arXiv subjects

Haruyuki Nakano

Publications and source records attributed to Haruyuki Nakano.

3 recordsLinked to original sources

arXiv2025

Optimizing a parameterized controlled gate using Free Quaternion Selection

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 single-qubit 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.

quant-ph↗

arXiv2022

Theoretical examination of QED Hamiltonian and negative-energy orbitals in relativistic molecular orbital theory

The relativistic Hartree-Fock and electron correlation methods without the negative-energy orbital problem are examined on the basis of the quantum electrodynamics (QED) Hamiltonian. First, several QED Hamiltonians previously proposed are sifted by the orbital rotation invariance, the charge conjugation and time reversal invariance, and the nonrelativistic limit. A new total energy expression is then proposed, in which a counter term corresponding to the energy of the polarized vacuum is subtracted from the total energy. This expression prevents the possibility of total energy divergence due to electron correlations, stemming from the fact that the QED Hamiltonian does not conserve the number of particles. Finally, based on the Hamiltonian and energy expression, the Dirac-Hartree-Fock (DHF) and electron correlation methods are reintroduced. The resulting QED-based DHF equation has the same form as the conventional DHF equation, but also formally describes systems specific to QED, such as the virtual positrons in the hydride ion and the positron in positronium. Three electron correlation methods are derived: the QED-based configuration interactions and single- and multireference perturbation methods. Numerical calculations show that the total energy of the QED Hamiltonian indeed diverges and that the counter term is effective in avoiding the divergence. The theoretical examinations in the present article suggest that the molecular orbital (MO) methods based on the QED Hamiltonian not only solve the problem of the negative-energy solutions of the relativistic MO method, but also provide a relativistic formalism to treat systems containing positrons.

physics.chem-ph↗

arXiv2021

The Generalized Occupation-Restricted-Multiple-Active-Space Concept in Multiconfigurational Self-Consistent Field Methods

A novel concept of multiconfigurational self-consistent field method, the generalized occupation-restricted-multiple-active-space (GORMAS) is presented. GORMAS wave functions are defined by substituting the complete active space (CAS) in ORMAS, given a pre- or a post-restriction. The GORMAS approach shows a flexible selection of active space, reduce the ineffective reference configurations from CAS dramatically. Test calculations in molecule or complex systems, CH$_2$O, (H$_2$O)$_2$ molecule, and oxoMn(salen) are presented. They show the GORMAS wave functions achieve the similar accuracy with under 15\% dimension of reference spaces.

physics.chem-ph↗