Abstract The fragment molecular orbital (FMO) scheme is one of the popular fragmentation‐based methods and has the potential advantage of making the circuit shallow for quantum chemical calculations on quantum computers. In this study, we used a GPU‐accelerated quantum simulator (cuQuantum) to perform the electron correlation part of the FMO calculation as unitary coupled‐cluster singles and doubles (UCCSD) with the variational quantum eigensolver (VQE) for hydrogen‐bonded (FH) and (FH)‐HO systems with the STO‐3G basis set. VQE‐UCCSD calculations were performed using both canonical and localized MO sets, and the results were examined from the point of view of size‐consistency and orbital‐invariance affected by the Trotter error. It was found that the use of localized MO leads to better results, especially for (FH)‐HO. The GPU acceleration was substantial for the simulations with larger numbers of qubits, and was about a factor of 6.7–7.7 for 18 qubit systems.
Abstract The fragment molecular orbital (FMO) scheme is one of the popular fragmentation‐based methods and has the potential advantage of making the circuit shallow for quantum chemical calculations on quantum computers. In this study, we used a GPU‐accelerated quantum simulator (cuQuantum) to perform the electron correlation part of the FMO calculation as unitary coupled‐cluster singles and doubles (UCCSD) with the variational quantum eigensolver (VQE) for hydrogen‐bonded (FH) and (FH)‐HO systems with the STO‐3G basis set. VQE‐UCCSD calculations were performed using both canonical and localized MO sets, and the results were examined from the point of view of size‐consistency and orbital‐invariance affected by the Trotter error. It was found that the use of localized MO leads to better results, especially for (FH)‐HO. The GPU acceleration was substantial for the simulations with larger numbers of qubits, and was about a factor of 6.7–7.7 for 18 qubit systems.
Abstract The fragmentation-based method has attracted interest as a way to reduce the computational cost of quantum chemical computations. Using the variational quantum eigensolver (VQE) of unitary coupled cluster singles and doubles (UCCSD), concurrent processing was used alongside the fragment molecular orbital scheme for the Li(I)–(H₂)n (n = 4 and 6) clusters on a supercomputer with a graphical processing unit (GPU)-accelerated quantum simulator. Energy and timing data of VQE-UCCSD are presented to highlight issues in practical applications.
Quantum computers offer significant potential for complex system analysis, yet their application in large systems is hindered by limitations such as qubit availability and quantum hardware noise. While the variational quantum eigensolver (VQE) was proposed to address these issues, its scalability remains limited. Many efforts, including new ansätze and Hamiltonian modifications, have been made to overcome these challenges. In this work, we introduced the novel Fragment Molecular Orbital/Variational Quantum Eigensolver (FMO/VQE) algorithm. This method combines the fragment molecular orbital (FMO) approach with VQE and efficiently utilizes qubits for quantum chemistry simulations. Employing the UCCSD ansatz, the FMO/VQE achieved an absolute error of just 0.053 mHa with 8 qubits in a [Formula: see text] system using the STO-3G basis set, and an error of 1.376 mHa with 16 qubits in a [Formula: see text] system with the 6-31G basis set. These results indicated a significant advancement in scalability over conventional VQE, maintaining accuracy with fewer qubits. Therefore, our FMO/VQE method exemplifies how integrating fragment-based quantum chemistry with quantum algorithms can enhance scalability, facilitating more complex molecular simulations and aligning with quantum computing advancements.
We present the quantum effective fragment molecular orbital (Q-EFMO) method, a hybrid framework that evaluates selected molecular-fragment correlation energies with the variational quantum eigensolver and assembles them through the size-consistent EFMO energy expression. A Hartree-Fock EFMO calculation supplies monomer references, many-body polarization, and distant-pair EFP interactions; independent VQE/UCCSD calculations provide correlation increments for monomers and selected near-field dimers. Consequently, the maximum quantum register is determined by the largest active fragment or fragment pair rather than by total system size. For a three-layer LiH benchmark in STO-3G, a full 2.5 to 3.5 Angstrom separation scan shows that two orbital-reduction schemes approach the full CCSD reference monotonically. The more aggressive scheme remains below 1 kcal/mol for separations of 2.6 Angstrom and greater and reaches 0.10 kcal/mol at 3.5 Angstrom, using 6 qubits for monomers and 12 for the largest dimers, compared with 14 qubits for the frozen-core dimer baseline. An implementation-specific cost proxy decreases from 1000 to 40, a factor of 25. These noise-free results establish the equations, software path, and resource scaling; broader chemical validation, larger bases, and hardware tests remain necessary.
