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Universal power laws have been scrutinised in physics and beyond, and a long-standing debate exists in econophysics regarding the strict universality of the nonlinear price impact, commonly referred to as the square-root law (SRL). The SRL posits that the average price impact $I$ follows a power law with respect to transaction volume $Q$, such that $I(Q) \propto Q^{\delta}$ with $\delta \approx 1/2$. Some researchers argue that the exponent $\delta$ should be system-specific, without universality. Conversely, others contend that $\delta$ should be exactly $1/2$ for all stocks across all countries, implying universality. However, resolving this debate requires high-precision measurements of $\delta$ with errors of around $0.1$ across hundreds of stocks, which has been extremely challenging due to the scarcity of large microscopic datasets -- those that enable tracking the trading behaviour of all individual accounts. Here we conclusively support the universality hypothesis of the SRL by a complete survey of all trading accounts for all liquid stocks on the Tokyo Stock Exchange (TSE) over eight years. Using this comprehensive microscopic dataset, we show that the exponent $\delta$ is equal to $1/2$ within statistical errors at both the individual stock level and the individual trader level. Additionally, we rejected two prominent models supporting the nonuniversality hypothesis: the Gabaix-Gopikrishnan-Plerou-Stanley and the Farmer-Gerig-Lillo-Waelbroeck models. Our work provides exceptionally high-precision evidence for the universality hypothesis in social science and could prove useful in evaluating the price impact by large investors -- an important topic even among practitioners., Comment: 28 pages, 16 figures

Quantum materials governed by emergent topological fermions have become a cornerstone of physics. Dirac fermions in graphene form the basis for moir\'e quantum matter, and Dirac fermions in magnetic topological insulators enabled the discovery of the quantum anomalous Hall effect. In contrast, there are few materials whose electromagnetic response is dominated by emergent Weyl fermions. Nearly all known Weyl materials are overwhelmingly metallic, and are largely governed by irrelevant, conventional electrons. Here we theoretically predict and experimentally observe a semimetallic Weyl ferromagnet in van der Waals (Cr,Bi)$_2$Te$_3$. In transport, we find a record bulk anomalous Hall angle $> 0.5$ along with non-metallic conductivity, a regime sharply distinct from conventional ferromagnets. Together with symmetry analysis, our data suggest a semimetallic Fermi surface composed of two Weyl points, with a giant separation $> 75\%$ of the linear dimension of the bulk Brillouin zone, and no other electronic states. Using state-of-the-art crystal synthesis techniques, we widely tune the electronic structure, allowing us to annihilate the Weyl state and visualize a unique topological phase diagram exhibiting broad Chern insulating, Weyl semimetallic and magnetic semiconducting regions. Our observation of a semimetallic Weyl ferromagnet offers an avenue toward novel correlated states and non-linear phenomena, as well as zero-magnetic-field Weyl spintronic and optical devices., Comment: Nature, in press

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

In order to solve problems of practical importance, quantum computers will likely need to incorporate quantum error correction, where a logical qubit is redundantly encoded in many noisy physical qubits. The large physical-qubit overhead typically associated with error correction motivates the search for more hardware-efficient approaches. Here, using a microfabricated superconducting quantum circuit, we realize a logical qubit memory formed from the concatenation of encoded bosonic cat qubits with an outer repetition code of distance $d=5$. The bosonic cat qubits are passively protected against bit flips using a stabilizing circuit. Cat-qubit phase-flip errors are corrected by the repetition code which uses ancilla transmons for syndrome measurement. We realize a noise-biased CX gate which ensures bit-flip error suppression is maintained during error correction. We study the performance and scaling of the logical qubit memory, finding that the phase-flip correcting repetition code operates below threshold, with logical phase-flip error decreasing with code distance from $d=3$ to $d=5$. Concurrently, the logical bit-flip error is suppressed with increasing cat-qubit mean photon number. The minimum measured logical error per cycle is on average $1.75(2)\%$ for the distance-3 code sections, and $1.65(3)\%$ for the longer distance-5 code, demonstrating the effectiveness of bit-flip error suppression throughout the error correction cycle. These results, where the intrinsic error suppression of the bosonic encodings allows us to use a hardware-efficient outer error correcting code, indicate that concatenated bosonic codes are a compelling paradigm for reaching fault-tolerant quantum computation., Comment: Comments on the manuscript welcome!

