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:2610.11797

Unitary Coupled Cluster Nuclear Shielding Constants in a Quantum Linear Response Framework

Juliane Holst Fuglsbjerg, Sonia Coriani, Jacob Kongsted, Stephan P. A. Sauer

Published Oct 8, 2026• 0 citations
arXivHTMLPDF

Abstract

We present calculations of nuclear shielding constants, a key ingredient in nuclear magnetic resonance spectroscopy, within a quantum-computing-suitable framework. We employ quantum linear response (qLR) theory in combination with the unitary coupled cluster (UCC) ansatz and its orbital-optimized (oo-UCC), factorized (fUCC), and orbital-optimized factorized (oo-fUCC) variants. The methods are assessed for seven small molecules against CASCI, CASSCF, CCSD, and CCSD(T) reference calculations. The different UCC-based qLR approaches yield shielding constants in good agreement with comparable classical methods. Factorization, which is necessary for quantum-computing implementations, has only a negligible effect on the calculated shielding constants. Orbital optimization, in contrast, leads to substantial improvements, with oo-UCC and oo-fUCC showing markedly better agreement with CCSD and CCSD(T). Our results establish oo-fUCC combined with qLR as a promising approach for computing nuclear shielding constants on quantum computers.

DOI
10.48550/arxiv.2610.11797

Related papers

Orbital-Optimized Unitary Coupled Cluster for Indirect Nuclear Spin-Spin Coupling Constants within a Quantum Linear Response Framework

Juliane H. Fuglsbjerg, Peter Reinholdt, Erik Kjellgren +4 more

We present a quantum linear response (qLR) approach within an active-space framework for computing indirect nuclear spin-spin coupling constants, a key ingredient in NMR spectra predictions. The method employs the unitary coupled cluster (UCC) ansatz and its orbital-optimized variant (ooUCC), both suitable for quantum computing implementations, to evaluate spin-spin coupling constants via qLR. Test calculations on five small molecules are compared with CASCI, CASSCF, and conventional CCSD results. qLR with UCC/ooUCC yields spin-spin coupling constants comparable to classical methods. We further examine the role of orbital optimization and find that ooUCC markedly affects the computed couplings; orbital-optimized results show better agreement with CCSD. These findings indicate that orbital optimization is important for accurate NMR coupling predictions within quantum-computing-friendly correlated methods.

physics.chem-phCross-listedarXiv:2511.09730•Journal of Chemical Theory and Computation•Nov 14, 2025•1 citation

Quantum-Inspired Algorithm for the Factorized Form of Unitary Coupled Cluster Theory

Jia Chen, Hai‐Ping Cheng, James K. Freericks

The factorized form of unitary coupled cluster theory (UCC) is a promising wave-function ansatz for the variational quantum eigensolver algorithm. Here, we present a quantum-inspired classical algorithm for UCC based on an exact operator identity for the individual UCC factors. We implement this algorithm for calculations of the H 10 linear chain and the H 2 O molecule with single and double ζ basis sets to provide insights into UCC as a wave-function ansatz. We find that for weakly correlated molecules, the factorized form of the UCC provides similar accuracy to conventional coupled cluster theory (CC); for strongly correlated molecules, where CC often breaks down, UCC significantly outperforms the configuration interaction (CI) ansatz. As a result, the factorized form of the UCC is an accurate, efficient, and reliable electronic structure method in both the weakly and strongly correlated regions. This classical algorithm now allows robust benchmarking of anticipated results from quantum computers and application of coupled-cluster techniques to more strongly correlated molecules.

