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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

Utilizing singular value decomposition, our investigation focuses on the spectrum of the singular values within a sparse non-Hermitian Sachdev-Ye-Kitaev (SYK) model. Unlike the complex eigenvalues typical of non-Hermitian systems, singular values are inherently real and positive. Our findings reveal a congruence between the statistics of singular values and those of the analogous Hermitian Gaussian ensembles. An increase in sparsity results in the non-Hermitian SYK model deviating from its chaotic behavior, a phenomenon precisely captured by the singular value ratios. Our analysis of the singular form factor ({\upsigma}FF), analogous to the spectral form factor (SFF) indicates the disappearance of the linear ramp with increased sparsity. Additionally, we define singular complexity, inspired by the spectral complexity in Hermitian systems, whose saturation provides a critical threshold of sparseness. Such disintegration is likely associated with the breakdown of the existing holographic dual for non-Hermitian systems., Comment: v1: 10 pages, 6 figures

1-out-of-n oblivious signature by Chen (ESORIC 1994) is a protocol between the user and the signer. In this scheme, the user makes a list of n messages and chooses the message that the user wants to obtain a signature from the list. The user interacts with the signer by providing this message list and obtains the signature for only the chosen message without letting the signer identify which messages the user chooses. Tso et al. (ISPEC 2008) presented a formal treatment of 1-out-of-n oblivious signatures. They defined unforgeability and ambiguity for 1-out-of-n oblivious signatures as a security requirement. In this work, first, we revisit the unforgeability security definition by Tso et al. and point out that their security definition has problems. We address these problems by modifying their security model and redefining unforgeable security. Second, we improve the generic construction of a 1-out-of-n oblivious signature scheme by Zhou et al. (IEICE Trans 2022). We reduce the communication cost by modifying their scheme with a Merkle tree. Then we prove the security of our modified scheme.

A method is developed to calculate the electron flow between an atomic monolayer sheet and a tube with use of tunneling matrix elements between monolayer sheets and applied to the spin current from monolayer silicene with sublattice-staggered current-induced spin polarization to silicene tube. Calculated sheet-to-tube spin current exhibits an oscillation as a function of the tube circumferential length since the Fermi points in the tube cross the Fermi circle in the sheet. It is also shown that the spin current with spin in the out-of-plane direction, which is absent in the sheet-sheet junction (including twisted sheets) with the $C_3$ rotational symmetry, appears in an oscillating form owing to the broken $C_3$ symmetry in the tube-sheet junction., Comment: 17 pages, 5 figures

Generating a nonequilibrium spin polarization with a driving force has been first realized by the electric current in a system with broken inversion symmetry and extended to that induced by the thermal current and that appearing in an inversion-symmetric system with locally-broken inversion symmetry. This paper theoretically explores the spin polarization generated by the thermal current and the locally-broken inversion symmetry in a symmetric double-quantum-well structure (DQWS). This thermally-induced spin polarization (TISP) appears in the antiparallel configuration with the TISP of two wells in opposite directions. The calculation using the Boltzmann equation in the relaxation-time approximation under the condition of zero charge current shows that the local TISP exhibits the maximum at a finite Rashba spin-orbit interaction when the electron density is fixed. This is because the local TISP in the DQWS is enhanced at the chemical potential near the bottom of the first-excited subband. This enhancement also occurs in a single quantum well with globally-broken inversion symmetry. Another finding is that the maximum of the local TISP appears at a nonzero interwell coupling. The spin current by the diffusion of the local TISP into an adjacent electrode is also calculated., Comment: 22 pages, 5 figures, submitted to Physica Status Solidi (RRL)

We model backreaction in AdS$_2$ JT gravity via a proposed boundary dual Sachdev-Ye-Kitaev quantum dot coupled to Dirac fermion matter and study it from the perspective of quantum entanglement and chaos. The boundary effective action accounts for the backreaction through a linear coupling of the Dirac fermions to the Gaussian-random two-body Majorana interaction term in the low-energy limit. We calculate the time evolution of the entanglement entropy between graviton and Dirac fermion fields for a separable initial state and find that it initially increases and then saturates to a finite value. Moreover, in the limit of a large number of fermions, we find a maximally entangled state between the Majorana and Dirac fields in the saturation region, implying a transition of the von Neumann algebra of observables from type I to type II. This transition in turn indicates a loss of information in the holographically dual emergent spacetime. We corroborate these observations with a detailed numerical computation of the averaged nearest-neighbor gap ratio of the boundary spectrum and provide a useful complement to quantum entanglement studies of holography., Comment: 16 pages, 2 figures, 1 table, minor changes, reference added

