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Results for “unitary coupled cluster theory”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Toward the “platinum standard” of quantum chemistry on quantum computers: Perturbative quadruple corrections in unitary coupled cluster theory

We propose a non-iterative, post-hoc correction to the unitary coupled cluster theory with the single, double, and triple excitations (UCCSDT) Ansatz, which considers the leading-order effects of neglected quadruple excitations. We present two ways to derive this correction, henceforth referred to as [Q-6], which leads to an improvement in the correlation energy shown to be truncated to sixth-order in many-body perturbation theory. Furthermore, a comparison between the UCC-based [Q-6] correction proposed in this work and analogous, “platinum standard” quadruple corrections proposed in conventional coupled cluster theory recognizes that [Q-6] is distinct from prior corrections since it is constructed entirely from internally connected components. Although trotterized (t) and full operator variants of UCCSDT exhibit errors in scans of small molecule potential energy surfaces that routinely exceed 1.6 mH, we find that t/UCCSDT[Q-6] is, nevertheless, able to achieve chemical accuracy as measured by the mean unsigned error.

Correlation energy↗
DOE OSTI2026

Analysis of Fourth-, Fifth-, and Infinite-Order Triple Excitations in Unitary Coupled Cluster Theory

Here, in this work, we introduce a perturbative correction to the unitary coupled cluster method with single and double excitations (UCCSD) that incorporates the effects of missing triple excitations through fifth-order in many-body perturbation theory (MBPT). Referred to as UCCSD[T-5], this method is benchmarked alongside the previously developed UCCSD[T] to lend insight into the behavior of perturbative triples corrections relative to UCCSDT, which inherently provides an infinite-order treatment of triple excitations, as well as full configuration interaction (FCI). Two key findings emerge from this analysis. First, UCCSD[T] consistently yields ground-state energies in closest agreement with FCI, outperforming both UCCSD[T-5] and UCCSDT. Second, UCCSD[T-5] largely emulates the behavior of UCCSDT, suggesting a close relationship between fifth- and infinite-order triple-excitation contributions. Given the growing interest in UCC ansätze for quantum computing and the limitations of current quantum hardware, these results highlight the potential of classically computed perturbative corrections within UCC theory to capture triple-excitation effects without the additional quantum resources required by the UCCSDT ansatz.

Windom, Zachary W. [Oak Ridge National Laboratory ↗
DOE OSTI2022

AGP-based unitary coupled cluster theory for quantum computers

Electronic structure methods typically benefit from symmetry breaking and restoration, specially in the strong correlation regime. Here, the same goes for ansätze on a quantum computer. We develop a unitary coupled cluster method based on the antisymmetrized geminal power (AGP)—a state formally equivalent to the number-projected Bardeen–Cooper–Schrieffer wavefunction. We demonstrate our method for the single-band Fermi–Hubbard Hamiltonian in one and two dimensions. We also explore post-selection as a state preparation step to obtain correlated AGP and prove that it scales no worse than O(√M) in the number of measurements, thereby making it a less expensive alternative to gauge integration to restore particle number symmetry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

A new “gold standard”: Perturbative triples corrections in unitary coupled cluster theory and prospects for quantum computing

A major difficulty in quantum simulation is the adequate treatment of a large collection of entangled particles, synonymous with electron correlation in electronic structure theory, with coupled cluster (CC) theory being the leading framework for dealing with this problem. Augmenting computationally affordable low-rank approximations in CC theory with a perturbative account of higher-rank excitations is a tractable and effective way of accounting for the missing electron correlation in those approximations. This is perhaps best exemplified by the “gold standard” CCSD(T) method, which bolsters the baseline CCSD with the effects of triple excitations using considerations from many-body perturbation theory (MBPT). Despite this established success, such a synergy between MBPT and the unitary analog of CC theory (UCC) has not been explored. In this work, we propose a similar approach wherein converged UCCSD amplitudes are leveraged to evaluate energy corrections associated with triple excitations, leading to the UCCSD[T] method. In terms of quantum computing, this correction represents an entirely classical post-processing step that improves the energy estimate by accounting for triple excitation effects without necessitating new quantum algorithm developments or increasing demand for quantum resources. The rationale behind this choice is shown to be rigorous by studying the properties of finite-order UCC energy functionals, and our efforts do not support the addition of the fifth-order contributions as in the (T) correction. We assess the performance of these approaches on a collection of small molecules and demonstrate the benefits of harnessing the inherent synergy between MBPT and UCC theories.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

