Physics Informed Generative Machine Learning for Accelerated Quantum-centric Supercomputing

TL;DR

This work tackles noise-induced limitations in quantum-centric supercomputing for electronic structure by fusing physics-informed perturbative screening with RBM-based generative learning to guide configuration recovery. The PIGen-SQD framework anchors hardware samples via MBPT up to rank 4 and uses RBMs to self-consistently expand a focused, symmetry-preserving subspace, dramatically reducing the diagonalization burden while preserving chemical accuracy. Demonstrations on IBM Heron R2 hardware for H2O, N2, and C2H2 show up to ~90% reduction in subspace size and orders-of-magnitude improvements in energy accuracy over standard SQD. The approach offers a scalable path toward reliable quantum simulations on utility-scale hardware and lays groundwork for future enhancements with advanced generative models and alternative QCSC variants.

Abstract

Quantum centric supercomputing (QCSC) framework, such as sample-based quantum diagonalization (SQD) holds immense promise toward achieving practical quantum utility to solve challenging problems. QCSC leverages quantum computers to perform the classically intractable task of sampling the dominant fermionic configurations from the Hilbert space that have substantial support to a target state, followed by Hamiltonian diagonalization on a classical processor. However, noisy quantum hardware produces erroneous samples upon measurements, making robust and efficient configuration-recovery strategies essential for a scalable QCSC pipeline. Toward this, in this work, we introduce PIGen-SQD, an efficiently designed QCSC workflow that utilizes the capability of generative machine learning (ML) along with physics-informed configuration screening via implicit low-rank tensor decompositions for accurate fermionic state reconstruction. The physics-informed pruning is based on a class of efficient perturbative measures that, in conjunction with hardware samples, provide a substantial overlap with the target state. This distribution induces an anchoring effect on the generative ML models to stochastically explore only the dominant sector of the Hilbert space for effective identification of additional important configurations in a self-consistent manner. Our numerical experiments performed on IBM Heron R2 quantum processors demonstrate this synergistic workflow produces compact, high-fidelity subspaces that substantially reduce diagonalization cost while maintaining chemical accuracy under strong electronic correlations. By embedding classical many body intuitions directly into the generative ML model, PIGen-SQD advances the robustness and scalability of QCSC algorithms, offering a promising pathway toward chemically reliable quantum simulations on utility-scale quantum hardware.

Figures (9)

• Figure 1: Hardware coupling map layout and qubit assignments for $\boldsymbol{\mathrm{H_2O}}$ (24 qubits), $\boldsymbol{\mathrm{N_2}}$ (32 qubits) and $\boldsymbol{\mathrm{C_2H_2}}$ (40 qubits) on ibm_kingston (156 qubits IBM Heron R2 processor). Each circle represents a qubit and is assigned a number written at the center of it. Alpha and beta molecular orbitals are mapped onto red and blue colored qubits respectively. The green colored qubits connect adjacent alpha and beta qubits.
• Figure 2: Cost comparison between numerical worst case scenarios for perturbative triples and quadruples selection and the corresponding asymptotic scaling of the term $v_{ie}^{ab} t_{jk}^{ec}$ with respect to the number of qubits. Cost of CCSD and CCSDT is also plotted for reference. Here $n_o$ and $n_V$ are the number of occupied and virtual spin orbitals respectively. Our analysis shows the maximum cost for triples is almost two orders-of-magnitude less compared to the asymptotic scaling making it an efficient method for approximate perturbative selection of excited configurations. The corresponding quadruples selection cost scales almost similar to CCSD.
• Figure 3: Convergence profile of PIGen-SQD with RBM driven sampling v/s random sampling from the symmetry space. The RBM-guided, self-consistent recovery of important configurations leads to noticeably faster convergence and more accurate energy estimates (top row), while simultaneously requiring a significantly smaller diagonalization space and search space (bottom row). This demonstrates that the RBM effectively learns the underlying structure of the Hilbert space and preferentially samples the most relevant regions, resulting in substantially improved efficiency and accuracy compared to random sampling.
• Figure 4: Comparison between various PIGen-SQD macro-cycle initialization scheme characterized via different ranks n (n=2,3,4 here) of perturbative estimates and raw (symmetry preserved) hardware samples on the self consistent configuration recovery process for two different geometries of $\boldsymbol{\mathrm{H_2O}}$ ((A), (B)) and $\boldsymbol{\mathrm{N_2}}$ ((C), (D)). Y-axes show the energy difference compared to FCI with grey shaded regions showing the chemical accuracy. The inset bar plots denote the dimension of the search space to reach chemical accuracy for each initialization scheme. Quite evidently, initializing the configuration recovery with perturbative estimates up to rank 4 shows faster convergence with reduced dimensional search space and better energy estimation.
• Figure 5: Potential energy curve of $\boldsymbol{\mathrm{H_2O}}$ with SQD, PIGen-SQD and other standard methods for comparison. Energy values and energy errors (in log scale) with FCI in $E_h$ are shown in y-axes panel (A) and (B) with the ratio of bond distance against equilibrium distance $\frac{R}{R_{eq}}$ plotted along x-axes of all the panels. The number of configurations in symmetry space, core space and diagonalization space in SQD and PIGen-SQD are shown in panel (C). The dotted lines in panel (C) show the search space dimension for PIGen-SQD.