Enhancing quantum computations with the synergy of auxiliary field quantum Monte Carlo and computational basis tomography

TL;DR

QC-CBT-AFQMC introduces a practical quantum-classical hybrid that replaces expensive post-processing in QC-AFQMC with Computational Basis Tomography (CBT). CBT reconstructs a compact multi-determinant trial from quantum computations using shallow Clifford circuits, reducing measurement and circuit costs to enable efficient AFQMC calculations of dynamical correlation outside the active space. The method delivers accurate potential energy curves and reaction barriers for benchmark molecules and cycloaddition reactions, with CBS extrapolations validating its robustness. This approach expands the near-term applicability of quantum-assisted chemistry by lowering resource barriers while maintaining high fidelity to established high-level references.

Abstract

We introduce QC-CBT-AFQMC, a hybrid algorithm that incorporates computational basis tomography (CBT) into the quantum-classical auxiliary-field quantum Monte Carlo (QC-AFQMC) method proposed by Huggins et al. [Nature 603, 416-420 (2022)], replacing the use of classical shadows. While the original QC-AFQMC showed high accuracy for quantum chemistry calculations, it required exponentially costly post-processing. Subsequent work using Matchgate shadows [Commun. Math. Phys. 404, 629 (2023)] improved scalability, but still suffers from prohibitive computational requirements that limit practical applications. Our QC-CBT-AFQMC approach uses shallow Clifford circuits with a quadratic reduction of two-qubit gates over the original algorithm, significantly reducing computational requirements and enabling accurate calculations under limited measurement budgets. We demonstrate its effectiveness on the hydroxyl radical, ethylene, and nitrogen molecule, producing potential energy curves that closely match established benchmarks. We also examine the influence of CBT measurement counts on accuracy, showing that subtracting the active space AFQMC energy mitigates measurement-induced errors. Furthermore, we apply QC-CBT-AFQMC to estimate reaction barriers in [3+2]-cycloaddition reactions, achieving agreement with high-level references and successfully incorporating complete basis set extrapolation techniques. These results highlight QC-CBT-AFQMC as a practical quantum-classical hybrid method that bridges the capabilities of quantum devices and accurate chemical simulations.

Figures (10)

• Figure 1: Schematic of the QC-CBT-AFQMC methodology. Blue frames highlight the selected active space for the quantum computer part. The CBT algorithm captures the most important configurations from the quantum computer state and translates them to the classical computer. AFQMC generates walkers from the CBT state, where the orbitals also rotate. This is depicted as rotated orbital diagrams.
• Figure 2: Quantum circuit implementing the operators $\langle0000|U_{1,14} = (\langle0001| + \langle1110|)/\sqrt{2}$, and $\langle0000|V_{1,14} = (\langle0001| + i\langle1110|)/\sqrt{2}$. The blue dashed box indicates a fan-out gate from the flag qubit $q_2$ to the other qubits, corresponting to different bits in binary representations of $1$ and $14$. The additional $S$ gate transforms $U_{1,14}$ into $V_{1,14}$.
• Figure 3: Potential energy curves for the OH radical obtained using a ($3$,$3$) active space and the aug-cc-pVDZ basis set. These results highlight how QC-CBT-AFQMC recovers dynamical correlation effects missing from the active space alone, closely matching benchmark methods and accurately describing the bond dissociation.
• Figure 4: Potential energy curves for ethylene as the HC-CH dihedral angle varies, computed with a ($2$,$2$) active space and a cc-pVDZ basis set. The QC-CBT-AFQMC(c) approach improves upon CASCI and VQE.
• Figure 5: Potential energy curves for N2, obtained with a ($6$,$6$) active space and the aug-cc-pVDZ basis set. QC-CBT-AFQMC(c) accurately captures the multireference character of the stretched N-N bond, showing improved agreement with MRCISD+Q references over other methods.