Variational quantum eigensolver (VQE) is a promising method for ground-state calculations on current noisy intermediate-scale quantum computers. However, the research progress of excited-state calculations on quantum computers is relatively slow. In order to extend the framework of VQE for excited-state calculations, we propose a new algorithm, orthogonal state reduction variational eigensolver (OSRVE), to determine the energies of excited states. Theoretical derivations prove that the optimized state in the OSRVE method can ensure the energy minimum and orthogonality constraint simultaneously, and OSRVE is also applicable for the degenerate state. The performance of OSRVE is demonstrated by numerical calculations of the H 4 and H 2 O molecules. Compared with other excited-state calculation algorithms, OSRVE has obvious advantages in calculating lower-order excited states. This work extends the VQE algorithm to excited-state calculations, and OSRVE can be implemented on near-term quantum computers.Variational quantum eigensolver (VQE) is a promising method for ground-state calculations on current noisy intermediate-scale quantum computers. However, the research progress of excited-state calculations on quantum computers is relatively slow. In order to extend the framework of VQE for excited-state calculations, we propose a new algorithm, orthogonal state reduction variational eigensolver (OSRVE), to determine the energies of excited states. Theoretical derivations prove that the optimized state in the OSRVE method can ensure the energy minimum and orthogonality constraint simultaneously, and OSRVE is also applicable for the degenerate state. The performance of OSRVE is demonstrated by numerical calculations of the H 4 and H 2 O molecules. Compared with other excited-state calculation algorithms, OSRVE has obvious advantages in calculating lower-order excited states. This work extends the VQE algorithm to excited-state calculations, and OSRVE can be implemented on near-term quantum computers.

Journal of Chemical Theory and ComputationMay 27, 202225 citations

Computing static molecular properties using variational quantum eigensolver

Wataru Mizukami, Kosuke Mitarai, Nakagawa Yuya

日本物理学会講演概要集Jan 1, 20200 citations

An Introduction to Variational Quantum Eigensolver Applied to Chemistry

Matheus da Silva Fonseca, Caio Moraes Porto, Nicolás A. C. Carpio +4 more

Brazilian Journal of PhysicsNov 6, 20255 citations

Molecular Symmetry in VQE: A Dual Approach for Trapped-Ion Simulations of Benzene

Joshua J. Goings, Luning Zhao, Jacek Jakowski +2 more

Understanding complex chemical systems—such as biomolecules, catalysts, and novel materials—is a central goal of quantum simulations. Near-term strategies hinge on the use of variational quantum eigensolver (VQE) algorithms combined with a suitable ansatz. However, straightforward application of many chemically-inspired ansatze yields prohibitively deep circuits. In this work, we employ several circuit optimization methods tailored for trapped-ion quantum devices to enhance the feasibility of intricate chemical simulations. The techniques aim to lessen the depth of the unitary coupled cluster with singles and doubles (uCCSD) ansatz's circuit compilation, a considerable challenge on current noisy quantum devices. Furthermore, we use symmetry-inspired classical post-selection methods to further refine the outcomes and minimize errors in energy measurements, without adding quantum overhead. Our strategies encompass optimal mapping from orbital to qubit, term reordering to minimize entangling gates, and the exploitation of molecular spin and point group symmetry to eliminate redundant parameters. The inclusion of error mitigation via post-selection based on known molecular symmetries improves the results to near milli-Hartree accuracy. These methods, when applied to a benzene molecule simulation, enabled the construction of an 8-qubit circuit with 69 two-qubit entangling operations, pushing the limits for variational quantum eigensolver (VQE) circuits executed on quantum hardware to date.11This manuscript has been authored in part by UT-Battelle, LLC, under contract DE-AC05-000R22725 with the US Department of Energy (DOE). The publisher acknowledges the US government license to provide public access under the DOE Public Access Plan(https://energy.gov/doe-public-access-plan).Understanding complex chemical systems—such as biomolecules, catalysts, and novel materials—is a central goal of quantum simulations. Near-term strategies hinge on the use of variational quantum eigensolver (VQE) algorithms combined with a suitable ansatz. However, straightforward application of many chemically-inspired ansatze yields prohibitively deep circuits. In this work, we employ several circuit optimization methods tailored for trapped-ion quantum devices to enhance the feasibility of intricate chemical simulations. The techniques aim to lessen the depth of the unitary coupled cluster with singles and doubles (uCCSD) ansatz's circuit compilation, a considerable challenge on current noisy quantum devices. Furthermore, we use symmetry-inspired classical post-selection methods to further refine the outcomes and minimize errors in energy measurements, without adding quantum overhead. Our strategies encompass optimal mapping from orbital to qubit, term reordering to minimize entangling gates, and the exploitation of molecular spin and point group symmetry to eliminate redundant parameters. The inclusion of error mitigation via post-selection based on known molecular symmetries improves the results to near milli-Hartree accuracy. These methods, when applied to a benzene molecule simulation, enabled the construction of an 8-qubit circuit with 69 two-qubit entangling operations, pushing the limits for variational quantum eigensolver (VQE) circuits executed on quantum hardware to date.11This manuscript has been authored in part by UT-Battelle, LLC, under contract DE-AC05-000R22725 with the US Department of Energy (DOE). The publisher acknowledges the US government license to provide public access under the DOE Public Access Plan(https://energy.gov/doe-public-access-plan).