Real-world physical systems, like composite materials and porous media, exhibit complex heterogeneities and multiscale nature, posing significant computational challenges. Computational homogenization is useful for predicting macroscopic properties from the microscopic material constitution. It involves defining a representative volume element (RVE), solving governing equations, and evaluating its properties such as conductivity and elasticity. Despite its effectiveness, the approach can be computationally expensive. This study proposes a tensor-train (TT)-based asymptotic homogenization method to address these challenges. By deriving boundary value problems at the microscale and expressing them in the TT format, the proposed method estimates material properties efficiently. We demonstrate its validity and effectiveness through numerical experiments applying the proposed method for homogenization of thermal conductivity and elasticity in two- and three-dimensional materials, offering a promising solution for handling the multiscale nature of heterogeneous systems., Comment: 25 pages, 7 figures

Soft robots have gained significant attention due to their flexibility and safety, particularly in human-centric applications. The co-design of structure and controller in soft robotics has presented a longstanding challenge owing to the complexity of the dynamics involved. Despite some pioneering work dealing with the co-design of soft robot structures and actuation, design freedom has been limited by stochastic design search approaches. This study proposes the simultaneous optimization of structure and controller for soft robots in locomotion tasks, integrating topology optimization-based structural design with neural network-based feedback controller design. Here, the feedback controller receives information about the surrounding terrain and outputs actuation signals that induce the expansion and contraction of the material. We formulate the simultaneous optimization problem under uncertainty in terrains and construct an optimization algorithm that utilizes automatic differentiation within topology optimization and neural networks. We present numerical experiments to demonstrate the validity and effectiveness of our proposed method., Comment: 23 pages, 22 figures

Partial differential equations (PDEs) are crucial for modeling various physical phenomena such as heat transfer, fluid flow, and electromagnetic waves. In computer-aided engineering (CAE), the ability to handle fine resolutions and large computational models is essential for improving product performance and reducing development costs. However, solving large-scale PDEs, particularly for systems with spatially varying material properties, poses significant computational challenges. In this paper, we propose a quantum algorithm for solving second-order linear PDEs of non-conservative systems with spatially varying parameters, using the linear combination of Hamiltonian simulation (LCHS) method. Our approach transforms those PDEs into ordinary differential equations represented by qubit operators, through spatial discretization using the finite difference method. Then, we provide an algorithm that efficiently constructs the operator corresponding to the spatially varying parameters of PDEs via a logic minimization technique, which reduces the number of terms and subsequently the circuit depth. We also develop a scalable method for realizing a quantum circuit for LCHS, using a tensor-network-based technique, specifically a matrix product state (MPS). We validate our method with applications to the acoustic equation with spatially varying parameters and the dissipative heat equation. Our approach includes a detailed recipe for constructing quantum circuits for PDEs, leveraging efficient encoding of spatially varying parameters of PDEs and scalable implementation of LCHS, which we believe marks a significant step towards advancing quantum computing's role in solving practical engineering problems., Comment: 21 pages, 5 figures

QRAO (Quantum Random Access Optimization) is a relaxation algorithm that reduces the number of qubits required to solve a problem by encoding multiple variables per qubit using QRAC (Quantum Random Access Code). Reducing the number of qubits is a common way of dealing with the impact of noise on a quantum algorithm. Our interest lies in the impact of noise on the quality of the binary solution of QRAO, which is unknown. We demonstrate that the mean approximation ratio of the (3, 1)-QRAC Hamiltonian, i.e., the Hamiltonian utilizing the encoding of 3 bits into 1 qubit by QRAC, is less affected by noise compared to the Ising Hamiltonian used in quantum annealer and QAOA (Quantum Approximate Optimization Algorithm). Based on this observation, we discuss a plausible mechanism behind the robustness of QRAO under depolarizing noise. Finally, we assess the number of shots required to estimate the values of binary variables correctly under depolarizing noise and show that the (3, 1)-QRAC Hamiltonian requires less shots to achieve the same accuracy compared to the Ising Hamiltonian., Comment: 9 pages, 5 figures

