Open source variational quantum eigensolver extension of the quantum learning machine for quantum chemistry

Abstract

Quantum chemistry (QC) is one of the most promising applications of quantum computing. However, present quantum processing units (QPUs) are still subject to large errors. Therefore, noisy intermediate-scale quantum (NISQ) hardware is limited in terms of qubit counts/circuit depths. Variational quantum eigensolver (VQE) algorithms can potentially overcome such issues. Here, we introduce the OpenVQE open-source QC package. It provides tools for using and developing chemically-inspired adaptive methods derived from unitary coupled cluster (UCC). It facilitates the development and testing of VQE algorithms and is able to use the Atos Quantum Learning Machine (QLM), a general quantum programming framework enabling to write/optimize/simulate quantum computing programs. We present a specific, freely available QLM open-source module, myQLM-fermion. We review its key tools for facilitating QC computations (fermionic second quantization, fermion-spin transforms, etc.). OpenVQE largely extends the QLM's QC capabilities by providing:(i) the functions to generate the different types of excitations beyond the commonly used UCCSD ansatz; (ii) a new Python implementation of the "adaptive derivative assembled pseudo-Trotter method" (ADAPT-VQE). Interoperability with other major quantum programming frameworks is ensured thanks to the myQLM-interop package, which allows users to build their own code and easily execute it on existing QPUs. The combined OpenVQE/myQLM-fermion libraries facilitate the implementation, testing and development of variational quantum algorithms, while offering access to large molecules as the noiseless Schrödinger-style dense simulator can reach up to 41 qubits for any circuit.Extensive benchmarks are provided for molecules associated to qubit counts

Extension of the Trotterized Unitary Coupled Cluster to Triple Excitations

“…In the multiqubit register, we assign each qubit to a spin–orbital, thus LiH (BeH 2 and H 2 O) is (are) represented by 12 (14) qubits. We used the Quantum Learning Machine (QLM) simulator that is able to simulate up to 40 qubits (with large memory), and we used the noiseless simulation mode (i.e., such an ideal simulator mimics the behavior of performing the experiment with an infinite number of shots) in order to minimize computational run time and memory demands. First, we tested the two methods on the LiH molecule at two bond lengths: R = 1.0 Å and R = 3.0 Å.…”

“…As mentioned in the literature, ,,,, testing the Trotterization effect in the UCC ansatz is important since, as seen in equation , using t > 1 might in principle, decreases the Trotterization error. Besides the Trotterization study, a different method called the disentangled UCC ansatz has been introduced, and in ref the ordering of operators in this ansatz has been discussed.…”

“…The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpca.3c01753. Detailed sketch algorithm that describe the triple excitations within spin and point group symmetries is presented and coded in our openVQE package, 50 convergence study of LiH, data related to the computed total energies for sym-UCCSD and sym-UCCSDT found in Tables S1−S4, comparison of errors between sym-UCCSDT, CCSD(T) and CCSDT-full, and CCSD, CCSD(T) and CCSDT-full total energies (PDF)…”

“…The essential tools needed to perform the VQE process (such as Fermionic second quantization of Ĥ eq , Fermion-qubit transforms using Jordan–Wigner representation, Trotterization, etc.) are implemented in the myQLM-Fermion package. , We use the UCC family module from our OpenVQE package , to implement UCCSDT excitations (eqs –). We also used the PySCF package to evaluate the molecular orbital integrals h pq and h pqrs which are given in eq .…”

“…are implemented in the myQLM-Fermion package. 48,49 We use the UCC family module from our OpenVQE package 49,50 to implement UCCSDT excitations (eqs 4−6). We also used the PySCF package 51 to evaluate the molecular orbital integrals h pq and h pqrs which are given in eq 1.…”