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In variational algorithms, quantum circuits are conventionally parametrized with respect to single-qubit gates. In this study, we parameterize a generalized controlled gate and propose an algorithm to estimate the optimal parameters for locally minimizing the cost value, where we extend the free quaternion selection method, an optimization method for a single-qubit gate. To benchmark the performance, we apply the proposed method to various optimization problems, including the Variational Quantum Eigensolver (VQE) for Ising and molecular Hamiltonians, Variational Quantum Algorithms (VQA) for fidelity maximization, and unitary compilation of time evolution operators. In these applications, the proposed method shows efficient optimization and greater expressibility with shallower circuits than other methods. Furthermore, this method is also capable of generalizing and fully optimizing particle-number-conserving gates, which are in demand in chemical systems applications. Taking advantage of this property, we have actually approximated time evolution operators of molecular Hamiltonian and simulated the dynamics with shallower circuits in comparison to the standard implementation by Trotter decomposition., Comment: 21 pages, 15 figures

The concept of zero forcing involves a dynamic coloring process by which blue vertices cause white vertices to become blue, with the goal of forcing the entire graph blue while choosing as few as possible vertices to be initially blue. Past research in this area has focused on structural arguments, with approaches varying from graph substructures to the interplay between local and global graph structures. This paper explores the use of these structural concepts when determining the zero forcing number of complex classes of graphs, specifically two infinite classes of graphs each defined on multiple parameters.

We develop an energy calculation algorithm leveraging quantum phase difference estimation (QPDE) scheme and a tensor-network-based unitary compression method in the preparation of superposition states and time-evolution gates. Alongside its efficient implementation, this algorithm reduces depolarization noise affections exponentially. We demonstrated energy gap calculations for one-dimensional Hubbard models on IBM superconducting devices using circuits up to 32-system (plus one-ancilla) qubits, a five-fold increase over previous QPE demonstrations, at the 7242 controlled-Z gate level of standard transpilation, utilizing a Q-CTRL error suppression module. Additionally, we propose a technique towards molecular executions using spatial orbital localization and index sorting, verified by a 13- (17-)qubit hexatriene (octatetraene) simulation. Since QPDE can handle the same objectives as QPE, our algorithm represents a leap forward in quantum computing on real devices., Comment: 27 pages, Code repository

We introduce a unital associative algebra ${\mathcal{SV}ir\!}_{q,k}$, having $q$ and $k$ as complex parameters, generated by the elements $K^\pm_m$ ($\pm m\geq 0$), $T_m$ ($m\in \mathbb{Z}$), and $G^\pm_m$ ($m\in \mathbb{Z}+{1\over 2}$ in the Neveu-Schwarz sector, $m\in \mathbb{Z}$ in the Ramond sector), satisfying relations which are at most quartic. Calculations of some low-lying Kac determinants are made, providing us with a conjecture for the factorization property of the Kac determinants. The analysis of the screening operators gives a supporting evidence for our conjecture. It is shown that by taking the limit $q\rightarrow 1$ of ${\mathcal{SV}ir\!}_{q,k}$ we recover the ordinary ${\mathcal N}=2$ superconformal algebra. We also give a nontrivial Heisenberg representation of the algebra ${\mathcal{SV}ir\!}_{q,k}$, making a twist of the $U(1)$ boson in the Wakimoto representation of the quantum affine algebra $U_q(\widehat{\mathfrak{sl}}_2)$, which naturally follows from the construction of ${\mathcal{SV}ir\!}_{q,k}$ by gluing the deformed $Y$-algebras of Gaiotto and Rap$\check{\mathrm{c}}$\'{a}k., Comment: 83 pages

As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction of an uncertainty set, we adopt the segmented least squares so that a data set that is not fitted well by the linear regression model can be dealt with. Since the obtained uncertainty set is nonconvex, the optimization problem solved for the uncertainty analysis is nonconvex. We recast this optimization problem as a mixed-integer programming problem to find a global optimal solution. This global optimality, together with a fundamental property of the order statistics, guarantees that the obtained bound for the structural response is conservative, in the sense that, at least a specified confidence level, probability that the structural response is in this bound is no smaller than a specified target value. We present numerical examples for three different types of skeletal structures.