Quantum optimization methods use a continuous degree-of-freedom of quantum states to heuristically solve combinatorial problems, such as the MAX-CUT problem, which can be attributed to various NP-hard combinatorial problems. This paper shows that some existing quantum optimization methods can be unified into a solver that finds the binary solution that is most likely measured from the optimal quantum state. Combining this finding with the concept of quantum random access codes (QRACs) for encoding bits into quantum states on fewer qubits, we propose an efficient recursive quantum relaxation method called recursive quantum random access optimization (RQRAO) for MAX-CUT. Experiments on standard benchmark graphs with several hundred nodes in the MAX-CUT problem, conducted in a fully classical manner using a tensor network technique, show that RQRAO outperforms the Goemans--Williamson method and is comparable to state-of-the-art classical solvers. The codes will be made available soon., Comment: 31 pages, 10 figures, 3 tables

Simultaneous multislice (SMS) imaging is a one of the acceleration technique of magnetic resonance imaging. SMS requires accurate sensitivity distributions in the slice plane for each receiving coil. This requirement is difficult to satisfy in practice, limiting the applications of this imaging technique. Here, images are reconstructed by applying deep learning and amplitude modulation to each slice image. Simulation experiments show that image reconstruction can be achieved for both real- and complex-valued images. Image quality tends to decrease with increasing number of simultaneously acquired images. It is also shown that a larger difference in the phase modulation coefficients between slices tends to increase the quality of the reconstructed images. Simulation experiments and initial MR imaging experiments show promising results for this method.

Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a potential and promising approach to achieve this purpose. Actually, there are several oracle-based Hamiltonian simulations with potential quantum speedup, but their detailed implementations and accordingly the detailed computational complexities are all unclear. This paper presents a method that enables us to explicitly implement the quantum circuit for Hamiltonian simulation; the key technique is the explicit gate construction of differential operators contained in the target partial differential equation discretized by the finite difference method. Moreover, we show that the space and time complexities of the constructed circuit are exponentially smaller than those of conventional classical algorithms. We also provide numerical experiments and an experiment on a real device for the wave equation to demonstrate the validity of our proposed method., Comment: 25 pages, 6 figures

The Circle of Willis (CoW) is an important network of arteries connecting major circulations of the brain. Its vascular architecture is believed to affect the risk, severity, and clinical outcome of serious neuro-vascular diseases. However, characterizing the highly variable CoW anatomy is still a manual and time-consuming expert task. The CoW is usually imaged by two angiographic imaging modalities, magnetic resonance angiography (MRA) and computed tomography angiography (CTA), but there exist limited public datasets with annotations on CoW anatomy, especially for CTA. Therefore we organized the TopCoW Challenge in 2023 with the release of an annotated CoW dataset. The TopCoW dataset was the first public dataset with voxel-level annotations for thirteen possible CoW vessel components, enabled by virtual-reality (VR) technology. It was also the first large dataset with paired MRA and CTA from the same patients. TopCoW challenge formalized the CoW characterization problem as a multiclass anatomical segmentation task with an emphasis on topological metrics. We invited submissions worldwide for the CoW segmentation task, which attracted over 140 registered participants from four continents. The top performing teams managed to segment many CoW components to Dice scores around 90%, but with lower scores for communicating arteries and rare variants. There were also topological mistakes for predictions with high Dice scores. Additional topological analysis revealed further areas for improvement in detecting certain CoW components and matching CoW variant topology accurately. TopCoW represented a first attempt at benchmarking the CoW anatomical segmentation task for MRA and CTA, both morphologically and topologically., Comment: 24 pages, 11 figures, 9 tables. Summary Paper for the MICCAI TopCoW 2023 Challenge

Engineering heterostructures with various types of quantum materials can provide an intriguing playground for studying exotic physics induced by the proximity effect. Here, we report the successful synthesis of iron-based superconductor FeSe$_{x}$Te$_{1-x}$ (FST) thin films across the entire composition range of $0 \leq x \leq 1$ and its heterostructure with a magnetic topological insulator by using molecular beam epitaxy. Superconductivity is observed in the FST films with an optimal superconducting transition temperature $T_c$ $\sim$ 12 K at around x = 0.1. We found that superconductivity survives in the very Te-rich films ($x \leq 0.05$), showing stark contrast to bulk crystals with suppression of superconductivity due to an appearance of bicollinear antiferromagnetism accompanied by a monoclinic structural transition. By examining thickness $t$ dependence of magnetic susceptibility and electrical transport properties, we observed a trend where anomalies associated with the first order structural transition broaden in films with below $t \sim$ 100 nm. We infer this observation suggests a suppression of the structural instability near substrates. Furthermore, we fabricated an all chalcogenide-based heterointerface between FST and a magnetic topological insulator (Cr,Bi,Sb)$_{2}$Te$_{3}$ for the first time, observing both superconductivity and a large anomalous Hall conductivity. The anomalous Hall conductivity increases with decreasing temperature, approaching the quantized value of $e^2/h$ down to the measurable minimum temperature at $T_c$. The result suggests coexistence of magnetic and superconducting gaps at low temperatures opening at the top and bottom surfaces, respectively. Our novel magnetic topological insulator/superconductor heterostructure could be an ideal platform to explore chiral Majorana edge mode.