An Attractive Way to Correct for Missing Singles Excitations in Unitary Coupled Cluster Doubles Theory

Coupled cluster methods based exclusively on double excitations are comparatively “cheap” and interesting model chemistries, as they are typically able to capture the bulk of the dynamic electron correlation effects. The trade-off in such approximations is that the effect of neglected excitations, particularly single excitations, can be considerable. Using standard and electron-pair-restricted T 2 operators to define two flavors of unitary coupled cluster doubles (UCCD) methods, we investigate the extent to which missing single excitations can be recovered from low-order corrections in many-body perturbation theory (MBPT) within the unitary coupled cluster (UCC) formalism. Here, our analysis includes the derivations of finite-order UCC energy functionals, which are used as a basis to define perturbative estimates of missed single excitations. This leads to the novel UCCD[4S] and UCCD[6S] methods, which consider energy corrections for missing single excitations through fourth- and sixth-order in MBPT, respectively. We also apply the same methodology to the electron-pair-restricted ansatz, but the improvements are only marginal. Our findings show that augmenting UCCD with these post hoc perturbative corrections can lead to UCCSD-quality results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Unitary coupled-cluster based self-consistent polarization propagator theory: A quadratic unitary coupled-cluster singles and doubles scheme

The development of a quadratic unitary coupled-cluster singles and doubles (qUCCSD) based self-consistent polarization propagator method is reported here. We present a simple strategy for truncating the commutator expansion of the unitary version of coupled-cluster transformed Hamiltonian $\bar{H}$. The qUCCSD method for the electronic ground state includes up to double commutators for the amplitude equations and up to cubic commutators for the energy expression. The qUCCSD excited-state eigenvalue equations include up to double commutators for the singles–singles block of $\bar{H}$, single commutators for the singles–doubles and doubles–singles blocks, and the bare Hamiltonian for the doubles–doubles block. Benchmark qUCCSD calculations of the ground-state properties and excitation energies for representative molecules demonstrate significant improvement of the accuracy and robustness over the previous UCC3 scheme derived using Møller–Plesset perturbation theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Equation-of-motion internally contracted multireference unitary coupled-cluster theory

The accurate computation of excited states remains a challenge in electronic structure theory, especially for systems with a ground state that requires a multireference treatment. In this work, we introduce a novel equation-of-motion (EOM) extension of the internally contracted multireference unitary coupled-cluster framework (ic-MRUCC), termed EOM-ic-MRUCC. EOM-ic-MRUCC follows the transform-then-diagonalize approach, in analogy to its non-unitary counterpart. By employing a projective approach to optimize the ground state, the method retains additive separability and proper scaling with system size. We show that excitation energies are size-intensive if the EOM operator satisfies the “killer” and the projective conditions. Furthermore, we propose to represent changes in the reference state upon electron excitation via projected many-body operators that span the active orbitals and show that the EOM equations formulated in this way are invariant with respect to active orbital rotations. We test the EOM-ic-MRUCC method truncated to single and double excitations by computing the potential energy curves for several excited states of a BeH2 model system, the HF molecule, and water undergoing symmetric dissociation. Across these systems, our method delivers accurate excitation energies and potential energy curves within 5 mE h (∼0.14 eV) from full configuration interaction. Here, we find that truncating the Baker–Campbell–Hausdorff series to fourfold commutators contributes negligible errors (on the order of 10 −5 E h or less), offering a practical route to highly accurate excited-state calculations with reduced computational overhead.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRSDate not supplied

Efficient Implementation for Unitary Coupled Cluster State Preparation for Near-Term Quantum Computers

Unitary coupled cluster theory (UCC) is a common wave function ansatz for quantum simulation of molecular electronic structure using the variational quantum eigenvalue solver (VQE). Even for small molecules using a double-ζ basis, the number of variational parameters required to minimize the electronic energy (i.e., optimize the circuit) is large and beyond the reach of current quantum computers. For example, a circuit simulating C2 using the UCCSD ansatz and the cc-pVDZ basis set with frozen-core will require over 10,000 variational parameters and a Hilbert space of over 10^(8) determinants. To make progress on simulating such molecular systems on near-term quantum computers, we explore how much of the optimization can be approximately prepared with classical simulation while reducing the number of optimization steps performed on a quantum device. Recently, Chen, Cheng, and Freericks [J. Chem. Theory Comput. 2021, 17, 841-847] presented an algorithm for the factorized form of the UCC ansatz that allows for efficient UCC optimizations on classical hardware. We flip the algorithm around and use it to prepare approximate quantum circuits for systems that require a large number of qubits to represent. We will present results from our implementation and discuss strategies for incorporating this implementation for algorithms involving near-term quantum computers.