Cell-free massive MIMO (CF-mMIMO), where each user equipment (UE) is connected to multiple access points (APs), is emerging as an important component for 5G and 6G cellular systems. Accurate channel models based on measurements are required to optimize their design and deployment. This paper presents an extensive measurement campaign for CF-mMIMO in an urban environment. A new "virtual AP" technique measures channels between 80 UE locations and more than 20,000 possible microcellular AP locations. Measurements are done at 3.5 GHz carrier frequency with 350 MHz bandwidth (BW). The paper describes the measurement setup and data processing, shows sample results and their physical interpretation, and provides statistics for key quantities such as pathloss, shadowing, delay spread (DS), and delay window. We find pathloss coefficients of 2.9 and 10.4 for line-of-sight (LOS) and non line-of-sight (NLOS), respectively, where the high LOS coefficient is mainly because larger distance leads to more grazing angle of incidence and thus lower antenna gain in our setup. Shadowing standard deviations are 5.1/16.6 dB, and root mean squared (RMS) DSs of -80.6/-72.6 dBs. The measurements can also be used for parameterizing a CUNEC-type model, which will be reported in future work., Comment: submitted to IEEE TWC

The design of cell-free massive MIMO (CF-mMIMO) systems requires accurate, measurement-based channel models. This paper provides the first results from the by far most extensive outdoor measurement campaign for CF-mMIMO channels in an urban environment. We measured impulse responses between over 20,000 potential access point (AP) locations and 80 user equipments (UEs) at 3.5 GHz with 350 MHz bandwidth (BW). Measurements use a "virtual array" approach at the AP and a hybrid switched/virtual approach at the UE. This paper describes the sounder design, measurement environment, data processing, and sample results, particularly the evolution of the power-delay profiles (PDPs) as a function of the AP locations, and its relation to the propagation environment., Comment: Submitted to: VTC 2024-Fall

Rectification phenomenon caused by the simultaneous breaking of time reversal and spatial inversion symmetries has been extended to a wide range of (quasi)particles and waves; however, the nonreciprocal diffraction, which is the imbalance of upward and downward deflections, was previously observed only for photons and remained to be extended to other (quasi)particles. In this study, we present evidence of the nonreciprocal diffraction of surface acoustic wave (SAW) utilizing a magnetoelastic grating on a SAW device. Asymmetric diffraction intensities were observed when the ferromagnetic resonance was acoustically excited. Based on a theoretical model, we attribute the microscopic origin of this phenomenon to the resonant scattering involving ferromagnetic resonance excitations. The novel property may pave an avenue to further development of SAW devices for various purposes, including microwave communications and quantum engineering applications., Comment: 15 pages, 12 figures

The maximum (or minimum) generalized eigenvalue of symmetric positive semidefinite matrices that depend on optimization variables often appears as objective or constraint functions in structural topology optimization when we consider robustness, vibration, and buckling. It can be an unbounded or discontinuous function where matrices become singular (where a topological change of the structural design occurs). Based on variational analysis, we redefine the maximum (and minimum) generalized eigenvalue function as an extended real-valued function and propose a real-valued continuous approximation of it. Then, we show that the proposed approximation epi-converges to the original redefined function, which justifies solving problems with the approximation instead. We consider two specific topology optimization problems: robust compliance optimization and eigenfrequency optimization and conduct simple numerical experiments., Comment: 28 pages, 9 figures

Bachmann and Tasaka discovered a relationship between multiple Eisenstein series (MES) of level 1 and formal iterated integrals corresponding to multiple zeta value. They also constructed shuffle regularized MES of level 1, which satisfies the shuffle relation that is same as multiple zeta values. In this paper, we expand their results for arbitrary level and give some linear relations among MES of level $N$., Comment: 26 pages

Dynamical response functions are fundamental quantities to describe the excited-state properties in quantum many-body systems. Quantum algorithms have been proposed to evaluate these quantities by means of quantum phase estimation (QPE), where the energy spectra are directly extracted from the QPE measurement outcomes in the frequency domain. Accurate estimation of excitation energies and transition probabilities with these QPE-based approaches is, however, challenging because of the problem of spectral leakage (or peak broadening) which is inherent in the QPE algorithm. To overcome this issue, in this work we consider an extension of the QPE-based approach adopting the optimal entangled input states, which is known to achieve the Heisenberg-limited scaling for the estimation precision. We show that with this method the peaks in the calculated energy spectra are more localized than those calculated by the original QPE-based approaches, suggesting the mitigation of the spectral leakage problem. By analyzing the probability distribution with the entangled phase estimation, we propose a simple scheme to better estimate both the transition energies and the corresponding transition probabilities of the peaks of interest in the spectra. The validity of our prescription is demonstrated by numerical simulations in various quantum many-body problems: the spectral function of a simple electron-plasmon model in condensed-matter physics, the dipole transitions of the H$_2$O molecule in quantum chemistry, and the electromagnetic transitions of the $^6$Li nucleus in nuclear physics.