Locomotive soft robots (SoRos) have gained prominence due to their adaptability. Traditional locomotive SoRo design is based on limb structures inspired by biological organisms and requires human intervention. Evolutionary robotics, designed using evolutionary algorithms (EAs), have shown potential for automatic design. However, EA-based methods face the challenge of high computational cost when considering multiphysics in locomotion, including materials, actuations, and interactions with environments. Here, we present a design approach for pneumatic SoRos that integrates gradient-based topology optimization with multiphysics material point method (MPM) simulations. This approach starts with a simple initial shape (a cube with a central cavity). The topology optimization with MPM then automatically and iteratively designs the SoRo shape. We design two SoRos, one for walking and one for climbing. These SoRos are 3D printed and exhibit the same locomotion features as in the simulations. This study presents an efficient strategy for designing SoRos, demonstrating that a purely mathematical process can produce limb-like structures seen in biological organisms., Comment: 36 total pages (27 pages, 9 supplementary pages), 5 Figures, 9 Supplementary figures. 1 Supplementary table

In this research, we focus on the order-splitting behavior. The order splitting is a trading strategy to execute their large potential metaorder into small pieces to reduce transaction cost. This strategic behavior is believed to be important because it is a promising candidate for the microscopic origin of the long-range correlation (LRC) in the persistent order flow. Indeed, in 2005, Lillo, Mike, and Farmer (LMF) introduced a microscopic model of the order-splitting traders to predict the asymptotic behavior of the LRC from the microscopic dynamics, even quantitatively. The plausibility of this scenario has been qualitatively investigated by Toth et al. 2015. However, no solid support has been presented yet on the quantitative prediction by the LMF model in the lack of large microscopic datasets. In this report, we have provided the first quantitative statistical analysis of the order-splitting behavior at the level of each trading account. We analyse a large dataset of the Tokyo stock exchange (TSE) market over nine years, including the account data of traders (called virtual servers). The virtual server is a unit of trading accounts in the TSE market, and we can effectively define the trader IDs by an appropriate preprocessing. We apply a strategy clustering to individual traders to identify the order-splitting traders and the random traders. For most of the stocks, we find that the metaorder length distribution obeys power laws with exponent $\alpha$, such that $P(L)\propto L^{-\alpha-1}$ with the metaorder length $L$. By analysing the sign correlation $C(\tau)\propto \tau^{-\gamma}$, we directly confirmed the LMF prediction $\gamma \approx \alpha-1$. Furthermore, we discuss how to estimate the total number of the splitting traders only from public data via the ACF prefactor formula in the LMF model. Our work provides the first quantitative evidence of the LMF model., Comment: 33 pages, 19 figures

The Lillo-Mike-Farmer (LMF) model is an established econophysics model describing the order-splitting behaviour of institutional investors in financial markets. In the original article (LMF, Physical Review E 71, 066122 (2005)), LMF assumed the homogeneity of the traders' order-splitting strategy and derived a power-law asymptotic solution to the order-sign autocorrelation function (ACF) based on several heuristic reasonings. This report proposes a generalised LMF model by incorporating the heterogeneity of traders' order-splitting behaviour that is exactly solved without heuristics. We find that the power-law exponent in the order-sign ACF is robust for arbitrary heterogeneous intensity distributions. On the other hand, the prefactor in the ACF is very sensitive to heterogeneity in trading strategies and is shown to be systematically underestimated in the original homogeneous LMF model. Our work highlights that the ACF prefactor should be more carefully interpreted than the ACF power-law exponent in data analyses., Comment: additional theoretical analyses

