Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Chemical Theory and Computation

Quantum Algorithm of the Divide-and-Conquer Unitary Coupled Cluster Method with a Variational Quantum Eigensolver

Takeshi Yoshikawa, Tomoya Takanashi, Hiromi Nakai

Published Aug 4, 2022• 9 citations
Publisher

Abstract

The variational quantum eigensolver (VQE) with shallow or constant-depth quantum circuits is one of the most pursued approaches in the noisy intermediate-scale quantum (NISQ) devices with incoherent errors. In this study, the divide-and-conquer (DC) linear scaling technique, which divides the entire system into several fragments, is applied to the VQE algorithm based on the unitary coupled cluster (UCC) method, denoted as DC-qUCC/VQE, to reduce the number of required qubits. The unitarity of the UCC ansatz that enables the evaluation of the total energy as well as various molecular properties as expectation values can be easily implemented on quantum devices because the quantum gates are unitary operators themselves. Based on this feature, the present DC-qUCC/VQE algorithm is designed to conserve the total number of electrons in the entire system using the density matrix evaluated on a quantum computer. Numerical assessments clarified that the energy errors of the DC-qUCC/VQE calculations decrease by using the constraint of the total number of electrons. Furthermore, the DC-qUCC/VQE algorithm could reduce the number of quantum gates and shows the possibility of decreasing incoherent errors.

DOI
10.1021/acs.jctc.2c00602

Related papers

Offline Quantum Circuit Pruning for Quantum Chemical Calculations

Satoshi Imamura, Akihiko Kasagi, Eiji Yoshida

A variational quantum eigensolver (VQE) designed for noisy intermediate-scale quantum (NISQ) computers is a promising hybrid quantum-classical algorithm for quantum chemical calculations (QCC). Its accuracy and computational cost strongly depend on an ansatz, and unitary coupled-cluster (UCC) ansatze are well-known chemistry-inspired ansatze that can achieve a high accuracy for QCC. However, UCC-based quantum circuits have a high depth and a lot of 2-qubit controlled NOT (CNOT) gates which are sensitive to noises, leading to the low accuracy of VQE running on NISQ computers. To address this issue, we propose a novel offline quantum circuit pruning technique that reduces the number of CNOT gates and depth of UCC-based quantum circuits by reducing the number of excitation operators per parameter to a user-specified value. It is applied only once before VQE is executed (i.e., offline), which is the advantage over state-of-the-art quantum circuit pruning techniques. The evaluation using a quantum computer simulator with a noise model based on a real NISQ device shows that our offline pruning technique improves the accuracy of UCCSD-VQE while sustaining the potential accuracy of the UCCSD ansatz and has a synergy with a well-known noise mitigation method called zero noise extrapolation (ZNE).

IEEE International Conference on Quantum Computing and Engineering (QCE)•Sep 17, 2023•5 citations

Circuit-Depth Reduction of Unitary-Coupled-Cluster Ansatz by Energy Sorting

Yi Fan, Changsu Cao, Xusheng Xu +3 more

Quantum computation represents a revolutionary approach to solving problems in quantum chemistry. However, due to the limited quantum resources in the current noisy intermediate-scale quantum (NISQ) devices, quantum algorithms for large chemical systems remain a major task. In this work, we demonstrate that the circuit depth of the unitary coupled cluster (UCC) and UCC-based ansatzes in the algorithm of the variational quantum eigensolver can be significantly reduced by an energy-sorting strategy. Specifically, subsets of excitation operators are first prescreened from the operator pool according to its contribution to the total energy. The quantum circuit ansatz is then iteratively constructed until convergence of the final energy to a typical accuracy. For demonstration, this method has been successfully applied to molecular and periodic systems. Particularly, a reduction of 50%-98% in the number of operators is observed while retaining the accuracy of the original UCCSD operator pools. This method can be straightforwardly extended to general parametric variational ansatzes.

arXiv:2106.15210•The Journal of Physical Chemistry Letters•Oct 20, 2023•25 citations

Reducing Unitary Coupled Cluster Circuit Depth by Classical Stochastic Amplitude Pre-Screening

Maria-Andreea Filip, Nathan Fitzpatrick, David Muñoz Ramo +1 more

Unitary Coupled Cluster (UCC) approaches are an appealing route to utilising quantum hardware to perform quantum chemistry calculations, as quantum computers can in principle perform UCC calculations in a polynomially scaling fashion, as compared to the exponential scaling required on classical computers. Current noisy intermediate scale quantum (NISQ) computers are limited by both hardware capacity in number of logical qubits and the noise introduced by the deep circuits required for UCC calculations using the Variational Quantum Eigensolver (VQE) approach. We present a combined classical--quantum approach where a stochastic classical UCC pre-processing step is used to determine the important excitations in the UCC ansatz. The reduced number of selected excitations are then used in a UCC-based VQE calculation. This approach gives a systematically improvable approximation, and we show that significant reductions in quantum resources can be achieved, with simulations on the CH$_2$, N$_2$ and N$_2$H$_2$ molecules giving sub-milliHartree errors.

