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Simulating polaritonic ground states on noisy quantum devices

Mohammad Hassan, Fabijan Pavošević, Derek S. Wang, Johannes Flick

TL;DR

This paper tackles the challenge of simulating strongly coupled electron-photon (polaritonic) systems on noisy quantum hardware by developing a PUCC-based VQE framework that incorporates symmetry-based qubit reductions and advanced error mitigation. The method minimizes the QED Hamiltonian $E_{ ext{QED}}$ using the PUCC ansatz $| ext{PUCC}\rangle=e^{\hat{T}-\hat{T}^\dagger}|0^{e}0^{ph}\rangle$ with a truncated cluster operator $\hat{T}$, enabling accurate ground-state energies and photon-number observables for H$_2$ inside a single-mode cavity. Through a combination of Bravyi-Kitaev tapering, direct boson mapping, and error mitigation schemes such as ZNE and RS (including rZNE), the study demonstrates chemical accuracy across regimes of bond length and coupling, even on noisy devices. The results validate the practical viability of polaritonic quantum chemistry on near-term quantum hardware and point to future work on excited states via QED-qEOM and broader polaritonic systems.

Abstract

The recent advent of quantum algorithms for noisy quantum devices offers a new route toward simulating strong light-matter interactions of molecules in optical cavities for polaritonic chemistry. In this work, we introduce a general framework for simulating electron-photon coupled systems on small, noisy quantum devices. This method is based on the variational quantum eigensolver (VQE) with the polaritonic unitary coupled cluster (PUCC) ansatz. To achieve chemical accuracy, we exploit various symmetries in qubit reduction methods, such as electron-photon parity, and use recently developed error mitigation schemes, such as the reference zero-noise extrapolation method. We explore the robustness of the VQE-PUCC approach across a diverse set of regimes for the bond length, cavity frequency, and coupling strength of the H$_2$ molecule in an optical cavity. To quantify the performance, we measure two properties: ground-state energy, fundamentally relevant to chemical reactivity, and photon number, an experimentally accessible general indicator of electron-photon correlation.

Simulating polaritonic ground states on noisy quantum devices

TL;DR

This paper tackles the challenge of simulating strongly coupled electron-photon (polaritonic) systems on noisy quantum hardware by developing a PUCC-based VQE framework that incorporates symmetry-based qubit reductions and advanced error mitigation. The method minimizes the QED Hamiltonian using the PUCC ansatz with a truncated cluster operator , enabling accurate ground-state energies and photon-number observables for H inside a single-mode cavity. Through a combination of Bravyi-Kitaev tapering, direct boson mapping, and error mitigation schemes such as ZNE and RS (including rZNE), the study demonstrates chemical accuracy across regimes of bond length and coupling, even on noisy devices. The results validate the practical viability of polaritonic quantum chemistry on near-term quantum hardware and point to future work on excited states via QED-qEOM and broader polaritonic systems.

Abstract

The recent advent of quantum algorithms for noisy quantum devices offers a new route toward simulating strong light-matter interactions of molecules in optical cavities for polaritonic chemistry. In this work, we introduce a general framework for simulating electron-photon coupled systems on small, noisy quantum devices. This method is based on the variational quantum eigensolver (VQE) with the polaritonic unitary coupled cluster (PUCC) ansatz. To achieve chemical accuracy, we exploit various symmetries in qubit reduction methods, such as electron-photon parity, and use recently developed error mitigation schemes, such as the reference zero-noise extrapolation method. We explore the robustness of the VQE-PUCC approach across a diverse set of regimes for the bond length, cavity frequency, and coupling strength of the H molecule in an optical cavity. To quantify the performance, we measure two properties: ground-state energy, fundamentally relevant to chemical reactivity, and photon number, an experimentally accessible general indicator of electron-photon correlation.
Paper Structure (6 sections, 11 equations, 5 figures, 2 tables)

This paper contains 6 sections, 11 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Theory
  3. Error Mitigation
  4. Technical Details
  5. Results
  6. Summary and Conclusion

Figures (5)

  • Figure 1: (a) Schematic of an H$_2$ Molecule in an optical cavity. A cavity mode of frequency $\omega$ interacts with the electronic system of H$_2$ with bond length $R$ via the electron-photon coupling strength $\lambda$. (b) The reduced ansatz circuit obtained by using a Bravyi-Kitaev mapping and tapering off a qubit using Z$_2$ symmetries. (c) and (d) show FCI calculations for H$_2$ interacting with a single photon mode. (c) The energy difference of the system between the coupling strength $\lambda_x$ and $\lambda=0$ a.u. ($\omega=2$ eV, $R_0=0.735 \textnormal{\AA}$). (d) Dissociation curves at increasing values of $\lambda_x$ ($\omega=2$ eV).
  • Figure 2: (a) Potential energy surface for H$_2$ coupled to a single photon mode. Results are shown for different levels of error mitigation. The inset shows the error bars near equilibrium. (b) The error relative to the FCI energies for different levels of error mitigation. The gray shaded region is the region in which results are chemically accurate. The first few points for the unmitigated energies are cutoff due to high errors. The results obtained using combinations of ZNE, readout-error mitigation, and RS mitigation are not shown in (a) due to their close overlap with the rZNE results, but their associated errors are shown in (b). Chemical accuracy can be achieved with combinations of ZNE, readout-error mitigation, and RS mitigation, and can consistently be achieved with rZNE.
  • Figure 3: (a) Energy with respect to coupling strength in the x-direction for H$_2$ coupled to a single photon in a single photon mode. Results are shown for different levels of error mitigation. (b) The error relative to the FCI energies for different levels of error mitigation. The shaded region is the region in which results are chemically accurate.
  • Figure 4: (a) Average photon number with respect to coupling strength in the x-direction for H$_2$ coupled to a single photon in a single photon mode. Results are shown for different levels of error mitigation. (b) The error relative to the FCI average photon number for different levels of error mitigation.
  • Figure 5: (a) The average number (n=10) of iterations that it takes for the VQE to converge vs. the coupling strength in the x-direction ($\lambda_x$). (b) The average number (n=10) of iterations that it takes for the VQE to converge vs. the bond length. In both subplots, the error bars are the standard deviation of the iterations.