The quantum channel decomposition techniques, which contain the so-called probabilistic error cancellation and gate/wire cutting, are powerful approach for simulating a hard-to-implement (or an ideal) unitary operation by concurrently executing relatively easy-to-implement (or noisy) quantum channels. However, such virtual simulation necessitates an exponentially large number of decompositions, thereby significantly limiting their practical applicability. This paper proposes a channel decomposition method for target unitaries that have their input and output conditioned on specific quantum states, namely unitaries with pre- and post-selection. Specifically, we explicitly determine the requisite number of decomposing channels, which could be significantly smaller than the selection-free scenario. Furthermore, we elucidate the structure of the resulting decomposed unitary. We demonstrate an application of this approach to the quantum linear solver algorithm, highlighting the efficacy of the proposed method., Comment: published version, 11 pages, 5 figures

Variational Quantum Eigensolver (VQE) is a hybrid algorithm for finding the minimum eigenvalue/vector of a given Hamiltonian by optimizing a parametrized quantum circuit (PQC) using a classical computer. Sequential optimization methods, which are often used in quantum circuit tensor networks, are popular for optimizing the parametrized gates of PQCs. This paper focuses on the case where the components to be optimized are single-qubit gates, in which the analytic optimization of a single-qubit gate is sequentially performed. The analytical solution is given by diagonalization of a matrix whose elements are computed from the expectation values of observables specified by a set of predetermined parameters which we call the parameter configurations. In this study, we first show that the optimization accuracy significantly depends on the choice of parameter configurations due to the statistical errors in the expectation values. We then identify a metric that quantifies the optimization accuracy of a parameter configuration for all possible statistical errors, named configuration overhead/cost or C-cost. We theoretically provide the lower bound of C-cost and show that, for the minimum size of parameter configurations, the lower bound is achieved if and only if the parameter configuration satisfies the so-called equiangular line condition. Finally, we provide numerical experiments demonstrating that the optimal parameter configuration exhibits the best result in several VQE problems. We hope that this general statistical methodology will enhance the efficacy of sequential optimization of PQCs for solving practical problems with near-term quantum devices., Comment: 20 pages, 5 figures

Generalized eigenvalue problems (GEPs) play an important role in the variety of fields including engineering, machine learning and quantum chemistry. Especially, many problems in these fields can be reduced to finding the minimum or maximum eigenvalue of GEPs. One of the key problems to handle GEPs is that the memory usage and computational complexity explode as the size of the system of interest grows. This paper aims at extending sequential quantum optimizers for GEPs. Sequential quantum optimizers are a family of algorithms that iteratively solve the analytical optimization of single-qubit gates in a coordinate descent manner. The contribution of this paper is as follows. First, we formulate the GEP as the minimization/maximization problem of the fractional form of the expectations of two Hermitians. We then showed that the fractional objective function can be analytically minimized or maximized with respect to a single-qubit gate by solving a GEP of a 4 $\times$ 4 matrix. Second, we show that a system of linear equations (SLE) characterized by a positive-definite Hermitian can be formulated as a GEP and thus be attacked using the proposed method. Finally, we demonstrate two applications to important engineering problems formulated with the finite element method. Through the demonstration, we have the following bonus finding; a problem having a real-valued solution can be solved more effectively using quantum gates generating a complex-valued state vector, which demonstrates the effectiveness of the proposed method., Comment: 19 pages, 10 figures

Topology optimization is a powerful tool utilized in various fields for structural design. However, its application has primarily been restricted to static or passively moving objects, mainly focusing on hard materials with limited deformations and contact capabilities. Designing soft and actively moving objects, such as soft robots equipped with actuators, poses challenges due to simulating dynamics problems involving large deformations and intricate contact interactions. Moreover, the optimal structure depends on the object's motion, necessitating a simultaneous design approach. To address these challenges, we propose "4D topology optimization," an extension of density-based topology optimization that incorporates the time dimension. This enables the simultaneous optimization of both the structure and self-actuation of soft bodies for specific dynamic tasks. Our method utilizes multi-indexed and hierarchized density variables distributed over the spatiotemporal design domain, representing the material layout, actuator layout, and time-varying actuation. These variables are efficiently optimized using gradient-based methods. Forward and backward simulations of soft bodies are done using the material point method, a Lagrangian-Eulerian hybrid approach, implemented on a recent automatic differentiation framework. We present several numerical examples of self-actuating soft body designs aimed at achieving locomotion, posture control, and rotation tasks. The results demonstrate the effectiveness of our method in successfully designing soft bodies with complex structures and biomimetic movements, benefiting from its high degree of design freedom., Comment: 36 pages, 27 figures; for supplementary video, see https://youtu.be/sPY2jcAsNYs

