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

arXiv:1506.00443 · Physical Review A

Quantum implementation of the unitary coupled cluster for simulating molecular electronic structure

Yangchao Shen, Xiang Zhang, Shuaining Zhang, Jing-Ning Zhang, Man‐Hong Yung, Kihwan Kim

Published Feb 15, 2017• 295 citations
arXivHTMLPDF

Abstract

In classical computational chemistry, the coupled-cluster ansatz is one of the most commonly used ab initio methods, which is critically limited by its nonunitary nature. The unitary modification as an ideal solution to the problem is, however, extremely inefficient in classical conventional computation. Here, we provide experimental evidence that indeed the unitary version of the coupled-cluster ansatz can be reliably performed in a physical quantum system, a trapped-ion system. We perform a simulation on the electronic structure of a molecular ion (${\mathrm{HeH}}^{+}$), where the ground-state energy surface curve is probed, the energies of the excited states are studied, and bond dissociation is simulated nonperturbatively. Our simulation takes advantages from quantum computation to overcome the intrinsic limitations in classical computation, and our experimental results indicate that the method is promising for preparing molecular ground states for quantum simulations.

DOI
10.1103/physreva.95.020501

Related papers

Quantum orbital-optimized unitary coupled cluster methods in the strongly correlated regime: Can quantum algorithms outperform their classical equivalents?

Igor O. Sokolov, Panagiotis Kl. Barkoutsos, Pauline J. Ollitrault +4 more

The Coupled Cluster (CC) method is used to compute the electronic correlation energy in atoms and molecules and often leads to highly accurate results. However, due to its single-reference nature, standard CC in its projected form fails to describe quantum states characterized by strong electronic correlations and multi-reference projective methods become necessary. On the other hand, quantum algorithms for the solution of many-electron problems have also emerged recently. The quantum unitary variant of CC (UCC) with singles and doubles (q-UCCSD) is a popular wavefunction Ansatz for the variational quantum eigensolver algorithm. The variational nature of this approach can lead to significant advantages compared to its classical equivalent in the projected form, in particular, for the description of strong electronic correlation. However, due to the large number of gate operations required in q-UCCSD, approximations need to be introduced in order to make this approach implementable in a state-of-the-art quantum computer. In this work, we evaluate several variants of the standard q-UCCSD Ansatz in which only a subset of excitations is included. In particular, we investigate the singlet and pair q-UCCD approaches combined with orbital optimization. We show that these approaches can capture the dissociation/distortion profiles of challenging systems, such as H4, H2O, and N2 molecules, as well as the one-dimensional periodic Fermi–Hubbard chain. These results promote the future use of q-UCC methods for the solution of challenging electronic structure problems in quantum chemistry.

arXiv:1911.10864•The Journal of Chemical Physics•Mar 25, 2020•164 citations

Accuracy and Resource Estimations for Quantum Chemistry on a Near-Term Quantum Computer

Michael Kühn, Sebastian Zanker, Peter Deglmann +2 more

One of the most important application areas of molecular quantum chemistry is the study and prediction of chemical reactivity. Large-scale, fully error-tolerant quantum computers could provide exact or near-exact solutions to the underlying electronic structure problem with exponentially less effort than a classical computer thus enabling highly accurate predictions for comparably large molecular systems. In the nearer future, however, only “noisy” devices with a limited number of qubits that are subject to decoherence will be available. For such near-term quantum computers the hybrid quantum-classical variational quantum eigensolver algorithm in combination with the unitary coupled-cluster ansatz (UCCSD-VQE) [Peruzzo et al. Nat. Commun. 2014, 5, 4213 and McClean et al. New J. Phys. 2016, 18, 023023] has become an intensively discussed approach that could provide accurate results before the dawn of error-tolerant quantum computing. In this work we present an implementation of UCCSD-VQE that allows for the first time to treat both open- and closed-shell molecules. We study the accuracy of the obtained energies for nine small molecular systems as well as for four exemplary chemical reactions by comparing to well-established electronic structure methods like (nonunitary) coupled-cluster and density functional theory. Finally, we roughly estimate the required quantum hardware resources to obtain “useful” results for practical purposes.