We conducted measurements of $K^- + {^3{\rm He}} \to \pi \!Y \!N + N'$ reactions using a $1~{\rm GeV}/c$ $K^-$-beam, with the objective of understanding the broad decay width of $\bar{K} \!N \!N$ (approximately twice as broad as that of $\Lambda(1405)$ considered to be the $\bar{K} \!N$ quasi-bound state). We successfully reproduced distributions of the $\pi \! Y \! N$ invariant mass and momentum transfer for $\pi \! Y \! N$ using model fitting functions for $\bar{K} \!N \!N$ formation and quasi-free $\bar{K}$ absorption (${\rm QF}_{\bar{K}-{\rm abs}}$) processes. The model can describe the experimental data quite well, and four $\bar{K} \! N \! N \to \pi \! Y \! N $ cross-sections were obtained. The results indicate that mesonic decay is the dominant decay branch of $\bar{K} \! N \! N$. The results also suggest that $\Gamma_{\pi \Lambda N} \sim \Gamma_{\pi \Sigma N}$, which indicates that the $I_{\bar{K} \! N}=1$ absorption channel, in addition to the $I_{\bar{K} \! N}=0$ absorption channel, substantially contribute to the $\bar{K} \! N \! N$ decay, making the $\bar{K} \! N \! N$ state approximately twice as unstable as $\Lambda$(1405).

One of the trendsetting themes in soft robotics has been the goal of developing the ultimate universal soft robotic gripper. One that is capable of manipulating items of various shapes, sizes, thicknesses, textures, and weights. All the while still being lightweight and scalable in order to adapt to use cases. In this work, we report a soft gripper that enables delicate and precise grasps of fragile, deformable, and flexible objects but also excels in lifting heavy objects of up to 1617x its own body weight. The principle behind the soft gripper is based on extending the capabilities of electroadhesion soft grippers through the enhancement principles found in metamaterial adhesion cut and patterning. This design amplifies the adhesion and grasping payload in one direction while reducing the adhesion capabilities in the other direction. This counteracts the residual forces during peeling (a common problem with electroadhesive grippers), thus increasing its speed of release. In essence, we are able to tune the maximum strength and peeling speed, beyond the capabilities of previous electroadhesive grippers. We study the capabilities of the system through a wide range of experiments with single and multiple-fingered peel tests. We also demonstrate its modular and adaptive capabilities in the real-world with a two-finger gripper, by performing grasping tests of up to $5$ different multi-surfaced objects., Comment: 7 pages, 9 figures, Accepted in IEEE International Conference on Soft Robotics 2024 (Robosoft)

Evaluating the relative performance of different quantum algorithms for quantum computers is of great significance in the research of quantum algorithms. In this study, we consider the problem of quantum chemistry, which is considered one of the important applications of quantum algorithms. While evaluating these algorithms in systems with a large number of qubits is essential to see the scalability of the algorithms, the solvable models usually used for such evaluations typically have a small number of terms compared to the molecular Hamiltonians used in quantum chemistry. The large number of terms in molecular Hamiltonians is a major bottleneck when applying quantum algorithms to quantum chemistry. Various methods are being considered to address this problem, highlighting its importance in developing quantum algorithms for quantum chemistry. Based on these points, a solvable model with a number of terms comparable to the molecular Hamiltonian is essential to evaluate the performance of such algorithms. In this paper, we propose a set of exactly solvable Hamiltonians that has a comparable order of terms with molecular Hamiltonians by applying a spin-involving orbital rotation to the one-dimensional Fermi-Hubbard Hamiltonian. We verify its similarity to the molecular Hamiltonian from some prospectives and investigate whether the difficulty of calculating the ground-state energy changes before and after orbital rotation by applying the density matrix renormalization group up to 24 sites corresponding to 48 qubits. This proposal would enable proper evaluation of the performance of quantum algorithms for quantum chemistry, serving as a guiding framework for algorithm development., Comment: 10 pages

Photonic reservoir computing has been successfully utilized in time-series prediction as the need for hardware implementations has increased. Prediction of chaotic time series remains a significant challenge, an area where the conventional reservoir computing framework encounters limitations of prediction accuracy. We introduce an attention mechanism to the reservoir computing model in the output stage. This attention layer is designed to prioritize distinct features and temporal sequences, thereby substantially enhancing the prediction accuracy. Our results show that a photonic reservoir computer enhanced with the attention mechanism exhibits improved prediction capabilities for smaller reservoirs. These advancements highlight the transformative possibilities of reservoir computing for practical applications where accurate prediction of chaotic time series is crucial.