Recently, the importance of analysing data and collecting valuable insight efficiently has been increasing in various fields. Estimating mutual information (MI) plays a critical role to investigate the relationship among multiple random variables with a nonlinear correlation. Particularly, the task to determine whether they are independent or not is called the independence test, whose core subroutine is estimating MI from given data. It is a fundamental tool in statistics and data analysis that can be applied in a wide range of application such as hypothesis testing, causal discovery and more. In this paper, we propose a method for estimating mutual information using the quantum kernel. We investigate the performance under various problem settings, such as different sample size or the shape of the probability distribution. As a result, the quantum kernel method showed higher performance than the classical one under the situation that the number of samples is small, the variance is large or the variables posses highly non-linear relationships. We discuss this behavior in terms of the central limit theorem and the structure of the corresponding quantum reproducing kernel Hilbert space., Comment: 20 pages, 10 figures

Integration of quantum chemistry simulations, machine learning techniques, and optimization calculations is expected to accelerate material discovery by making large chemical spaces amenable to computational study; a challenging task for classical computers. In this work, we develop a combined quantum-classical computing scheme involving the computational-basis Variational Quantum Deflation (cVQD) method for calculating excited states of a general classical Hamiltonian, such as Ising Hamiltonian. We apply this scheme to the practical use case of generating photochromic diarylethene (DAE) derivatives for photopharmacology applications. Using a data set of 384 DAE derivatives quantum chemistry calculation results, we show that a factorization-machine-based model can construct an Ising Hamiltonian to accurately predict the wavelength of maximum absorbance of the derivatives, $\lambda_{\rm max}$, for a larger set of 4096 DAE derivatives. A 12-qubit cVQD calculation for the constructed Ising Hamiltonian provides the ground and first four excited states corresponding to five DAE candidates possessing large $\lambda_{\rm max}$. On a quantum simulator, results are found to be in excellent agreement with those obtained by an exact eigensolver. Utilizing error suppression and mitigation techniques, cVQD on a real quantum device produces results with accuracy comparable to the ideal calculations on a simulator. Finally, we show that quantum chemistry calculations for the five DAE candidates provides a path to achieving large $\lambda_{\rm max}$ and oscillator strengths by molecular engineering of DAE derivatives. These findings pave the way for future work on applying hybrid quantum-classical approaches to large system optimization and the discovery of novel materials., Comment: 13pages, 9 figures

We construct a model of Pauli spin operators with all-to-all 4-local interactions by replacing Majorana fermions in the SYK model with spin operators. Equivalently, we replace fermions with hard-core bosons. We study this model numerically and compare the properties with those of the SYK model. We observe a striking quantitative coincidence between the spin model and the SYK model, which suggests that this spin model is strongly chaotic and, perhaps, can play some role in holography. We also discuss the path-integral approach with multi-local fields and the possibility of quantum simulations. This model may be an interesting target for quantum simulations because Pauli spins are easier to implement than fermions on qubit-based quantum devices., Comment: 35 pages, 16 figures; version accepted for publication in JHEP

Synchronized aggregate signature is a special type of signature that all signers have a synchronized time period and allows aggregating signatures which are generated in the same period. This signature has a wide range of applications for systems that have a natural reporting period such as log and sensor data, or blockchain protocol. In CT-RSA 2016, Pointcheval and Sanders proposed the new randomizable signature scheme. Since this signature scheme is based on type-3 pairing, this signature achieves a short signature size and efficient signature verification. In this paper, we design the Pointchcval-Sanders signature-based synchronized aggregate signature scheme and prove its security under the generalized Pointcheval-Sanders assumption in the random oracle model. Our scheme offers the most efficient aggregate signature verification among synchronized aggregate signature schemes based on bilinear groups.