Quantum Computing↗
NASA NTRSDate not supplied

Efficient Implementation for Unitary Coupled Cluster State Preparation for Near-Term Quantum Computers

Unitary coupled cluster theory (UCC) is a common wave function ansatz for quantum simulation of molecular electronic structure using the variational quantum eigenvalue solver (VQE). Even for small molecules using a double-ζ basis, the number of variational parameters required to minimize the electronic energy (i.e., optimize the circuit) is large and beyond the reach of current quantum computers. For example, a circuit simulating C2 using the UCCSD ansatz and the cc-pVDZ basis set with frozen-core will require over 10,000 variational parameters and a Hilbert space of over 10^(8) determinants. To make progress on simulating such molecular systems on near-term quantum computers, we explore how much of the optimization can be approximately prepared with classical simulation while reducing the number of optimization steps performed on a quantum device. Recently, Chen, Cheng, and Freericks [J. Chem. Theory Comput. 2021, 17, 841-847] presented an algorithm for the factorized form of the UCC ansatz that allows for efficient UCC optimizations on classical hardware. We flip the algorithm around and use it to prepare approximate quantum circuits for systems that require a large number of qubits to represent. We will present results from our implementation and discuss strategies for incorporating this implementation for algorithms involving near-term quantum computers.

Quantum Computing↗
DOE OSTI2026

Toward scalable quantum computations of atomic nuclei

We solve the nuclear two-body and three-body bound states via quantum simulations of pionless effective field theory on a lattice in position space. While the employed lattice remains small, the usage of local Hamiltonians including two- and three-body forces ensures that the number of Pauli terms scales linearly with increasing numbers of lattice sites. We use an adaptive ansatz grown from unitary coupled cluster theory to parametrize the ground states of the deuteron and 3 He, compute their corresponding energies, and analyze the scaling of the required computational resources. Our quantum simulations reproduce exact benchmarks for 2 H and 3 He within 100 keV, requiring at most 30 layers in the ansatz and thus resulting in modest circuit depths. Additionally, we find the number of shots required to reach a given precision scales linearly in the lattice size and more mildly in the system size. Furthermore, based on the agreement with exact benchmarks and mild scaling, we conclude that this can be an efficient, scalable approach for quantum computations of nuclear ground states, particularly to prepare initial states for quantum phase estimation or other filtering algorithms.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Numerical simulations of noisy quantum circuits for computational chemistry

The opportunities afforded by near-term quantum computers to calculate the ground-state properties of small molecules depend on the structure of the computational ansatz as well as the errors induced by device noise. Here we investigate the behavior of these noisy quantum circuits using numerical simulations to estimate the accuracy and fidelity of the prepared quantum states relative to the ground truth obtained by conventional means. We implement several different types of ansatz circuits derived from unitary coupled cluster theory for the purposes of estimating the ground-state energy of sodium hydride using the variational quantum eigensolver algorithm. We show how relative error in the energy and the fidelity scale with the levels of gate-based noise, the internuclear configuration, the ansatz circuit depth, and the parameter optimization methods.

36 MATERIALS SCIENCE↗
NASA NTRSDate not supplied

Efficient Implementation for Unitary Coupled Cluster State Preparation for Near-Term Quantum Computers

Unitary coupled cluster theory (UCC) is a common wave function ansatz for quantum simulation of molecular electronic structure using the variational quantum eigenvalue solver (VQE). Even for small molecules using a double-ζ basis, the number of variational parameters required to minimize the electronic energy (i.e., optimize the circuit) is large and beyond the reach of current quantum computers. For example, a circuit simulating C2 using the UCCSD ansatz and the cc-pVDZ basis set with frozen-core will require over 10,000 variational parameters and a Hilbert space of over 10^8 determinants. To make progress on simulating such molecular systems on near-term quantum computers, we explore how much of the optimization can be approximately prepared with classical simulation while reducing the number of optimization steps performed on a quantum device. Recently, Chen, Cheng, and Freericks [J. Chem. Theory Comput. 2021, 17, 841-847] presented an algorithm for the factorized form of the UCC ansatz that allows for efficient UCC optimizations on classical hardware. We flip the algorithm around and use it to prepare approximate quantum circuits for systems that require a large number of qubits to represent. We will present results from our implementation and discuss strategies for incorporating this implementation for algorithms involving near-term quantum computers.

