Parallelized Givens Ansatz for Molecular ground-states: Bridging Accuracy and Efficiency on NISQ Platforms

TL;DR

This work tackles the challenge of accurate quantum chemistry on near-term quantum hardware by introducing Parallelized Givens Singles and Doubles (PGSD), a low-depth, symmetry-preserving VQE ansatz built from commuting Givens rotation gates. It pairs PGSD with a systematic active-space selection based on CCSD amplitudes to capture the majority of correlation energy while keeping circuit depth manageable. In noiseless simulations, PGSD achieves energies close to UCCSD and CASCI benchmarks across H2O, N2, and O2, while in noisy simulations it significantly outperforms UCCSD in energy accuracy due to reduced gate counts and depth. The approach demonstrates practical potential for quantum chemistry on current devices and lays groundwork for further enhancements such as higher-order excitations and vibrational structure calculations.

Abstract

In recent years, the Variational Quantum Eigensolver (VQE) has emerged as one of the most popular algorithms for solving the electronic structure problem on near-term quantum computers. The utility of VQE is often hindered by the limitations of current quantum hardware, including short qubit coherence times and low gate fidelities. These limitations become particularly pronounced when VQE is used along with deep quantum circuits, such as those required by the "Unitary Coupled Cluster Singles and Doubles" (UCCSD) ansatz, often resulting in significant errors. To address these issues, we propose a low-depth ansatz based on parallelized Givens rotations, which can recover substantial correlation energy while drastically reducing circuit depth and two-qubit gate counts for an arbitrary active space (AS). Also, considering the current hardware architectures with low qubit counts, we introduce a systematic way to select molecular orbitals to define active spaces (ASs) that retain significant electron correlation. We validate our approach by computing bond dissociation profiles of water and strongly correlated systems, such as molecular nitrogen and oxygen, across various ASs. Noiseless simulations using the new ansatz yield ground-state energies comparable to those from the UCCSD ansatz while reducing circuit depth by 50-70%. Moreover, in noisy simulations, our approach achieves energy error rates an order of magnitude lower than that of UCCSD. Considering the efficiency and practical usage of our ansatz, we hope that it becomes a potential choice for performing quantum chemistry calculations on near-term quantum devices.

Figures (7)

• Figure 1: Four-qubit Givens circuits representing the ground-state of a fermionic system with two MOs and two electrons. A circuit with (a) Pauli-X and single excitation gates ($U_{SE}$) representing the wavefunction defined in Eq. \ref{['1a_main_jpca_revised:eq: Psi_S ansatz']}. (b) Pauli-X, single ($U_{SE}$) and double ($U_{DE}$) excitation gates representing the wavefunction defined in Eq. \ref{['1a_main_jpca_revised:eq: Psi_SD']}.
• Figure 2: An 8-qubit PGSD circuit designed for an AS(4e, 4o) in which commuting single and double excitation gates are applied in one layer (marked by two dashed barriers). At this level of representation, the PGSD ansatz has a depth of 12.
• Figure 3: Visualization of the MOs obtained from an RHF calculation of water using STO-6G basis at $R_{OH}=0.958~\text{\normalfont\AA}$. The text below each MO indicates the orbital index (starting from zero), the orbital energy, and the occupation number (zero for unoccupied or two for occupied).
• Figure 4: Symmetric dissociation profiles of H2O computed with (a) RHF, CCSD, FCI and CASCI methods (b) VQE using UCCSD and PGSD ansatzes at a constant H-O-H angle of $104.48 \degree$. The CASCI, AS-CCSD and VQE calculations are performed in an AS(6e, 5o), where the orbitals are chosen dynamically (as explained in the text). (c) shows the absolute deviation of Full-CCSD, AS-CCSD and CASCI relative to FCI, whereas (d) shows the absolute deviation of VQE energies computed with UCCSD and PGSD ansatzes (using Qiskit) and AS-CCSD energies (using PySCF) relative to CASCI.
• Figure 5: The energy profiles of (a) a singlet N2 (triple bond stretch) in an AS(4e, 4o) and (b) a triplet O2 (double bond stretch) in an AS(8e, 6o) computed using various electronic structure methods. The absolute energy errors of UCCSD, PGSD and AS-CCSD methods relative to CASCI for N2 and O2 are shown in (c) and (d), respectively. The orbitals in the AS were carefully chosen to include the two pairs of degenerate orbitals (see text for discussion).