In financial markets, the market order sign exhibits strong persistence, widely known as the long-range correlation (LRC) of order flow; specifically, the sign correlation function displays long memory with power-law exponent $\gamma$, such that $C(\tau) \propto \tau^{-\gamma}$ for large time-lag $\tau$. One of the most promising microscopic hypotheses is the order-splitting behaviour at the level of individual traders. Indeed, Lillo, Mike, and Farmer (LMF) introduced in 2005 a simple microscopic model of order-splitting behaviour, which predicts that the macroscopic sign correlation is quantitatively associated with the microscopic distribution of metaorders. While this hypothesis has been a central issue of debate in econophysics, its direct quantitative validation has been missing because it requires large microscopic datasets with high resolution to observe the order-splitting behaviour of all individual traders. Here we present the first quantitative validation of this LFM prediction by analysing a large microscopic dataset in the Tokyo Stock Exchange market for more than nine years. On classifying all traders as either order-splitting traders or random traders as a statistical clustering, we directly measured the metaorder-length distributions $P(L)\propto L^{-\alpha-1}$ as the microscopic parameter of the LMF model and examined the theoretical prediction on the macroscopic order correlation: $\gamma \approx \alpha - 1$. We discover that the LMF prediction agrees with the actual data even at the quantitative level. Our work provides the first solid support of the microscopic model and solves directly a long-standing problem in the field of econophysics and market microstructure., Comment: 4 pages, 4 figures

The two-dimensional causal dynamical triangulations ($2$d CDT) is a lattice model of quantum geometry. In $2$d CDT, one can deal with the quantum effects analytically and explore the physics through the continuum limit. The continuum theory is known to be two-dimensional projectable Horava-Lifshitz quantum gravity ($2$d projectable HL QG). In this chapter, we wish to review the very relation between $2$d CDT and $2$d projectable HL QG in detail., Comment: Invited chapter for the "Handbook of Quantum Gravity" (Eds. C. Bambi, L. Modesto and I.L. Shapiro, Springer Singapore, expected in 2023); v2: references added, minor typos corrected; v3: minor corrections

We propose an algorithm for variational quantum algorithms (VQAs) to optimize the structure of parameterized quantum circuits (PQCs) efficiently. The algorithm optimizes the PQC structure on-the-fly in VQA by sequentially replacing a single-qubit gate with the optimal one to minimize the objective function. To directly find the optimal gate, our method uses the factorization of matrices whose elements are evaluated on a set of the slightly-modified circuits. The matrix factorization enables us to not only unify the existing sequential methods for further extension but also provide rigorous proofs of their limitation and potential in comparison with conventional gradient-based optimizers. Firstly, when the circuits are sufficiently deep, the sequential methods encounter a barren plateau that the spectrum of the matrix concentrates on a single value exponentially fast with respect to the number of qubits. Secondly, if the objective functions are local observables, they can avoid barren plateaus as long as the depth of the n-qubit PQCs is $O(\log{n})$. Although the family of these optimizers does not directly employ gradients of the objective function, our results establish their connection with conventional optimizations providing a consistent picture of the barren plateau. We also perform numerical experiments showing the advantages over conventional VQAs and confirm the successful optimization getting over the barren plateau in the ground state problem of the mixed field Ising model up to 12 qubits., Comment: 25 pages, 9 figures

Free Material Optimization (FMO), a branch of topology optimization, in which the design variables are the full constitutive tensors, can provide the most general form of the design problems. Considering the microstructure composed of isotropic materials, the constitutive tensors are yet positive definite and symmetric. On the other hand, it has been reported that the symmetry of this constitutive tensor can be broken in appearance by considering other physical phenomena. In the present study, we focus on the thermal Hall effect, which is explained as the phenomena that induces the temperature gradient orthogonal to a given temperature gradient across a solid when a magnetic field is applied to the solid. This effect makes the thermal conductivity tensor asymmetric and justifies extending the space of the constitutive tensors to be an asymmetric domain. We propose the FMO for asymmetric constitutive tensors, parameterizing the design space so that the physically available property could be naturally satisfied. Several numerical experiments are provided to show the validity and the utility of the proposed method., Comment: 12 pages, 9 figures

