Error-Mitigation Enabled Multicomponent Quantum Simulations Beyond the Born-Oppenheimer Approximation

TL;DR

The paper addresses the challenge of simulating electronic–nuclear coupling beyond the Born–Oppenheimer approximation by adopting the Nuclear–Electronic Orbital (NEO) framework and developing multicomponent unitary coupled cluster (mcUCC) approaches within the VQE paradigm. It combines a hardware-efficient Local Unitary Cluster Jastrow (LUCJ) ansatz with Physics-Inspired Extrapolation (PIE) error mitigation to demonstrate beyond-BO simulations for PsH and HHq on IBM Q hardware, achieving energies within chemical accuracy. Classical simulations delineate the trade-offs between operator pool size and correlation recovery, while the hardware demonstration shows substantial circuit-depth reduction and noise mitigation, yielding results close to full-configuration interaction benchmarks. Together, these results establish a practical path toward scalable, accurate multicomponent quantum chemistry on near-term quantum processors, unifying electronic and nuclear degrees of freedom in simulations.

Abstract

We introduce a multicomponent unitary coupled cluster framework for quantum simulations of molecular systems that incorporate both electronic and nuclear quantum effects beyond the Born-Oppenheimer approximation. Using the nuclear-electronic orbital formalism, we construct mcUCC ansätze for positronium hydride and molecular hydrogen with a quantum proton, and analyze hardware requirements for different excitation truncations. To further reduce resource costs effectively, we employ the local unitary cluster Jastrow ansatz and implement it experimentally on IBM Q's Heron superconducting hardware. With the Physics-Inspired Extrapolation error mitigation protocol, the computed ground-state energies remain within chemical accuracy, consistent with the stated uncertainty level. These results provide the first demonstration of error-mitigated multicomponent correlated simulations on quantum hardware and outline a path toward scalable algorithms unifying electronic and nuclear degrees of freedom.

Figures (5)

• Figure 1: Schematic representation of the (VQE) algorithm. The molecular Hamiltonian is precomputed classically, while the quantum device evaluates expectation values and supplies energy feedback to the classical optimizer.
• Figure 2: Top: Schematic representations of the hydrogen molecule with a quantum mechanical proton ($\mathrm{HHq}$) and positronium hydride ($\mathrm{PsH}$). Bottom: Spin–orbital configurations for both systems under the chosen bases: 6-31G for electronic and positronic orbitals in $\mathrm{PsH}$; STO-3G for electronic orbitals and 2s for protonic orbital in $\mathrm{HHq}$.
• Figure 3: Example circuit block for the LUCJ ansatz applied to $\mathrm{PsH}$, following Eq. \ref{['eq:LUCJansatz']}. Orbitals $\{0,1\}$ correspond to the two electronic spatial orbitals, while $p$ labels the positron without any spin orbital. The complete circuit decomposition is shown in Fig. \ref{['fig:topology_circuit']}.
• Figure 4: (Left) Topology of the 133-qubit IBM Heron superconducting processor (ibm torino); the 6-qubit subset used for the demonstration is highlighted in dark blue. (Right) LUCJ circuit expressed in the $\{\mathrm{rz},\mathrm{rxx},\mathrm{ryy},\mathrm{rzz},\mathrm{x}\}$ gate basis. Each qubit corresponds to one spatial or spin orbital, and the circuit is initialized in the NEO-HF reference state.
• Figure 5: Extrapolated energy results using the PIE method for $\mathrm{HHq}$ and $\mathrm{PsH}$. The logarithm of the negative energy is plotted as a function of the number of circuit foldings, with the zero-noise limit obtained from a linear fit. Raw quantum circuit executions correspond to experimental data at $\lambda=1$, while the noise-mitigated energies are denoted by red dots at $\lambda=0$.