Photonic computing has been widely used to accelerate the computational performance in machine learning. Photonic decision-making is a promising approach that uses photonic computing technologies to solve the multi-armed bandit problem based on reinforcement learning. Photonic decision making using chaotic mode competition dynamics has been proposed. However, the experimental conditions for achieving superior decision-making performance have not yet been established. In this study, we experimentally investigate the mode competition dynamics in a chaotic multimode semiconductor laser in the presence of optical feedback and injection. We control chaotic mode-competition dynamics via optical injection, and we found that positive wavelength detuning results in an efficient mode concentration to one of the longitudinal modes with a small optical injection power. We experimentally investigate two-dimensional bifurcation map of the laser dynamics of the total intensity. Complex mixed dynamics are observed in the presence of optical feedback and injection. We experimentally conduct decision making to solve the bandit problem using chaotic mode-competition dynamics. A fast mode concentration property is observed at positive wavelength detuning, which resulted in a fast convergence of the correct decision rate. Our findings could be useful in accelerating the decision-making performance in adaptive optical networks using reinforcement learning., Comment: 19 pages, 14 figures

Smoothing accelerated gradient methods achieve faster convergence rates than that of the subgradient method for some nonsmooth convex optimization problems. However, Nesterov's extrapolation may require gradients at infeasible points, and thus they cannot be applied to some structural optimization problems. We introduce a variant of smoothing accelerated projected gradient methods where every variable is feasible. The $O(k^{-1}\log k)$ convergence rate is obtained using the Lyapunov function. We conduct a numerical experiment on the robust compliance optimization of a truss structure., Comment: 6 pages, 2 figures

We study properties and algorithms of a minimization problem of the maximum generalized eigenvalue of symmetric-matrix-valued affine functions, which is nonsmooth and quasiconvex, and has application to eigenfrequency optimization of truss structures. We derive an explicit formula of the Clarke subdifferential of the maximum generalized eigenvalue and prove the maximum generalized eigenvalue is a pseudoconvex function, which is a subclass of a quasiconvex function, under suitable assumptions. Then, we consider smoothing methods to solve the problem. We introduce a smooth approximation of the maximum generalized eigenvalue and prove the convergence rate of the smoothing projected gradient method to a global optimal solution in the considered problem. Also, some heuristic techniques to reduce the computational costs, acceleration and inexact smoothing, are proposed and evaluated by numerical experiments., Comment: 33 pages, 16 figures

We consider how gauge theories can be described by matrix models. Conventional matrix regularization is defined for scalar functions and is not applicable to gauge fields, which are connections of fiber bundles. We clarify how the degrees of freedom of gauge fields are related to the matrix degrees of freedom, by formulating the Seiberg-Witten map between them., Comment: 32 pages, 0 figures

We propose high-frequency gravitational wave (GW) detectors with Rydberg atoms. Rydberg atoms are ultra-sensitive detectors of electric fields. By setting up a constant magnetic field, a weak electric field is generated upon the arrival of GWs. The weak electric field signal is then detected by an electromagnetically induced transparency (EIT) in the system of the Rydberg atoms. Recently, the minimum detectable electric field with the Rydberg atoms is further improved by employing superheterodyne detection method. Hence, even the weak signal generated by GWs turns out to be detectable. We calculate the amplitude of Rabi frequency of the Rydberg atoms induced by the GWs and show that the sensitivity of the Rydberg atoms becomes maximum when the size of the Rydberg atoms is close to the wavelength of GWs. We evaluate the minimum detectable amplitude of GWs with Rubidium Rydberg atoms and find that the detector can probe GWs with a frequency $f=4.2$ GHz and an amplitude around $10^{-20}$., Comment: 31 pages, 9 figures

Zero forcing is a dynamic coloring process on graphs. Initially, each vertex of a graph is assigned a color of either blue or white, and then a process begins by which blue vertices force white vertices to become blue. The zero forcing number is the cardinality of the smallest set of initially blue vertices which can force the entire graph to become blue, and the propagation time is the minimum number of steps in such a zero forcing process. In this paper we will determine the zero forcing numbers and propagation times of two infinite classes of graphs called gear graphs and helm graphs.

We consider the Helmholtz-Weyl decomposition on a time dependent bounded domain $\Omega(t)$ in $\mathbb{R}^3$. Especially, we investigate the domain dependence of each component in the decomposition, namely, the harmonic vector fields (i.e., $\mathrm{div}$ and $\mathrm{rot}$ free vectors), vector potentials, and scalar potentials equipped with suitable boundary conditions, when $\Omega(t)$ moves along to $t\in\mathbb{R}$. As an application, we construct a time periodic solution of the incompressible Navier-Stokes equations for some large boundary data with non-zero fluxes.

We explore the feasibility of fault-tolerant quantum computation using the bit-flip repetition code in a biased noise channel where only the bit-flip error can occur. While several logic gates can potentially produce phase-flip errors even in such a channel, we propose bias-preserving implementation of $S$, $H$, $\mathrm{CZ}$, and $R_z$ gates. We demonstrate that our scheme improves the computational precision in several tasks such as the time evolution of quantum systems and variational quantum eigensolver., Comment: 27 pages, 18 figures