Journal of Chemical Theory and Computation•Jan 27, 2021•44 citations

A Quantum-Inspired Algorithm for the Factorized Form of Unitary Coupled Cluster Theory

Jia Chen, Hai‐Ping Cheng, James K. Freericks

The factorized form of unitary coupled cluster theory (UCC) is a promising wave-function ansatz for the variational quantum eigensolver algorithm. Here, we present a quantum inspired algorithm for UCC based on an exact operator identity for the individual UCC factors. We implement this algorithm for calculations of the H$_{10}$ linear chain and the H$_2$O molecule with single and double $ζ$ basis sets to provide insights about UCC as a wave-function ansatz. We find that as an electronic structure method, UCC could potentially be valuable for strongly correlated systems, for which conventional coupled cluster theory has difficulties. On quantum computers, the factorized form of UCC can also serve as an initial state preparation method for the quantum phase-estimation algorithm, since it yields higher overlap with the ground state than many other common variational ansatzes. This classical algorithm for UCC also enables widespread testing of the technique, which will be useful for benchmarking quantum computations.

arXiv:2008.06637•Aug 15, 2020•0 citations

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

Analytical Nuclear Gradients and Hessians on Quantum Hardware via Orbital-Optimized VQE with Error Mitigation

Renato Olarte Hernandez, Karl Michael Ziems, Erik Kjellgren +3 more

Nuclear gradients and Hessians are fundamental quantities in computational chemistry, essential for a wide range of applications including geometry optimization, vibrational spectroscopy, and molecular property calculations. In this work, we present their analytical implementation on quantum hardware. The methodology is formulated within an active-space framework combining orbital optimization and linear-response theory. On the quantum-computing side, the approach employs the tiled unitary product state (tUPS) ansatz to directly evaluate the tensor elements required for solving the response equations. Moreover, the expectation values are corrected using an adapted confusion-matrix error-mitigation scheme in combination with post-selection criteria. The resulting workflow is assessed on molecular hydrogen and on water through the calculation of potential energy surfaces, nuclear gradients, Hessians, and vibrational frequencies, enabling the evaluation of both its capabilities and current limitations. The results demonstrate good performance for the hydrogen molecule, whereas the water molecule provides a more demanding test of quantum-hardware resources and highlights the trade-offs associated with error-mitigation strategies. The quantified analysis of the results identify the main sources of errors, suggesting improvement directions for more accurate quantum computer applications.

physics.chem-phCross-listedarXiv:2608.08758•Aug 11, 2026•0 citations

Low-Depth Unitary Coupled Cluster Theory for Quantum Computation

Jia Chen, Hai‐Ping Cheng, James K. Freericks

The unitary coupled cluster (UCC) approximation is one of the more promising wave function ansätzes for electronic structure calculations on quantum computers via the variational quantum eigensolver algorithm. However, for large systems with many orbitals, the required number of UCC factors still leads to very deep quantum circuits, which can be challenging to implement. Based on the observation that most UCC amplitudes are small for both weakly correlated and strongly correlated molecules, we devise an algorithm that employs a Taylor expansion in the small amplitudes, trading off circuit depth for extra measurements. Strong correlations can be taken into account by performing the expansion about a small set of UCC factors, which are treated exactly. Near equilibrium, the Taylor series expansion often works well without the need to include any exact factors; as the molecule is stretched and correlations increase, we find only a small number of factors need to be treated exactly.