arXiv:1812.06814•Journal of Chemical Theory and Computation•Aug 12, 2019•72 citations

Scalable Quantum Simulation of Molecular Energies

P. J. J. O’Malley, Ryan Babbush, Ian Kivlichan +29 more

We report the first electronic structure calculation performed on a quantum computer without exponentially costly precompilation.We use a programmable array of superconducting qubits to compute the energy surface of molecular hydrogen using two distinct quantum algorithms.First, we experimentally execute the unitary coupled cluster method using the variational quantum eigensolver.Our efficient implementation predicts the correct dissociation energy to within chemical accuracy of the numerically exact result.Second, we experimentally demonstrate the canonical quantum algorithm for chemistry, which consists of Trotterization and quantum phase estimation.We compare the experimental performance of these approaches to show clear evidence that the variational quantum eigensolver is robust to certain errors.This error tolerance inspires hope that variational quantum simulations of classically intractable molecules may be viable in the near future.

arXiv:1512.06860•Physical Review X•Jul 18, 2016•1,057 citations

Chemically aware unitary coupled cluster with ab initio calculations on an ion trap quantum computer: A refrigerant chemicals’ application

I. T. Khan, Maria Tudorovskaya, Josh J. M. Kirsopp +4 more

Circuit depth reduction is of critical importance for quantum chemistry simulations on current and near term quantum computers. This issue is tackled by introducing a chemically aware strategy for the unitary coupled cluster ansatz. The objective is to use the chemical description of a system to aid in the synthesis of a quantum circuit. We combine this approach with two flavors of symmetry verification for the reduction of experimental noise. These methods enable the use of Quantinuum's System Model H1 ion trap quantum computer for a 6-qubit quantum subspace expansion calculation. We present (i) calculations to obtain methane's optical spectra; (ii) an atmospheric gas reaction simulation involving [CH3⋅-H-OH]‡. Using our chemically aware unitary coupled cluster state-preparation strategy in tandem with state of the art symmetry verification methods, we improve device yield for CH4 at 6 qubits. This is demonstrated by a 90% improvement in two-qubit gate count and a reduction in relative error to 0.2% for electronic energy calculated on System Model H1.

arXiv:2210.14834•The Journal of Chemical Physics•Jun 2, 2023•23 citations

Quantum Simulation of Molecular Electronic States with a Transcorrelated Hamiltonian: Higher Accuracy with Fewer Qubits

Ashutosh Kumar, Ayush Asthana, Conner Masteran +5 more

Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron-electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. The transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.

Journal of Chemical Theory and Computation•Aug 19, 2022•44 citations

Bridging physical intuition and hardware efficiency for correlated electronic states: the local unitary cluster Jastrow ansatz for electronic structure

Mário Motta, Kevin J. Sung, K. Birgitta Whaley +2 more

A prominent goal in quantum chemistry is to solve the molecular electronic structure problem for the ground state energy with high accuracy. While classical quantum chemistry is a relatively mature field, the accurate and scalable prediction of strongly correlated states found, e.g., in bond breaking and polynuclear transition metal compounds remains an open problem. Within the context of a variational quantum eigensolver, we propose a new family of ansatzes which provides a more physically appropriate description of strongly correlated electrons than unitary coupled cluster with singles and doubles excitations, with vastly reduced quantum resource requirements. Specifically, we present a set of local approximations to the unitary cluster Jastrow wavefunction motivated by Hubbard physics. The resulting ansatz removes the need for SWAP gates and can be tailored to arbitrary qubit topologies (e.g., square, hex, heavy-hex). Our ansatz is well-suited to take advantage of continuous sets of quantum gates recently realized on superconducting devices with tunable couplers, while retaining a unique level of physical transparency and interpretability. As the capabilities of quantum computing devices continue to progress, we expect that the local cluster Jastrow ansatz to be a natural choice to encode both statically and dynamically correlated electronic wavefunctions.