arXiv:2108.10912•Aug 24, 2021•0 citations

Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz

Jonathan Romero, Ryan Babbush, Jarrod R. McClean +3 more

Abstract The variational quantum eigensolver (VQE) algorithm combines the ability of quantum computers to efficiently compute expectation values with a classical optimization routine in order to approximate ground state energies of quantum systems. In this paper, we study the application of VQE to the simulation of molecular energies using the unitary coupled cluster (UCC) ansatz. We introduce new strategies to reduce the circuit depth for the implementation of UCC and improve the optimization of the wavefunction based on efficient classical approximations of the cluster amplitudes. Additionally, we propose an analytical method to compute the energy gradient that reduces the sampling cost for gradient estimation by several orders of magnitude compared to numerical gradients. We illustrate our methodology with numerical simulations for a system of four hydrogen atoms that exhibit strong correlation and show that the circuit depth of VQE using a UCC ansatz can be reduced without introducing significant loss of accuracy in the final wavefunctions and energies.

arXiv:1701.02691•Quantum Science and Technology•Jul 17, 2018•726 citations

The Best of Both Worlds: Optimizing Quantum Hardware Resources with Classical Stochastic Methods

Maria-Andreea Filip, Nathan Fitzpatrick, David Muñoz Ramo +1 more

Unitary Coupled Cluster (UCC) approaches are an appealing route to utilising quantum hardware to perform quantum chemistry calculations, as quantum computers can in principle perform UCC calculations in a polynomially scaling fashion, as compared to the exponential scaling required on classical computers. Current noisy intermediate scale quantum (NISQ) computers are limited by both hardware capacity in number of logical qubits and the noise introduced by the deep circuits required for UCC calculations using the Variational Quantum Eigensolver (VQE) approach. We present a combined classical--quantum approach where a stochastic classical UCC pre-processing step is used to determine the important excitations in the UCC ansatz. The reduced number of selected excitations are then used in a UCC-based VQE calculation. This approach gives a systematically improvable approximation, and we show that significant reductions in quantum resources can be achieved, with sub-milliHartree errors in the CH$_2$, N$_2$ and N$_2$H$_2$ molecules.

•Aug 24, 2021•0 citations

Reducing unitary coupled cluster circuit depth by classical stochastic amplitude prescreening

Maria-Andreea Filip, Nathan Fitzpatrick, David Muñoz Ramo +1 more

Unitary coupled cluster (UCC) approaches are an appealing route to utilizing quantum hardware to perform quantum chemistry calculations, as quantum computers can in principle perform UCC calculations in a polynomially scaling fashion, as compared with the exponential scaling required on classical computers. Current noisy intermediate scale quantum computers are limited by both hardware capacity in number of logical qubits and the noise introduced by the deep circuits required for UCC calculations using the variational quantum eigensolver (VQE) approach. We present a combined classical-quantum approach where a stochastic classical UCC preprocessing step is used to determine the important excitations in the UCC Ansatz. The reduced number of selected excitations are then used in a UCC-based VQE calculation. This approach gives a systematically improvable approximation, and we show that significant reductions in quantum resources can be achieved, with simulations on the ${\mathrm{CH}}_{2}, {\mathrm{N}}_{2}$, and ${\mathrm{N}}_{2}{\mathrm{H}}_{2}$ molecules giving submillihartree errors.

