Fragment, Entangle, and Consolidate: Strong Correlation through Bi-fold Quantum Circuits

TL;DR

The paper tackles the challenge of strong electronic correlation in quantum chemistry on near-term quantum devices by proposing a bi-fold scheme that first builds a multireference product state (MRPS) from chemistry-inspired fragmentation using a hardware-efficient Ansatz, then adds inter-fragment correlations via an adaptive, unitary coupled cluster–type approach (ADAPT-VQE) using the MRPS as reference. This modular design separates intra-fragment and inter-fragment correlations, enabling parallel fragment optimization and reduced parameter count, with qubit-ADAPT-VQE delivering substantial gate-count reductions. Across H$_4$, cyclobutadiene, and water, the MRPS-based initialization and adaptive inter-fragment correlation achieve energies within chemical accuracy ($\le 1\ \mathrm{\,kcal/mol}$) and accurate potential energy profiles, demonstrating robustness to strong correlation and geometry. The approach offers scalable, hardware-aware quantum algorithms that can operate on NISQ devices and potentially unlock quantum advantage in chemical discovery.

Abstract

An accurate description of strong correlation is quintessential for the exploration of emerging chemical phenomena. While near-term variational quantum algorithms provide a theoretically scalable framework for quantum chemical problems, the accurate simulation of multireference effects remains elusive, hindering progress toward the rational design of novel chemical space. In this regard, we introduce a general and customizable scheme to handle strong electronic correlation, based on problem decomposition, entanglement buildup, and subsequent consolidation. Based on a problem-inspired molecular decomposition, the deployment of Hardware Efficient Ansatz to prepare entangled subsystems ensures efficient construction of a multireference state while concurrently adhering to the hardware topology. The dynamic correlation is subsequently introduced through a unitary coupled cluster framework, with static or dynamic ansatz parametrized by a set of inter-fragment generalized operators, and with the product state spanning various subsystems taken as the reference. The hybrid architecture ensures a judicious deployment of separate ansatze structures for capturing various degrees of correlation in a balanced manner, while concurrently retaining the scalability and flexibility provided by them individually. Over a number of numerical applications on a strongly correlated system, the proposed scheme is shown to be highly accurate, flexible, and robust in unlocking the potential to harness quantum advantage for quantum chemistry.

Figures (8)

• Figure 1: The procedure begins by constructing a multireference product state through parallel optimization of the subsystems, for instance, using HEA (as shown on the left side). Subsequently, inter-subsystem correlations are incorporated to recover the complete wavefunction with methods such as ADAPT-VQE.
• Figure 2: Models and molecular systems investigated in this work: H$_4$, cyclobutadiene (CBD) in $D_{2h}$ and $D_{4h}$ symmetries taken from Ref.monino2022reference, and water.
• Figure 3: (a) The error (in Hartree) in fragments’ state energy with respect to the exact energy (obtained via exact diagonalization of the corresponding fragment Hamiltonian) against the number of layers in HEA using linear entanglement blocks. (b) The same error for the square H$_4$ geometry with the number of layers using linear, full, circular, and pairwise entanglement blocks. It is to be noted that the Fock operator of the individual fragment Hamiltonian has an embedded Coulomb potential of the other fragments (Eq. \ref{['eq:eff-ham']}-\ref{['eq:fock']}).
• Figure 4: (a) Error (in Hartree) in the potential energy curve for the H$_4$ system calculated by full UCCGSD optimization starting with HF and MRPS initial states. The Shannon entropy values, indicating the degree of multiconfigurational character, are mentioned in red across these geometries. (b) The fidelities $|\langle \psi_\mathrm{exact} |\psi_\mathrm{MRPS}(\vec{\theta}) \rangle |^2$ and $|\langle \psi_\mathrm{exact} |\psi_\mathrm{HF} \rangle |^2$ shown along the potential energy curve for the H$_4$.
• Figure 5: Error in energy (in Hartree) vs. CNOT gate counts for calculating the potential energy curve (PEC) of H$_4$ using MRPS-fermionic-ADAPT-VQE and MRPS-qubit-ADAPT-VQE. Different points refer to different geometries in the PEC.