (HHG) in solids1,2,3, much effort has been devoted to understand its generation mechanism and both inter- and intraband transitions are known to be essential1,2,3,4,5,6,7,8,9,10. However, intraband transitions are affected by the electronic structure of a solid, and how they contribute to nonlinear carrier generation and HHG remains an open question. Here we use mid-infrared laser pulses to study HHG in CdSe and CdS quantum dots, where quantum confinement can be used to control the intraband transitions. We find that both HHG intensity per excited volume and generated carrier density increase when the average quantum dot size is increased from about 2 to 3 nm. We show that the reduction in sub-bandgap energy in larger quantum dots enhances intraband transitions, and this—in turn—increases the rate of photocarrier injection by coupling with interband transitions, resulting in enhanced HHG

First application of the Trojan Horse Method with a Radioactive Ion Beam: study of the 18^{18}F(p,αp,{\alpha})15^{15}O}} reaction at astrophysical energies

Measurement of nuclear cross sections at astrophysical energies involving unstable species is one of the most challenging tasks in experimental nuclear physics. The use of indirect methods is often unavoidable in this scenario. In this paper the Trojan Horse Method is applied for the first time to a radioactive ion beam induced reaction studying the $^{18}$F($p,{\alpha}$)$^{15}$O process at low energies relevant to astrophysics via the three body reaction $^{2}$H($^{18}$F,${\alpha}^{15}$O)n. The knowledge of the $^{18}$F($p, {\alpha}$)$^{15}$O reaction rate is crucial to understand the nova explosion phenomena. The cross section of this reaction is characterized by the presence of several resonances in $^{19}$Ne and possibly interference effects among them. The results reported in Literature are not satisfactory and new investigations of the $^{18}$F($p,{\alpha}$)$^{15}$O reaction cross section will be useful. In the present work the spin-parity assignments of relevant levels have been discussed and the astrophysical S-factor has been extracted considering also interference effectsComment: 7 pages, 4 figure

Landau-Zener-Stueckelberg effect in a model of interacting tunneling systems

The Landau-Zener-Stueckelberg (LZS) effect in a model system of interacting tunneling particles is studied numerically and analytically. Each of N tunneling particles interacts with each of the others with the same coupling J. This problem maps onto that of the LZS effect for a large spin S=N/2. The mean-field limit N=>\infty corresponds to the classical limit S=>\infty for the effective spin. It is shown that the ferromagnetic coupling J>0 tends to suppress the LZS transitions. For N=>\infty there is a critical value of J above which the staying probability P does not go to zero in the slow sweep limit, unlike the standard LZS effect. In the same limit for J>0 LZS transitions are boosted and P=0 for a set of finite values of the sweep rate. Various limiting cases such as strong and weak interaction, slow and fast sweep are considered analytically. It is shown that the mean-field approach works well for arbitrary N if the interaction J is weak.Comment: 13 PR pages, 15 Fig

Anonymous Single-Sign-On for n designated services with traceability

Anonymous Single-Sign-On authentication schemes have been proposed to allow users to access a service protected by a verifier without revealing their identity which has become more important due to the introduction of strong privacy regulations. In this paper we describe a new approach whereby anonymous authentication to different verifiers is achieved via authorisation tags and pseudonyms. The particular innovation of our scheme is authentication can only occur between a user and its designated verifier for a service, and the verification cannot be performed by any other verifier. The benefit of this authentication approach is that it prevents information leakage of a user's service access information, even if the verifiers for these services collude which each other. Our scheme also supports a trusted third party who is authorised to de-anonymise the user and reveal her whole services access information if required. Furthermore, our scheme is lightweight because it does not rely on attribute or policy-based signature schemes to enable access to multiple services. The scheme's security model is given together with a security proof, an implementation and a performance evaluation.Comment: 3