Classical reservoir approach for efficient molecular ground state preparation

TL;DR

The paper introduces a quantum-native, hardware-friendly classical reservoir approach for ground-state preparation in electronic structure problems, using localized molecular orbitals and strictly local two-body operations on a square-lattice layout. The variational ansatz comprises three commuting operator groups arranged in layers, with spin-conserving initialization and gradient-descent optimization over a compact parameter set, achieving chemical accuracy across diverse molecules and bond lengths while significantly reducing CNOT counts compared with methods like ADAPT-VQE. By avoiding double excitations and long-range terms, and leveraging LMOs to concentrate correlation locally, the method delivers substantial resource efficiency and demonstrates strong potential for near-term quantum hardware. The work advocates a design philosophy prioritizing quantum-native constructions for efficient ground-state preparation with practical implications for quantum chemistry on near-term devices and future fault-tolerant platforms.

Abstract

Ground state preparation is a central application of quantum algorithms for electronic structure. We introduce the classical reservoir approach, a low cost variational ansatz tailored to near-term hardware, requiring only nearest-neighbor interactions on a machine with square-lattice connectivity. Unlike traditional methods built from the classically efficient Hartree Fock theory, our ansatz operates in localized molecular orbitals to study previously unexplored regions of the variational parameter space. Numerical benchmarks demonstrate chemical accuracy across diverse systems and bond lengths; notably, significantly reduced circuit depths are attainable when relaxed error thresholds (e.g., tens of E_h) are permissible. We benchmark the method on hydrogen chains, N_2, O_2, CO, BeH_2, and H_2O, the latter corresponding to an effective 24 qubit calculation.

Figures (4)

• Figure 1: Top: flow chart of the classical reservoir method. Bottom left: square qubit layout with the mapping of the spin orbitals, where $\alpha$ denotes spin-up electrons and $\beta$ denotes spin-down electrons. Bottom center: quantum circuit diagram of the method, beginning with a single layer of $X$ gates to generate a typical high-energy initial state (i.e., a doubly occupied configuration) as shown in Eq. \ref{['eq:ini state']}, followed by one ansatz layer consisting of two hopping layers implemented as Givens rotations (denoted by the symbol $G$) between adjacent same spin orbitals and one on-site potential layer between opposite spin orbitals implemented with $ZZ$ and $Z$ gates (denoted by the symbol $O$). Bottom right: schematic representation of the initialization, illustrating the idea of starting from a high-energy initial state rather than the Hartree–Fock state to "roll the rock" down to the lowest point, i.e., preparing the ground state.
• Figure 2: (a) Energy difference from FCI for $\mathrm{H_2O}$ using the 6-31G atomic basis at various geometries, plotted as a function of the number of ansatz layers. A secondary (top) $x$ axis shows the corresponding CNOT gate count. The red dashed line indicates the chemical-accuracy threshold. (b) Infidelity for the same set of geometries as a function of the number of ansatz layers.
• Figure 3: (a) Energy difference from FCI for $\mathrm{N_2}$ using the STO-6G atomic basis at various geometries, plotted as a function of the number of ansatz layers. (b) Infidelity for the same set of geometries as a function of the number of ansatz layers.
• Figure 4: (Color online) (a) Energy difference from FCI for $\mathrm{H_2O}$ using 15 ansatz layers as a function of the O–H bond length. (b) Correlation energy and the gap between the ground state and the first excited state within the same total spin sector. (c) Energy difference from FCI for $\mathrm{H_2O}$ computed using CCSD and CCSD(T) from PySCF sun2020recent as a function of the O–H bond length.