Chemical Science•Jan 1, 2023•54 citations
In classical computational chemistry, the coupled-cluster ansatz is one of the most commonly used ab initio methods, which is critically limited by its nonunitary nature. The unitary modification as an ideal solution to the problem is, however, extremely inefficient in classical conventional computation. Here, we provide experimental evidence that indeed the unitary version of the coupled-cluster ansatz can be reliably performed in a physical quantum system, a trapped-ion system. We perform a simulation on the electronic structure of a molecular ion (HeH+{\mathrm{HeH}}^{+}HeH+), where the ground-state energy surface curve is probed, the energies of the excited states are studied, and bond dissociation is simulated nonperturbatively. Our simulation takes advantages from quantum computation to overcome the intrinsic limitations in classical computation, and our experimental results indicate that the method is promising for preparing molecular ground states for quantum simulations.
The Coupled Cluster (CC) method is used to compute the electronic correlation energy in atoms and molecules and often leads to highly accurate results. However, due to its single-reference nature, standard CC in its projected form fails to describe quantum states characterized by strong electronic correlations and multi-reference projective methods become necessary. On the other hand, quantum algorithms for the solution of many-electron problems have also emerged recently. The quantum unitary variant of CC (UCC) with singles and doubles (q-UCCSD) is a popular wavefunction Ansatz for the variational quantum eigensolver algorithm. The variational nature of this approach can lead to significant advantages compared to its classical equivalent in the projected form, in particular, for the description of strong electronic correlation. However, due to the large number of gate operations required in q-UCCSD, approximations need to be introduced in order to make this approach implementable in a state-of-the-art quantum computer. In this work, we evaluate several variants of the standard q-UCCSD Ansatz in which only a subset of excitations is included. In particular, we investigate the singlet and pair q-UCCD approaches combined with orbital optimization. We show that these approaches can capture the dissociation/distortion profiles of challenging systems, such as H4, H2O, and N2 molecules, as well as the one-dimensional periodic Fermi–Hubbard chain. These results promote the future use of q-UCC methods for the solution of challenging electronic structure problems in quantum chemistry.
One of the most important application areas of molecular quantum chemistry is the study and prediction of chemical reactivity. Large-scale, fully error-tolerant quantum computers could provide exact or near-exact solutions to the underlying electronic structure problem with exponentially less effort than a classical computer thus enabling highly accurate predictions for comparably large molecular systems. In the nearer future, however, only “noisy” devices with a limited number of qubits that are subject to decoherence will be available. For such near-term quantum computers the hybrid quantum-classical variational quantum eigensolver algorithm in combination with the unitary coupled-cluster ansatz (UCCSD-VQE) [Peruzzo et al. Nat. Commun. 2014, 5, 4213 and McClean et al. New J. Phys. 2016, 18, 023023] has become an intensively discussed approach that could provide accurate results before the dawn of error-tolerant quantum computing. In this work we present an implementation of UCCSD-VQE that allows for the first time to treat both open- and closed-shell molecules. We study the accuracy of the obtained energies for nine small molecular systems as well as for four exemplary chemical reactions by comparing to well-established electronic structure methods like (nonunitary) coupled-cluster and density functional theory. Finally, we roughly estimate the required quantum hardware resources to obtain “useful” results for practical purposes.
We report the first electronic structure calculation performed on a quantum computer without exponentially costly precompilation.We use a programmable array of superconducting qubits to compute the energy surface of molecular hydrogen using two distinct quantum algorithms.First, we experimentally execute the unitary coupled cluster method using the variational quantum eigensolver.Our efficient implementation predicts the correct dissociation energy to within chemical accuracy of the numerically exact result.Second, we experimentally demonstrate the canonical quantum algorithm for chemistry, which consists of Trotterization and quantum phase estimation.We compare the experimental performance of these approaches to show clear evidence that the variational quantum eigensolver is robust to certain errors.This error tolerance inspires hope that variational quantum simulations of classically intractable molecules may be viable in the near future.
