arXiv subjects

Kenji Sugisaki

Publications and source records attributed to Kenji Sugisaki.

26 records · Page 2Linked to original sources

arXiv2024

Workflow for practical quantum chemical calculations with quantum phase estimation algorithm: electronic ground and π-π* excited states of benzene and its derivatives†

Quantum computers are expected to perform the full-configuration interaction calculations with less computational resources compared to classical ones, thanks to the use of the quantum phase estimation (QPE) algorithms. However, only a limited number of the QPE-based quantum chemical calculations have been reported even for numerical simulations on a classical computer, and the practical workflow for the QPE computation has not yet been established. In this paper, we report the QPE simulations of the electronic ground and the π-π* excited singlet state of benzene and its chloro- and nitroderivatives as the representative industrially important systems, with the aid of GPGPU acceleration of quantum circuit simulations. We adopted the pseudo-natural orbitals obtained from the MP2 calculation as the basis for the wave function expansion, the CISD calculation within the active space to find the main electronic configurations to be included in the input wave function of the excited state, and the technique to reduce the truncation error the calculated total energies. The proposed computational workflow is easily applicable to other molecules and can be a standard approach for performing the QPE-based quantum chemical calculations of practical molecules.

quant-ph↗

arXiv2024

Does the full configuration interaction method based on quantum phase estimation with Trotter decomposition satisfy the size consistency condition?

Electronic structure calculations of atoms and molecules are considered to be a promising application for quantum computers. Two key algorithms, the quantum phase estimation (QPE) and the variational quantum eigensolver (VQE), have been extensively studied. The condition that the energy of a dimer consisting of two monomers separated by a large distance should be equal to twice the energy of a monomer, known as size consistency, is essential in quantum chemical calculations. Recently, we reported that the size consistency condition can be violated by Trotterization in the unitary coupled cluster singles and doubles (UCCSD) ansatz in VQE when employing molecular orbitals delocalized to the dimer (K. Sugisaki {\it et al.}, {\it J. Comput. Chem.}, published online; \href{https://doi.org/10.1002/jcc.27438}{DOI:10.1002/jcc.27438}). It is well known that the full configuration interaction (full-CI) energy is invariant to arbitrary rotations of molecular orbitals, and therefore the QPE-based full-CI should theoretically satisfy the size consistency. However, Trotterization of the time evolution operator can break the size consistency conditions. In this work, we investigated whether the size consistency can be maintained with Trotterization of the time evolution operator in QPE-based full-CI calculations. Our numerical simulations revealed that size consistency in QPE-based full-CI is not automatically violated by using molecular orbitals delocalized to the dimer, but employing an appropriate Trotter decomposition condition is crucial to maintain size consistency. We also report on the acceleration of QPE simulations through the sequential addition of ancillary qubits.

quant-ph↗

arXiv2024

Entanglement-assisted phase estimation algorithm for calculating dynamical response functions

Dynamical response functions are fundamental quantities to describe the excited-state properties in quantum many-body systems. Quantum algorithms have been proposed to evaluate these quantities by means of quantum phase estimation (QPE), where the energy spectra are directly extracted from the QPE measurement outcomes in the frequency domain. Accurate estimation of excitation energies and transition probabilities with these QPE-based approaches is, however, challenging because of the problem of spectral leakage (or peak broadening) which is inherent in the QPE algorithm. To overcome this issue, in this work we consider an extension of the QPE-based approach adopting the optimal entangled input states, which is known to achieve the Heisenberg-limited scaling for the estimation precision. We show that with this method the peaks in the calculated energy spectra are more localized than those calculated by the original QPE-based approaches, suggesting the mitigation of the spectral leakage problem. By analyzing the probability distribution with the entangled phase estimation, we propose a simple scheme to better estimate both the transition energies and the corresponding transition probabilities of the peaks of interest in the spectra. The validity of our prescription is demonstrated by numerical simulations in various quantum many-body problems: the spectral function of a simple electron-plasmon model in condensed-matter physics, the dipole transitions of the H$_2$O molecule in quantum chemistry, and the electromagnetic transitions of the $^6$Li nucleus in nuclear physics.

quant-ph↗

arXiv2024

Size-consistency and orbital-invariance issues revealed by VQE-UCCSD calculations with the FMO scheme