Abstract Materials simulations involving strongly correlated electrons pose fundamental challenges to state‐of‐the‐art electronic structure methods but are hypothesized to be the ideal use case for quantum computing algorithms. To date, no quantum computer has simulated a molecule of a size and complexity relevant to real‐world applications, despite the fact that the variational quantum eigensolver (VQE) algorithm can predict chemically accurate total energies. Nevertheless, because of the many applications of moderately sized, strongly correlated systems, such as molecular catalysts, the successful use of the VQE stands as an important waypoint in the advancement toward useful chemical modeling on near‐term quantum processors. In this paper, we take a significant step in this direction. We lay out the steps, write, and run parallel code for an (emulated) quantum computer to compute the bond dissociation curves of the TiH, LiH, NaH, and KH diatomic hydride molecules using the VQE. TiH was chosen as a relatively simple chemical system that incorporates d orbitals and strong electron correlation. Because current VQE implementations on existing quantum hardware are limited by qubit error rates, the number of qubits available, and the allowable gate depth, recent studies using it have focused on chemical systems involving s and p block elements. Through VQE + UCCSD calculations of TiH, we evaluate the near‐term feasibility of modeling a molecule with d‐orbitals on real quantum hardware. We demonstrate that the inclusion of d‐orbitals and the use of the UCCSD ansatz, which are both necessary to capture the correct TiH physics, dramatically increase the cost of this problem. We estimate the approximate error rates necessary to model TiH on current quantum computing hardware using VQE + UCCSD and show them to likely be prohibitive until significant improvements in hardware and error correction algorithms are available.
Electronic structure calculations of atoms and molecules are considered to be a promising application for quantum computers. Two key algorithms, the quantum phase estimation (QPE) and the variational quantum eigensolver (VQE), have been extensively studied. The condition that the energy of a dimer consisting of two monomers separated by a large distance should be equal to twice the energy of a monomer, known as size consistency, is essential in quantum chemical calculations. Recently, we reported that the size consistency condition can be violated by Trotterization in the unitary coupled cluster singles and doubles ansatz in the VQE when employing molecular orbitals delocalized to the dimer [Sugisaki et al., J. Comput. Chem. 45, 2204 (2024)]. It is well known that the full configuration interaction (full-CI) energy is invariant to arbitrary rotations of molecular orbitals, and therefore, the QPE-based full-CI should theoretically satisfy the size consistency. However, Trotterization of the time evolution operator can break the size consistency conditions. In this work, we investigated whether size consistency can be maintained with Trotterization of the time evolution operator in QPE-based full-CI calculations. Our numerical simulations revealed that size consistency in the QPE-based full-CI is not automatically violated by using molecular orbitals delocalized to the dimer, but employing an appropriate Trotter decomposition condition is crucial to maintain size consistency. We also report on the acceleration of QPE simulations through the sequential addition of ancillary qubits.
The Trotterized Unitary Coupled Cluster Single and Double (UCCSD) ansatz has recently attracted interest due to its use in Variation Quantum Eigensolver (VQE) molecular simulations on quantum computers. However, when the size of molecules increases, UCCSD becomes less interesting as it cannot achieve sufficient accuracy. Including higher-order excitations is therefore mandatory to recover the UCC's missing correlation effects. In this Letter, we extend the Trotterized UCC approach via the addition of (true) Triple T excitations introducing UCCSDT. We also include both spin and orbital symmetries. Indeed, in practice, these later help to reduce unnecessarily circuit excitations and thus accelerate the optimization process enabling to tackle larger molecules. Our initial numerical tests (12-14 qubits) show that UCCSDT improves the overall accuracy by at least two-orders of magnitudes with respect to standard UCCSD. Overall, the UCCSDT ansatz is shown to reach chemical accuracy and to be competitive with the CCSD(T) gold-standard classical method of quantum chemistry.