Circuit depth reduction is of critical importance for quantum chemistry simulations on current and near term quantum computers. This issue is tackled by introducing a chemically aware strategy for the unitary coupled cluster ansatz. The objective is to use the chemical description of a system to aid in the synthesis of a quantum circuit. We combine this approach with two flavors of symmetry verification for the reduction of experimental noise. These methods enable the use of Quantinuum's System Model H1 ion trap quantum computer for a 6-qubit quantum subspace expansion calculation. We present (i) calculations to obtain methane's optical spectra; (ii) an atmospheric gas reaction simulation involving [CH3⋅-H-OH]‡. Using our chemically aware unitary coupled cluster state-preparation strategy in tandem with state of the art symmetry verification methods, we improve device yield for CH4 at 6 qubits. This is demonstrated by a 90% improvement in two-qubit gate count and a reduction in relative error to 0.2% for electronic energy calculated on System Model H1.
Simulation of electronic structure is one of the most promising applications on noisy intermediate-scale quantum (NISQ) era devices. However, NISQ devices suffer from a number of challenges like limited qubit connectivity, short coherence times, and sizable gate error rates. Thus, desired quantum algorithms should require shallow circuit depths and low qubit counts to take advantage of these devices. Here, we attempt to reduce quantum resource requirements for molecular simulations on a quantum computer while maintaining the desired accuracy with the help of classical quantum chemical theories of canonical transformation and explicit correlation. In this work, compact ab initio Hamiltonians are generated classically, in the second quantized form, through an approximate similarity transformation of the Hamiltonian with (a) an explicitly correlated two-body unitary operator with generalized pair excitations that remove the Coulombic electron-electron singularities from the Hamiltonian and (b) a unitary one-body operator to efficiently capture the orbital relaxation effects required for accurate description of the excited states. The resulting transcorrelated Hamiltonians are able to describe both the ground and the excited states of molecular systems in a balanced manner. Using the variational quantum eigensolver (VQE) method based on the unitary coupled cluster with singles and doubles (UCCSD) ansatz and only a minimal basis set (ANO-RCC-MB), we demonstrate that the transcorrelated Hamiltonians can produce ground state energies comparable to the reference CCSD energies with the much larger cc-pVTZ basis set. This leads to a reduction in the number of required CNOT gates by more than 3 orders of magnitude for the chemical species studied in this work. Furthermore, using the quantum equation of motion (qEOM) formalism in conjunction with the transcorrelated Hamiltonian, we are able to reduce the deviations in the excitation energies from the reference EOM-CCSD/cc-pVTZ values by an order of magnitude. The transcorrelated Hamiltonians developed here are Hermitian and contain only one- and two-body interaction terms and thus can be easily combined with any quantum algorithm for accurate electronic structure simulations.
A prominent goal in quantum chemistry is to solve the molecular electronic structure problem for the ground state energy with high accuracy. While classical quantum chemistry is a relatively mature field, the accurate and scalable prediction of strongly correlated states found, e.g., in bond breaking and polynuclear transition metal compounds remains an open problem. Within the context of a variational quantum eigensolver, we propose a new family of ansatzes which provides a more physically appropriate description of strongly correlated electrons than unitary coupled cluster with singles and doubles excitations, with vastly reduced quantum resource requirements. Specifically, we present a set of local approximations to the unitary cluster Jastrow wavefunction motivated by Hubbard physics. The resulting ansatz removes the need for SWAP gates and can be tailored to arbitrary qubit topologies (e.g., square, hex, heavy-hex). Our ansatz is well-suited to take advantage of continuous sets of quantum gates recently realized on superconducting devices with tunable couplers, while retaining a unique level of physical transparency and interpretability. As the capabilities of quantum computing devices continue to progress, we expect that the local cluster Jastrow ansatz to be a natural choice to encode both statically and dynamically correlated electronic wavefunctions.