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Quantum signal processing (QSP) and quantum singular value transformation (QSVT) have provided a unified framework for understanding many quantum algorithms, including factorization, matrix inversion, and Hamiltonian simulation. As a multivariable version of QSP, multivariable quantum signal processing (M-QSP) is proposed. M-QSP interleaves signal operators corresponding to each variable with signal processing operators, which provides an efficient means to perform multivariable polynomial transformations. However, the necessary and sufficient condition for what types of polynomials can be constructed by M-QSP is unknown. In this paper, we propose a classical algorithm to determine whether a given pair of multivariable Laurent polynomials can be implemented by M-QSP, which returns True or False. As one of the most important properties of this algorithm, it returning True is the necessary and sufficient condition. The proposed classical algorithm runs in polynomial time in the number of variables and signal operators. Our algorithm also provides a constructive method to select the necessary parameters for implementing M-QSP. These findings offer valuable insights for identifying practical applications of M-QSP., Comment: 20 pages, 2 figures

Producing a polarized lanthanum (La) target with high polarization and long relaxation time is crucial for realizing time-reversal violation experiments using polarized neutron beams. We use a LaAlO3 crystal doped with a small amount of Nd3+ ions for the polarized lanthanum target. Optimizing the amount of Nd3+ ions is considerably important because the achievable polarization and relaxation time strongly depend on this amount. We established a fundamental method to grow single crystals of Nd3+:LaAlO3 using an optical floating zone method that employs halogen lamps and evaluated the crystals with the dynamic nuclear polarization (DNP) method for polarizing nuclear spins. Two crystal samples were grown by ourselves and evaluated with the DNP at 1.3 K and 2.3 T for the first time except for the target materials of protons. The enhancement of NMR signals for 139La and 27Al was successfully observed, and the enhancement factors were eventually 3.5+-0.3 and 13+-3 for the samples with Nd3+ ions of 0.05 and 0.01 mol%, respectively. These enhancement factors correspond to absolute vector polarizations of 0.27+-0.02% (Nd 0.05 mol%) and 1.4+-0.3% (Nd 0.01 mol%). Although the obtained polarizations are still low, they are acceptable as a first step. The combination scheme of the crystal growth and evaluation of the crystals is found to be effectively applicable for optimizing the amount of Nd3+ ions for improving the performance of the polarized target., Comment: 18 pages, 7 figures, Resubmitted to Review of Scientific Instruments

Solving linear and nonlinear differential equations with large degrees of freedom is an important task for scientific and industrial applications. In order to solve such differential equations on a quantum computer, it is necessary to embed classical variables into a quantum state. While the Carleman and Koopman-von Neumann embeddings have been investigated so far, the class of problems that can be mapped to the Schr\"{o}dinger equation is not well understood even for linear differential equations. In this work, we investigate the conditions for linear differential equations to be mapped to the Schr\"{o}dinger equation and solved on a quantum computer. Interestingly, we find that these conditions are identical for both Carleman and Koopman-von Neumann embeddings. We also compute the computational complexity associated with estimating the expected values of an observable. This is done by assuming a state preparation oracle, block encoding of the mapped Hamiltonian via either Carleman or Koopman-von Neumann embedding, and block encoding of the observable using $O(\log M)$ qubits with $M$ is the mapped system size. Furthermore, we consider a general classical quadratic Hamiltonian dynamics and find a sufficient condition to map it into the Schr\"{o}dinger equation. As a special case, this includes the coupled harmonic oscillator model [Babbush et al., \cite{babbush_exponential_2023}]. We also find a concrete example that cannot be described as the coupled harmonic oscillator but can be mapped to the Schr\"{o}dinger equation in our framework. These results are important in the construction of quantum algorithms for solving differential equations of large-degree-of-freedom., Comment: 22 pages with no figures

We propose new entanglement measures as the detection performance based on the hypothesis testing setting. We clarify how our measures work for detecting an entangled state by extending the quantum Sanov theorem. Our analysis covers the finite-length setting. Exploiting this entanglement measure, we present how to derive entanglement witness to detect the given entangled state by using the geometrical structure of this measure. We derive their calculation formulas for maximally correlated states, and propose their algorithms that work for general entangled states. In addition, we investigate how our algorithm works for solving the membership problem for separability.

We propose a method of head-related transfer function (HRTF) interpolation from sparsely measured HRTFs using an autoencoder with source position conditioning. The proposed method is drawn from an analogy between an HRTF interpolation method based on regularized linear regression (RLR) and an autoencoder. Through this analogy, we found the key feature of the RLR-based method that HRTFs are decomposed into source-position-dependent and source-position-independent factors. On the basis of this finding, we design the encoder and decoder so that their weights and biases are generated from source positions. Furthermore, we introduce an aggregation module that reduces the dependence of latent variables on source position for obtaining a source-position-independent representation of each subject. Numerical experiments show that the proposed method can work well for unseen subjects and achieve an interpolation performance with only one-eighth measurements comparable to that of the RLR-based method., Comment: Accepted to International Workshop on Acoustic Signal Enhancement (IWAENC) 2022

This paper studies the identification and estimation of dynamic games when the underlying information structure is unknown to the researcher. To tractably characterize the set of Markov perfect equilibrium predictions while maintaining weak assumptions on players' information, we introduce \textit{Markov correlated equilibrium}, a dynamic analog of Bayes correlated equilibrium. The set of Markov correlated equilibrium predictions coincides with the set of Markov perfect equilibrium predictions that can arise when the players can observe more signals than assumed by the analyst. Using Markov correlated equilibrium as the solution concept, we propose tractable computational strategies for informationally robust estimation, inference, and counterfactual analysis that deal with the non-convexities arising in dynamic environments. We use our method to analyze the dynamic competition between Starbucks and Dunkin' in the US and the role of informational assumptions.

GPUs are widely used to accelerate deep learning with NNs (NNs). On the other hand, since GPU memory capacity is limited, it is difficult to implement efficient programs that compute large NNs on GPU. To compute NNs exceeding GPU memory capacity, data-swapping method and recomputing method have been proposed in existing work. However, in these methods, performance overhead occurs due to data movement or increase of computation. In order to reduce the overhead, it is important to consider characteristics of each layer such as sizes and cost for recomputation. Based on this direction, we proposed Profiling based out-of-core Hybrid method (PoocH). PoocH determines target layers of swapping or recomputing based on runtime profiling. We implemented PoocH by extending a deep learning framework, Chainer, and we evaluated its performance. With PoocH, we successfully computed an NN requiring 50 GB memory on a single GPU with 16 GB memory. Compared with in-core cases, performance degradation was 38 \% on x86 machine and 28 \% on POWER9 machine., Comment: 15 pages