We demonstrate a tensor renormalization group (TRG) calculation for a two-dimensional Lorentzian model of quantum Regge calculus (QRC). This model is expressed in terms of a tensor network by discretizing the continuous edge lengths of simplicial manifolds and identifying them as tensor indices. The expectation value of space-time area, which is obtained through the higher-order TRG method, nicely reproduces the exact value. The Lorentzian model does not have the spike configuration that was an obstacle in the Euclidean QRC, but it still has a length-divergent configuration called a pinched geometry. We find a possibility that the pinched geometry is suppressed by checking the average edge length squared in the limit where the number of simplices is large. This implies that the Lorentzian model may describe smooth geometries, although the investigation of the higher moments is required to make the statement more conclusive. Our results also indicate that TRG is a promising approach to numerical study of simplicial quantum gravity., Comment: 26 pages, 23 figures, minor corrections, references added

Experiments on disordered alloys suggest that spin glasses can be brought into low-energy states faster by annealing quantum fluctuations than by conventional thermal annealing. Due to the importance of spin glasses as a paradigmatic computational testbed, reproducing this phenomenon in a programmable system has remained a central challenge in quantum optimization. Here we achieve this goal by realizing quantum critical spin-glass dynamics on thousands of qubits with a superconducting quantum annealer. We first demonstrate quantitative agreement between quantum annealing and time-evolution of the Schr\"odinger equation in small spin glasses. We then measure dynamics in 3D spin glasses on thousands of qubits, where simulation of many-body quantum dynamics is intractable. We extract critical exponents that clearly distinguish quantum annealing from the slower stochastic dynamics of analogous Monte Carlo algorithms, providing both theoretical and experimental support for a scaling advantage in reducing energy as a function of annealing time.

To arrive at some viable product design, product development processes frequently use numerical simulations and mathematical programming techniques. Topology optimization, in particular, is one of the most promising techniques for generating insightful design choices. Topology optimization problems reduce to an NP-hard combinatorial optimization problem, where the combination of the existence or absence of the material at some positions is optimized. In this study, we examine the usage of quantum computers as a potential solution to topology optimization problems. The proposed method consists of two variational quantum algorithms (VQAs): the first solves the state equilibrium equation for all conceivable material configurations, while the second amplifies the likelihood of an optimal configuration in quantum superposition using the first VQA's quantum state. Several experiments, including a real device experiment, show that the proposed method successfully obtained the optimal configurations. These findings suggest that quantum computers could be a potential tool for solving topology optimization problems and they open the window to the near-future product designs., Comment: 16 pages, 6 figures

A finite residual linear term in the thermal conductivity at zero temperature in insulating magnets indicates the presence of gapless excitations of itinerant quasiparticles, which has been observed in some candidate materials of quantum spin liquids (QSLs). In the organic triangular insulator beta'-EtMe3Sb[Pd(dmit)2]2, a QSL candidate material, the low-temperature thermal conductivity depends on the cooling process and the finite residual term is observed only in samples with large thermal conductivity. Moreover, the cooling rate dependence is largely sample dependent. Here we find that, while the low-temperature thermal conductivity significantly depends on the cooling rate, the high-temperature resistivity is almost perfectly independent of the cooling rate. These results indicate that in the samples with the finite residual term, the mean free path of the quasiparticles that carry the heat at low temperatures is governed by disorders, whose characteristic length scale of the distribution is much longer than the electron mean free path that determines the high-temperature resistivity. This explains why recent X-ray diffraction and nuclear magnetic resonance measurements show no cooling rate dependence. Naturally, these measurements are unsuitable for detecting disorders of the length scale relevant for the thermal conductivity, just as they cannot determine the residual resistivity of metals. Present results indicate that very careful experiments are needed when discussing itinerant spin excitations in beta'-EtMe3Sb[Pd(dmit)2]2., Comment: 14 pages, 4 figures, to appear in Scientific Reports

Topology optimization methods have widely been used in various industries, owing to their potential for providing promising design candidates for mechanical devices. However, their applications are usually limited to the objects which do not move significantly due to the difficulty in computationally efficient handling of the contact and interactions among multiple structures or with boundaries by conventionally used simulation techniques. In the present study, we propose a topology optimization method for moving objects incorporating the material point method, which is often used to simulate the motion of objects in the field of computer graphics. Several numerical experiments demonstrate the effectiveness and the utility of the proposed method., Comment: 9 pages, 7 figures