Physical Review Research•Jun 27, 2022•9 citations
The variational quantum eigensolver (VQE) with shallow or constant-depth quantum circuits is one of the most pursued approaches in the noisy intermediate-scale quantum (NISQ) devices with incoherent errors. In this study, the divide-and-conquer (DC) linear scaling technique, which divides the entire system into several fragments, is applied to the VQE algorithm based on the unitary coupled cluster (UCC) method, denoted as DC-qUCC/VQE, to reduce the number of required qubits. The unitarity of the UCC ansatz that enables the evaluation of the total energy as well as various molecular properties as expectation values can be easily implemented on quantum devices because the quantum gates are unitary operators themselves. Based on this feature, the present DC-qUCC/VQE algorithm is designed to conserve the total number of electrons in the entire system using the density matrix evaluated on a quantum computer. Numerical assessments clarified that the energy errors of the DC-qUCC/VQE calculations decrease by using the constraint of the total number of electrons. Furthermore, the DC-qUCC/VQE algorithm could reduce the number of quantum gates and shows the possibility of decreasing incoherent errors.
A variational quantum eigensolver (VQE) designed for noisy intermediate-scale quantum (NISQ) computers is a promising hybrid quantum-classical algorithm for quantum chemical calculations (QCC). Its accuracy and computational cost strongly depend on an ansatz, and unitary coupled-cluster (UCC) ansatze are well-known chemistry-inspired ansatze that can achieve a high accuracy for QCC. However, UCC-based quantum circuits have a high depth and a lot of 2-qubit controlled NOT (CNOT) gates which are sensitive to noises, leading to the low accuracy of VQE running on NISQ computers. To address this issue, we propose a novel offline quantum circuit pruning technique that reduces the number of CNOT gates and depth of UCC-based quantum circuits by reducing the number of excitation operators per parameter to a user-specified value. It is applied only once before VQE is executed (i.e., offline), which is the advantage over state-of-the-art quantum circuit pruning techniques. The evaluation using a quantum computer simulator with a noise model based on a real NISQ device shows that our offline pruning technique improves the accuracy of UCCSD-VQE while sustaining the potential accuracy of the UCCSD ansatz and has a synergy with a well-known noise mitigation method called zero noise extrapolation (ZNE).
Quantum computation represents a revolutionary approach to solving problems in quantum chemistry. However, due to the limited quantum resources in the current noisy intermediate-scale quantum (NISQ) devices, quantum algorithms for large chemical systems remain a major task. In this work, we demonstrate that the circuit depth of the unitary coupled cluster (UCC) and UCC-based ansatzes in the algorithm of the variational quantum eigensolver can be significantly reduced by an energy-sorting strategy. Specifically, subsets of excitation operators are first prescreened from the operator pool according to its contribution to the total energy. The quantum circuit ansatz is then iteratively constructed until convergence of the final energy to a typical accuracy. For demonstration, this method has been successfully applied to molecular and periodic systems. Particularly, a reduction of 50%-98% in the number of operators is observed while retaining the accuracy of the original UCCSD operator pools. This method can be straightforwardly extended to general parametric variational ansatzes.
Unitary Coupled Cluster (UCC) approaches are an appealing route to utilising quantum hardware to perform quantum chemistry calculations, as quantum computers can in principle perform UCC calculations in a polynomially scaling fashion, as compared to the exponential scaling required on classical computers. Current noisy intermediate scale quantum (NISQ) computers are limited by both hardware capacity in number of logical qubits and the noise introduced by the deep circuits required for UCC calculations using the Variational Quantum Eigensolver (VQE) approach. We present a combined classical--quantum approach where a stochastic classical UCC pre-processing step is used to determine the important excitations in the UCC ansatz. The reduced number of selected excitations are then used in a UCC-based VQE calculation. This approach gives a systematically improvable approximation, and we show that significant reductions in quantum resources can be achieved, with simulations on the CH2_22​, N2_22​ and N2_22​H2_22​ molecules giving sub-milliHartree errors.
Abstract The variational quantum eigensolver (VQE) algorithm combines the ability of quantum computers to efficiently compute expectation values with a classical optimization routine in order to approximate ground state energies of quantum systems. In this paper, we study the application of VQE to the simulation of molecular energies using the unitary coupled cluster (UCC) ansatz. We introduce new strategies to reduce the circuit depth for the implementation of UCC and improve the optimization of the wavefunction based on efficient classical approximations of the cluster amplitudes. Additionally, we propose an analytical method to compute the energy gradient that reduces the sampling cost for gradient estimation by several orders of magnitude compared to numerical gradients. We illustrate our methodology with numerical simulations for a system of four hydrogen atoms that exhibit strong correlation and show that the circuit depth of VQE using a UCC ansatz can be reduced without introducing significant loss of accuracy in the final wavefunctions and energies.
Unitary Coupled Cluster (UCC) approaches are an appealing route to utilising quantum hardware to perform quantum chemistry calculations, as quantum computers can in principle perform UCC calculations in a polynomially scaling fashion, as compared to the exponential scaling required on classical computers. Current noisy intermediate scale quantum (NISQ) computers are limited by both hardware capacity in number of logical qubits and the noise introduced by the deep circuits required for UCC calculations using the Variational Quantum Eigensolver (VQE) approach. We present a combined classical--quantum approach where a stochastic classical UCC pre-processing step is used to determine the important excitations in the UCC ansatz. The reduced number of selected excitations are then used in a UCC-based VQE calculation. This approach gives a systematically improvable approximation, and we show that significant reductions in quantum resources can be achieved, with sub-milliHartree errors in the CH2_22​, N2_22​ and N2_22​H2_22​ molecules.
Unitary coupled cluster (UCC) approaches are an appealing route to utilizing quantum hardware to perform quantum chemistry calculations, as quantum computers can in principle perform UCC calculations in a polynomially scaling fashion, as compared with the exponential scaling required on classical computers. Current noisy intermediate scale quantum computers are limited by both hardware capacity in number of logical qubits and the noise introduced by the deep circuits required for UCC calculations using the variational quantum eigensolver (VQE) approach. We present a combined classical-quantum approach where a stochastic classical UCC preprocessing step is used to determine the important excitations in the UCC Ansatz. The reduced number of selected excitations are then used in a UCC-based VQE calculation. This approach gives a systematically improvable approximation, and we show that significant reductions in quantum resources can be achieved, with simulations on the CH2,N2{\mathrm{CH}}_{2}, {\mathrm{N}}_{2}CH2​,N2​, and N2H2{\mathrm{N}}_{2}{\mathrm{H}}_{2}N2​H2​ molecules giving submillihartree errors.