Information scrambling refers to the unitary dynamics that quickly spreads and encodes localized quantum information over an entire many-body system and makes the information accessible from any small subsystem. While information scrambling is the key to understanding complex quantum many-body dynamics and is well-understood in random unitary models, it has been hardly explored in Hamiltonian systems. In this Letter, we investigate the information recovery in various time-independent Hamiltonian systems, including chaotic spin chains and Sachdev-Ye-Kitaev (SYK) models. We show that information recovery is possible in certain, but not all, chaotic models, which highlights the difference between information recovery and quantum chaos based on the energy spectrum or the out-of-time-ordered correlators. We also show that information recovery probes transitions caused by the change of information-theoretic features of the dynamics., Comment: 8 pages, 6 figures, Supplemental Materials (13 pages, 11 figures). Substantial revision, including correction of the code and normalization for spin models, and estimation of lower bounds on the recovery error

To simulate bosons on a qubit- or qudit-based quantum computer, one has to regularize the theory by truncating infinite-dimensional local Hilbert spaces to finite dimensions. In the search for practical quantum applications, it is important to know how big the truncation errors can be. In general, it is not easy to estimate errors unless we have a good quantum computer. In this paper, we show that traditional sampling methods on classical devices, specifically Markov Chain Monte Carlo, can address this issue for a rather generic class of bosonic systems with a reasonable amount of computational resources available today. As a demonstration, we apply this idea to the scalar field theory on a two-dimensional lattice, with a size that goes beyond what is achievable using exact diagonalization methods. This method can be used to estimate the resources needed for realistic quantum simulations of bosonic theories, and also, to check the validity of the results of the corresponding quantum simulations., Comment: 22 pages, 4 figures

Quantum computing has a potential to accelerate the data processing efficiency, especially in machine learning, by exploiting special features such as the quantum interference. The major challenge in this application is that, in general, the task of loading a classical data vector into a quantum state requires an exponential number of quantum gates. The approximate amplitude encoding (AAE) method, which uses a variational means to approximately load a given real-valued data vector into the amplitude of a quantum state, was recently proposed as a general approach to this problem mainly for near-term devices. However, AAE cannot load a complex-valued data vector, which narrows its application range. In this work, we extend AAE so that it can handle a complex-valued data vector. The key idea is to employ the fidelity distance as a cost function for optimizing a parameterized quantum circuit, where the classical shadow technique is used to efficiently estimate the fidelity and its gradient. We apply this algorithm to realize the complex-valued-kernel binary classifier called the compact Hadamard classifier, and then give a numerical experiment showing that it enables classification of Iris dataset and credit card fraud detection., Comment: 13 pages, 8 figures

Wireless ad hoc federated learning (WAFL) is a fully decentralized collaborative machine learning framework organized by opportunistically encountered mobile nodes. Compared to conventional federated learning, WAFL performs model training by weakly synchronizing the model parameters with others, and this shows great resilience to a poisoned model injected by an attacker. In this paper, we provide our theoretical analysis of the WAFL's resilience against model poisoning attacks, by formulating the force balance between the poisoned model and the legitimate model. According to our experiments, we confirmed that the nodes directly encountered the attacker has been somehow compromised to the poisoned model but other nodes have shown great resilience. More importantly, after the attacker has left the network, all the nodes have finally found stronger model parameters combined with the poisoned model. Most of the attack-experienced cases achieved higher accuracy than the no-attack-experienced cases., Comment: 10 pages, 7 figures, to be published in IEEE International Conference on Trust, Privacy and Security in Intelligent Systems, and Applications 2022

Generative modeling is an unsupervised machine learning framework, that exhibits strong performance in various machine learning tasks. Recently we find several quantum version of generative model, some of which are even proven to have quantum advantage. However, those methods are not directly applicable to construct a generative model for learning a set of quantum states, i.e., ensemble. In this paper, we propose a quantum generative model that can learn quantum ensemble, in an unsupervised machine learning framework. The key idea is to introduce a new loss function calculated based on optimal transport loss, which have been widely used in classical machine learning due to its several good properties; e.g., no need to ensure the common support of two ensembles. We then give in-depth analysis on this measure, such as the scaling property of the approximation error. We also demonstrate the generative modeling with the application to quantum anomaly detection problem, that cannot be handled via existing methods. The proposed model paves the way for a wide application such as the health check of quantum devices and efficient initialization of quantum computation.