Open Source Variational Quantum Eigensolver Extension of the Quantum Learning Machine (QLM) 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 qubits counts and circuit depths. Specific algorithms such as Variational Quantum Eigensolvers (VQEs) can potentially overcome such issues.Here, we introduce a novel open-source QC package, denoted OpenVQE, providing tools for using and developing chemically-inspired adaptive methods derived from Unitary Coupled Cluster (UCC). It facilitates the development and testing of VQE algorithms. It is able to use the Atos Quantum Learning Machine (QLM), a general quantum programming framework enabling to write, optimize and simulate quantum computing programs. The QLM comes with a specific, freely available and open-source module, myQLM-fermion, that provides key tools to perform QC computations on a quantum computer (fermionic second quantization tools, UCC ansatz, etc). We give an extensive introduction to myQLM-fermion. Our package, Open-VQE, largely extends the QC capabilities of the QLM by providing: (i) the functions to generate the different types of excitations beyond the commonly used UCCSD ansatz; (ii) a new implementation of the "adaptive derivative assembled pseudo-Trotter method" (ADAPT-VQE), written in simple class structure python codes.Interoperability with other major quantum programming frameworks is ensured thanks to myQLM, which allows users to easily build their own code and execute it on existing QPUs such as IBM, Google, Rigetti or Microsoft, etc. The combined OpenVQE/myQLM-fermion libraries facilitate the implementation, testing and development of variational quantum algorithms, thus helping choose the best compromise to run QC computations on present quantum computers while offering the possibility to test large molecules. We provide extensive benchmarks for several molecules associated to qubit counts ranging from 4 up to 24 where we focus our work on reaching chemical accuracy, reducing the number of circuit gates and optimizing parameters and operators between "fixed-length" UCC and ADAPT-VQE ansatze.

Nuclear shell-model simulation in digital quantum computers

“…Moreover, UCC-VQE shell-model implementations have so far relied on Hartree-Fock reference states, which may not be optimal starting points for VQEs [45,84]. Either way, it appears that ADAPT-VQE shell-model simulations overperform their UCC-VQE counterparts in terms of layers, an observation that is in line with findings in quantum chemistry [27]. We note, however, that an unbiased comparison of quantum hardware efficiency between different methods requires a one-to-one quantification of the resources in each approach, including explicitly energy measurement overheads.…”

“…A VQE uses the Rayleigh-Ritz variational principle [62,63] to calculate the ground-state of a Hamiltonian starting from an initial ansatz. Our algorithm of choice is ADAPT-VQE [27,38,40,45,64], which iteratively builds a wavefunction of the form…”

“…Quantum computing promises to circumvent limitations associated to any exponentially-scaling many-body system using the principle of superposition of qubit states [18]. In the current noisy intermediate-scale quantum (NISQ) device era [19], variational quantum eigensolvers (VQE) [20,21] are among the most successful algorithms [22] exploiting the benefits of quantum computing to deal with complex many-body problems in physics [23,24] and chemistry [25][26][27]. VQEs encode a trial many-body wavefunction in a set of qubits, which are then measured to compute expectation values.…”