The fragment molecular orbital (FMO) scheme is one of the popular fragmentation-based methods and has the potential advantage of making the circuit flat in quantum chemical calculations on quantum computers. In this study, we used a GPU-accelerated quantum simulator (cuQuantum) to perform the electron correlation part of the FMO calculation as unitary coupled-cluster singles and doubles (UCCSD) with the variational quantum eigensolver (VQE) for hydrogen-bonded (FH)$_3$ and (FH)$_2$-H$_2$O systems with the STO-3G basis set. VQE-UCCD calculations were performed using both canonical and localized MO sets, and the results were examined from the point of view of size-consistency and orbital-invariance affected by the Trotter error. It was found that the use of localized MO leads to better results, especially for (FH)$_2$-H$_2$O. The GPU acceleration was substantial for the simulations with larger numbers of qubits, and was about a factor of 6.7--7.7 for 18 qubit systems.

quant-ph↗

arXiv2023

Projective Quantum Phase Difference Estimation Algorithm for the Direct Computation of Eigenenergy Gaps on a Quantum Computer

Quantum computers are capable of calculating the energy gap of two electronic states by using the quantum phase difference estimation (QPDE) algorithm. The Bayesian inference based implementations for the QPDE have been reported so far, but this approach is not projective, and the quality of the calculated energy gap depends on the input wave functions being used. Here, we report the inverse quantum Fourier transformation based QPDE with $N_a$ of ancillary qubits, which allows us to compute the difference of eigenenergies based on the single-shot projective measurement. As a proof-of-concept demonstrations, we report numerical experiments for the singlet--triplet energy gap of hydrogen molecule and the vertical excitation energies of halogen-substituted methylenes (CHF, CHCl, CF$_2$, CFCl and CCl$_2$) and formaldehyde (HCHO).

quant-ph↗

arXiv2023

Molecular electric dipole moments: from light to heavy molecules using a relativistic VQE algorithm

The quantum-classical hybrid Variational Quantum Eigensolver (VQE) algorithm is recognized to be the most suitable approach to obtain ground state energies of quantum many-body systems in the noisy intermediate scale quantum era. In this work, we extend the VQE algorithm to the relativistic regime and carry out quantum simulations to obtain ground state energies as well as molecular permanent electric dipole moments of single-valence diatomic molecules, beginning with the light BeH molecule and all the way to the heavy radioactive RaH molecule. We study the correlation trends in these systems as well as assess the precision in our results within our active space of 12 qubits.

physics.atom-ph↗

arXiv2023

Bayesian phase difference estimation algorithm for direct calculation of fine structure splitting: accelerated simulation of relativistic and quantum many-body effects

Despite rapid progress in the development of quantum algorithms in quantum computing as well as numerical simulation methods in classical computing for atomic and molecular applications, no systematic and comprehensive electronic structure study of atomic systems that covers almost all of the elements in the periodic table using a single quantum algorithm has been reported. In this work, we address this gap by implementing the recently-proposed quantum algorithm, the Bayesian Phase Difference Estimation (BPDE) approach, to compute accurately fine-structure splittings, which are relativistic in origin and it also depends on quantum many-body (electron correlation) effects, of appropriately chosen states of atomic systems, including highly-charged superheavy ions. Our numerical simulations reveal that the BPDE algorithm, in the Dirac--Coulomb--Breit framework, can predict the fine-structure splitting of Boron-like ions to within 605.3 cm$^{-1}$ of root mean square deviations from the experimental ones, in the (1s, 2s, 2p, 3s, 3p) active space. We performed our simulations of relativistic and electron correlation effects on Graphics Processing Unit (GPU) by utilizing NVIDIA's cuQuantum, and observe a $\times 42.7$ speedup as compared to the CPU-only simulations in an 18-qubit active space.

quant-ph↗

arXiv2020

Direct estimation of the energy gap between the ground state and excited state with quantum annealing

Quantum chemistry is one of the important applications of quantum information technology. Especially, an estimation of the energy gap between a ground state and excited state of a target Hamiltonian corresponding to a molecule is essential. In the previous approach, an energy of the ground state and that of the excited state are estimated separately, and the energy gap can be calculated from the subtraction between them. Here, we propose a direct estimation of the energy gap between the ground state and excited state of the target Hamiltonian with quantum annealing. The key idea is to combine a Ramsey type measurement with the quantum annealing. This provides an oscillating signal with a frequency of the energy gap, and a Fourier transform of the signal let us know the energy gap. Based on typical parameters of superconducting qubits, we numerically investigate the performance of our scheme when we estimate an energy gap between the ground state and first excited state of the Hamiltonian. We show robustness against non-adiabatic transitions between the ground state and first-excited state. Our results pave a new way to estimate the energy gap of the Hamiltonian for quantum chemistry.

quant-ph↗