Hiroshi C. Watanabe

Adaptive multiscale simulations, such as adaptive quantum mechanics (QM)/molecular mechanics (MM), are indispensable for investigating complex solution dynamics but historically suffer from a fundamental dilemma: the dynamic exchange of identical solvent molecules across different model resolutions introduces an energetic asymmetry under solvent exchange (specifically, a permutation asymmetry where physically identical molecules are treated indistinguishably yet subjected to different force fields depending on their instantaneous positions). This asymmetry forces a prohibitive trade-off between severe structural distortions and the violation of Hamiltonian conservation (continuous energy drift). To resolve this issue, we propose the “Integrated Molecular Model,” a paradigm-shifting framework that unifies multiple resolutions into a single, dynamically consistent potential. By employing a neural network that takes only the multiscale weight functions as input descriptors, our model learns to systematically cancel the nonphysical transition forces originating from spatial discontinuities. As a proof-of-concept, we validated this unified framework on bulk water, aqueous ionic solutions, and reactive hydronium ions. Our approach not only faithfully restores artifact-free solvation structures but also strictly conserves the Hamiltonian, enabling stable, long-term simulations under the microcanonical (NVE) ensemble. Consequently, the model successfully eliminates artificial thermostat-induced breathing modes, allowing for the rigorous evaluation of intrinsic dynamical properties such as diffusion coefficients. Furthermore, owing to its physically informed network design, the correction potential introduces less than 2% additional computational overhead and demonstrates remarkable zero-shot transferability across chemically similar ionic species. By eradicating the inherent asymmetry of adaptive multiscale modeling, this highly scalable framework establishes a robust foundation for high-fidelity simulations of complex condensed-phase phenomena, including reactive dynamics at solid–liquid interfaces and ion transport in battery electrolytes.

Adaptive multiscale simulations, such as adaptive QM/MM, are indispensable for investigating complex solution dynamics but historically suffer from a fundamental dilemma: the dynamic exchange of identical solvent molecules across different model resolutions introduces an energetic asymmetry under solvent exchange (specifically, a permutation asymmetry where physically identical molecules are treated indistinguishably yet subjected to different force fields depending on their instantaneous positions). This asymmetry forces a prohibitive trade-off between severe structural distortions and the violation of Hamiltonian conservation (continuous energy drift). To resolve this issue, we propose the ”Integrated Molecular Model,” a paradigm-shifting framework that unifies multiple resolutions into a single, dynamically consistent potential. By employing a neural network that takes only the multiscale weight functions as input descriptors, our model learns to systematically cancel the non-physical transition forces originating from spatial discontinuities. As a proof-of-concept, we validated this unified framework on bulk water, aqueous ionic solutions, and reactive hydronium ions. Our approach not only faithfully restores artifact-free solvation structures but also strictly conserves the Hamiltonian, enabling unprecedentedly stable, long-term simulations under the microcanonical (NVE) ensemble. Consequently, the model successfully eliminates artificial thermostat-induced breathing modes, allowing for the rigorous evaluation of intrinsic dynamical properties such as diffusion coefficients. Furthermore, owing to its physically informed network design, the correction potential introduces less than 2% additional computational overhead and demonstrates remarkable zero-shot transferability across chemically similar ionic species. By eradicating the inherent asymmetry of adaptive multiscale modeling, this highly scalable framework establishes a robust foundation for high-fidelity simulations of complex condensed-phase phenomena, including reactive dynamics at solid-liquid interfaces and ion transport in battery electrolytes.

Adaptive multiscale simulations, such as adaptive QM/MM, are indispensable for investigating complex solution dynamics but historically suffer from a fundamental dilemma: the dynamic exchange of identical solvent molecules across different model resolutions introduces a physical asymmetry. This asymmetry forces a prohibitive trade-off between severe structural distortions and the violation of Hamiltonian conservation (continuous energy drift). To definitively resolve this issue, we propose the ”Integrated Molecular Model,” a paradigm-shifting framework that mathematically unifies multiple resolutions into a single, dynamically consistent potential. By employing a neural network that takes only the multiscale weight functions as input descriptors, our model learns to systematically cancel the non-physical transition forces originating from spatial discontinuities. As a proof-of-concept, we validated this unified framework on bulk water, aqueous ionic solutions, and reactive hydronium ions. Our approach not only faithfully restores artifact-free solvation structures but also strictly conserves the Hamiltonian, enabling unprecedentedly stable, long-term simulations under the microcanonical (NVE) ensemble. Consequently, the model successfully eliminates artificial thermostat-induced breathing modes, allowing for the rigorous evaluation of intrinsic dynamical properties such as diffusion coefficients. Furthermore, owing to its physically informed network design, the correction potential introduces less than 2\% additional computational overhead and demonstrates remarkable zero-shot transferability across chemically similar ionic species. By fundamentally eradicating the inherent asymmetry of adaptive multiscale modeling, this highly scalable framework establishes a robust foundation for high-fidelity simulations of complex condensed-phase phenomena, including reactive dynamics at solid-liquid interfaces and ion transport in battery electrolytes.