arXiv:2308.00667IEEE International Conference on Quantum Computing and Engineering (QCE)Sep 17, 20237 citations

Symmetry-adapted variational quantum eigensolver

Kazuhiro Seki, Tomonori Shirakawa, Seiji Yunoki

We propose a scheme to restore spatial symmetry of Hamiltonian in the variational-quantum-eigensolver (VQE) algorithm for which the quantum circuit structures used usually break the Hamiltonian symmetry. The symmetry-adapted VQE scheme introduced here simply applies the projection operator, which is Hermitian but not unitary, to restore the spatial symmetry in a desired irreducible representation of the spatial group. The entanglement of a quantum state is still represented in a quantum circuit but the nonunitarity of the projection operator is treated classically as postprocessing in the VQE framework. By numerical simulations for a spin- $1/2$ Heisenberg model on a one-dimensional ring, we demonstrate that the symmetry-adapted VQE scheme with a shallower quantum circuit can achieve significant improvement in terms of the fidelity of the ground state and has a great advantage in terms of the ground-state energy with decent accuracy, as compared to the non-symmetry-adapted VQE scheme. We also demonstrate that the present scheme can approximate low-lying excited states that can be specified by symmetry sectors, using the same circuit structure for the ground-state calculation.We propose a scheme to restore spatial symmetry of Hamiltonian in the variational-quantum-eigensolver (VQE) algorithm for which the quantum circuit structures used usually break the Hamiltonian symmetry. The symmetry-adapted VQE scheme introduced here simply applies the projection operator, which is Hermitian but not unitary, to restore the spatial symmetry in a desired irreducible representation of the spatial group. The entanglement of a quantum state is still represented in a quantum circuit but the nonunitarity of the projection operator is treated classically as postprocessing in the VQE framework. By numerical simulations for a spin-$1/2$ Heisenberg model on a one-dimensional ring, we demonstrate that the symmetry-adapted VQE scheme with a shallower quantum circuit can achieve significant improvement in terms of the fidelity of the ground state and has a great advantage in terms of the ground-state energy with decent accuracy, as compared to the non-symmetry-adapted VQE scheme. We also demonstrate that the present scheme can approximate low-lying excited states that can be specified by symmetry sectors, using the same circuit structure for the ground-state calculation.

arXiv:1912.13146Physical Review AMay 28, 202081 citations

Calculation of a many body potential using a variational quantum eigensolver

Beekhuis, Gijs

Jan 1, 20180 citations

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Heisenberg model on a one-dimensional ring, we demonstrate that the symmetry-adapted VQE scheme with a shallower quantum circuit can achieve significant improvement in terms of the fidelity of the ground state and has a great advantage in terms of the ground-state energy with decent accuracy, as compared to the non-symmetry-adapted VQE scheme. We also demonstrate that the present scheme can approximate low-lying excited states that can be specified by symmetry sectors, using the same circuit structure for the ground-state calculation.