J Wayne Mullinax↗
DOE OSTI2025

Qubit-Efficient Quantum Chemistry with the ADAPT Variational Quantum Eigensolver and Double Unitary Downfolding

Here, in this work, we combine the recently developed double unitary coupled cluster (DUCC) theory with the adaptive, problem-tailored variational quantum eigensolver (ADAPT-VQE) to explore the accuracy of unitary downfolded Hamiltonians for quantum simulation of chemistry. We benchmark the ability of DUCC effective Hamiltonians to recover dynamical correlation energy outside of an active space. We consider the effects of strong correlation, commutator truncation, higher-body terms, and approximate external amplitudes on the accuracy of these effective Hamiltonians. When combining these DUCC Hamiltonians with ADAPT-VQE, we observe similar convergence of the ground state as compared with bare active space Hamiltonians, demonstrating that DUCC Hamiltonians provide increased accuracy without increasing the load on the quantum processor.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Classical Preoptimization Approach for ADAPT-VQE: Maximizing the Potential of High-Performance Computing Resources to Improve Quantum Simulation of Chemical Applications

The ADAPT-VQE algorithm is a promising method for generating a compact ansatz based on derivatives of the underlying cost function, and it yields accurate predictions of electronic energies for molecules. In this work, we report the implementation and performance of ADAPT-VQE with our recently developed sparse wave function circuit solver (SWCS) in terms of accuracy and efficiency for molecular systems with up to 52 spin orbitals. The SWCS can be tuned to balance computational cost and accuracy, which extends the application of ADAPT-VQE for molecular electronic structure calculations to larger basis sets and a larger number of qubits. Using this tunable feature of the SWCS, we propose an alternative optimization procedure for ADAPT-VQE to reduce the computational cost of the optimization. Furthermore, by preoptimizing a quantum simulation with a parametrized ansatz generated with ADAPT-VQE/SWCS, we aim to utilize the power of classical high-performance computing in order to minimize the work required on noisy intermediate-scale quantum hardware, which offers a promising path toward demonstrating quantum advantage for chemical applications.

ADAPT-VQE↗
NASA NTRSDate not supplied

Incorporating ADAPT-VQE with a Sparse Wavefunction Circuit Simulator to Find Compact Quantum Circuits for Chemical Applications

We implemented the ADAPT-VQE algorithm into our recent classical sparse wavefunction circuit simulator to demonstrate that classical resources can (1) efficiently find a physically motivated compact wavefunction ansatz for further refinement on near-term quantum hardware and (2) benchmark expected results of VQE-based algorithms once the quantum hardware is available to study large-scale applications. In particular, we study the role of the ADAPT-VQE operator pool, molecular basis set selection, and variations such as TETRIS-ADAPT-VQE on the performance of our classical circuit simulator. This work demonstrates the promise of using classical resources to generate highly accurate wavefunctions that can be prepared on quantum hardware to initiate other quantum algorithms such as phase estimation. Our approach harnesses the power of high-performance computing resources with the more limited available quantum computers to map a path toward quantum advantage for electronic structure calculations in chemistry and materials science.

Quantum Computing↗
DOE OSTI2025

Closed-form expressions for unitaries of spin-adapted fermionic operators

One of the open challenges in quantum computing simulations of problems of chemical interest is the proper enforcement of spin symmetry. Efficient quantum circuits implementing unitaries generated by spin-adapted operators remain elusive, while naïve Trotterization schemes break spin symmetry. Here, in this work, we analyze the mathematical structure of spin-adapted operators and derive closed-form expressions for unitaries generated by singlet spin-adapted generalised single and double excitations. These results represent significant progress toward the economical enforcement of spin symmetry in quantum simulations.

fermionic algebra↗
DOE OSTI2022

Quadratic Unitary Coupled-Cluster Singles and Doubles Scheme: Efficient Implementation, Benchmark Study, and Formulation of an Extended Version

An efficient implementation of the quadratic unitary coupled-cluster singles and doubles (qUCCSD) scheme for calculations of electronic ground and excited states using an unrestricted molecular spin–orbital formulation and an efficient tensor contraction library is reported. The accuracy of the qUCCSD scheme and the efficiency of the present implementation are demonstrated using extensive benchmark calculations of excitation energies and an application to S o → S 1 vertical excitation energies for cis- and trans-4a,4b-dihydrotriphenylene. The qUCCSD scheme has been shown to provide improved excitation energies compared with the UCC3 scheme formulated based on perturbation theory. Here, a UCC truncation scheme that can provide excitation energies correct through the fourth order is also presented to further improve the accuracy of the qUCCSD scheme.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