Adaptive multiscale simulations, such as adaptive QM/MM, are indispensable for investigating complex solution dynamics but historically suffer from a fundamental dilemma: the dynamic exchange of identical solvent molecules across different model resolutions introduces a physical asymmetry. This asymmetry forces a prohibitive trade-off between severe structural distortions and the violation of Hamiltonian conservation (continuous energy drift). To definitively resolve this issue, we propose the ”Integrated Molecular Model,” a paradigm-shifting framework that mathematically unifies multiple resolutions into a single, dynamically consistent potential. By employing a neural network that takes only the multiscale weight functions as input descriptors, our model learns to systematically cancel the non-physical transition forces originating from spatial discontinuities. As a proof-of-concept, we validated this unified framework on bulk water, aqueous ionic solutions, and reactive hydronium ions. Our approach not only faithfully restores artifact-free solvation structures but also strictly conserves the Hamiltonian, enabling unprecedentedly stable, long-term simulations under the microcanonical (NVE) ensemble. Consequently, the model successfully eliminates artificial thermostat-induced breathing modes, allowing for the rigorous evaluation of intrinsic dynamical properties such as diffusion coefficients. Furthermore, owing to its physically informed network design, the correction potential introduces less than 2\% additional computational overhead and demonstrates remarkable zero-shot transferability across chemically similar ionic species. By fundamentally eradicating the inherent asymmetry of adaptive multiscale modeling, this highly scalable framework establishes a robust foundation for high-fidelity simulations of complex condensed-phase phenomena, including reactive dynamics at solid-liquid interfaces and ion transport in battery electrolytes.

In variational quantum algorithms, parameterization is typically applied to single-qubit gates. In this study, we instead parameterize a generalized controlled gate and propose an algorithm to locally minimize the cost function by maximally optimizing these parameters. This method extends the Free Quaternion Selection (FQS) technique, which was originally developed for singlequbit gate optimization. To evaluate its performance, we apply the proposed method to a variety of quantum optimization tasks, including the Variational Quantum Eigensolver (VQE) for both Ising and molecular Hamiltonians, fidelity maximization in general variational quantum algorithms (VQAs), and unitary compilation of time evolution operators. Across these applications, our method demonstrates efficient optimization, enhanced expressibility, and the ability to construct shallower circuits compared to existing techniques. Moreover, the method can be generalized to optimize particle-number-conserving gates, which are particularly relevant for quantum chemistry. Leveraging this capability, we further demonstrate that the method achieves superior quantum compilation of molecular time-evolution operators by approximating them with shallower circuits than standard Trotter decomposition.

In variational quantum algorithms, it is important to balance conflicting requirements of expressibility and trainability of a parameterized quantum circuit (PQC). However, appropriate PQC designs are not necessarily trivial. Here, we propose an algorithm for optimizing the PQC structure, where single-qubit gates are sequentially replaced by the optimal ones via diagonalization of a matrix whose elements are evaluated on slightly modified circuits. This replacement leads to a better approximation of target states with limited circuit depth. Furthermore, we clarify the existence of a barren plateau in the sequential optimization in terms of the spectrum concentration of the matrix, which defines the cost landscape with respect to changes in the target gate. Then, we rigorously show the concentration is no faster than polynomials in the number of qubits when an n-qubit PQC depth is O ( log ⁡ n ) using local observables. Finally, numerical experiments are provided to show the convergence of our method which is faster than classical optimizers on both simulators and a real device. Our results provide evidences for sequential optimizers as better alternatives to optimize PQCs on near-term quantum devices.

The variational quantum eigensolver (VQE) is a hybrid algorithm to find the minimum eigenvalue/vector of the given Hamiltonian by optimizing a parameterized quantum circuit (PQC) using a classical computer. Sequential optimization methods, which are often used in quantum circuit tensor networks, are popular for optimizing the parameterized gates of PQCs. In this paper, we focus 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 refer to as the parameter configurations. In this paper, we first show that the optimization accuracy significantly depends on the choice of parameter configurations owing 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.

Variational quantum algorithms, which utilize Parametrized Quantum Circuits (PQCs), are promising tools to achieve quantum advantage for optimization problems on near-term quantum devices. Their PQCs have been conventionally constructed from parametrized rotational angles of single-qubit gates around predetermined set of axes, and two-qubit entangling gates, such as CNOT gates. We propose a method to construct a PQC by continuous parametrization of both the angles and the axes of its single-qubit rotation gates. The method is based on the observation that when rotational angles are fixed, optimal axes of rotations can be computed by solving a system of linear equations whose coefficients can be determined from the PQC with small computational overhead. The method can be further simplified to select axes freely from continuous parameters with rotational angles fixed to $\pi$ . We show the simplified free-axis selection method has better expressibility against other structural optimization methods when measured with Kullback-Leibler (KL) divergence. We also demonstrate PQCs with free-axis selection are more effective to search the ground states of Hamiltonians for condensed matter physics, quantum chemistry and combinatorial optimization. Because free-axis selection allows designing PQCs without specifying their single-qubit rotational axes, it may significantly improve the handiness of PQCs.