arXiv:2109.14134•Journal of Chemical Theory and Computation•Mar 22, 2022•7 citations
We present calculations of nuclear shielding constants, a key ingredient in nuclear magnetic resonance spectroscopy, within a quantum-computing-suitable framework. We employ quantum linear response (qLR) theory in combination with the unitary coupled cluster (UCC) ansatz and its orbital-optimized (oo-UCC), factorized (fUCC), and orbital-optimized factorized (oo-fUCC) variants. The methods are assessed for seven small molecules against CASCI, CASSCF, CCSD, and CCSD(T) reference calculations. The different UCC-based qLR approaches yield shielding constants in good agreement with comparable classical methods. Factorization, which is necessary for quantum-computing implementations, has only a negligible effect on the calculated shielding constants. Orbital optimization, in contrast, leads to substantial improvements, with oo-UCC and oo-fUCC showing markedly better agreement with CCSD and CCSD(T). Our results establish oo-fUCC combined with qLR as a promising approach for computing nuclear shielding constants on quantum computers.
We present a quantum linear response (qLR) approach within an active-space framework for computing indirect nuclear spin-spin coupling constants, a key ingredient in NMR spectra predictions. The method employs the unitary coupled cluster (UCC) ansatz and its orbital-optimized variant (ooUCC), both suitable for quantum computing implementations, to evaluate spin-spin coupling constants via qLR. Test calculations on five small molecules are compared with CASCI, CASSCF, and conventional CCSD results. qLR with UCC/ooUCC yields spin-spin coupling constants comparable to classical methods. We further examine the role of orbital optimization and find that ooUCC markedly affects the computed couplings; orbital-optimized results show better agreement with CCSD. These findings indicate that orbital optimization is important for accurate NMR coupling predictions within quantum-computing-friendly correlated methods.
The factorized form of unitary coupled cluster theory (UCC) is a promising wave-function ansatz for the variational quantum eigensolver algorithm. Here, we present a quantum-inspired classical algorithm for UCC based on an exact operator identity for the individual UCC factors. We implement this algorithm for calculations of the H 10 linear chain and the H 2 O molecule with single and double ζ basis sets to provide insights into UCC as a wave-function ansatz. We find that for weakly correlated molecules, the factorized form of the UCC provides similar accuracy to conventional coupled cluster theory (CC); for strongly correlated molecules, where CC often breaks down, UCC significantly outperforms the configuration interaction (CI) ansatz. As a result, the factorized form of the UCC is an accurate, efficient, and reliable electronic structure method in both the weakly and strongly correlated regions. This classical algorithm now allows robust benchmarking of anticipated results from quantum computers and application of coupled-cluster techniques to more strongly correlated molecules.
The factorized form of unitary coupled cluster theory (UCC) is a promising wave-function ansatz for the variational quantum eigensolver algorithm. Here, we present a quantum inspired algorithm for UCC based on an exact operator identity for the individual UCC factors. We implement this algorithm for calculations of the H10_{10}10​ linear chain and the H2_22​O molecule with single and double ζζζ basis sets to provide insights about UCC as a wave-function ansatz. We find that as an electronic structure method, UCC could potentially be valuable for strongly correlated systems, for which conventional coupled cluster theory has difficulties. On quantum computers, the factorized form of UCC can also serve as an initial state preparation method for the quantum phase-estimation algorithm, since it yields higher overlap with the ground state than many other common variational ansatzes. This classical algorithm for UCC also enables widespread testing of the technique, which will be useful for benchmarking quantum computations.
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.
Nuclear gradients and Hessians are fundamental quantities in computational chemistry, essential for a wide range of applications including geometry optimization, vibrational spectroscopy, and molecular property calculations. In this work, we present their analytical implementation on quantum hardware. The methodology is formulated within an active-space framework combining orbital optimization and linear-response theory. On the quantum-computing side, the approach employs the tiled unitary product state (tUPS) ansatz to directly evaluate the tensor elements required for solving the response equations. Moreover, the expectation values are corrected using an adapted confusion-matrix error-mitigation scheme in combination with post-selection criteria. The resulting workflow is assessed on molecular hydrogen and on water through the calculation of potential energy surfaces, nuclear gradients, Hessians, and vibrational frequencies, enabling the evaluation of both its capabilities and current limitations. The results demonstrate good performance for the hydrogen molecule, whereas the water molecule provides a more demanding test of quantum-hardware resources and highlights the trade-offs associated with error-mitigation strategies. The quantified analysis of the results identify the main sources of errors, suggesting improvement directions for more accurate quantum computer applications.
The unitary coupled cluster (UCC) approximation is one of the more promising wave function ansätzes for electronic structure calculations on quantum computers via the variational quantum eigensolver algorithm. However, for large systems with many orbitals, the required number of UCC factors still leads to very deep quantum circuits, which can be challenging to implement. Based on the observation that most UCC amplitudes are small for both weakly correlated and strongly correlated molecules, we devise an algorithm that employs a Taylor expansion in the small amplitudes, trading off circuit depth for extra measurements. Strong correlations can be taken into account by performing the expansion about a small set of UCC factors, which are treated exactly. Near equilibrium, the Taylor series expansion often works well without the need to include any exact factors; as the molecule is stretched and correlations increase, we find only a small number of factors need to be treated exactly.