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arXiv:2011.05553 · ACS Photonics

Analog Quantum Simulation of Non-Condon Effects in Molecular Spectroscopy

Hamza Jnane, Nicolas P. D. Sawaya, Borja Peropadre, Alán Aspuru‐Guzik, Raúl García−Patrón, Joonsuk Huh

Published Apr 28, 2021• 13 citations
arXivHTMLPDF

Abstract

In this work, we present a linear optical implementation for analog quantum simulation of molecular vibronic spectra, incorporating the non-Condon scattering operation with a quadratically small truncation error. To date, analog and digital quantum algorithms for achieving quantum speedup have been suggested only in the Condon regime, which refers to a transition dipole moment that is independent of nuclear coordinates. For analog quantum optical simulation beyond the Condon regime (i.e., non-Condon transitions), the resulting nonunitary scattering operations must be handled appropriately in a linear optical network. In this paper, we consider the first- and second-order Herzberg–Teller expansions of the transition dipole moment operator for the non-Condon effect for implementation on linear optical quantum hardware. We believe that the method opens a new way to approximate arbitrary nonunitary operations in analog and digital quantum simulations. We report in silico simulations of the vibronic spectra for naphthalene, phenanthrene, and benzene to support our findings.

DOI
10.1021/acsphotonics.1c00059

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For roughly a century, spectroscopy has been our window into the molecular domain. It has served as a benchmark for the development of new theoretical methods in quantum chemistry, which in turn have aided the assignment and characterization of molecular spectra. The advent of quantum computing is no exception. Quantum computers have the potential to greatly increase the scale and accuracy of simulated molecular systems. However, current "digital" quantum computers will remain limited in size and number of operations in the near future due to environmental noise. Conversely, analog quantum computers may be used to simulate realistic molecular systems with current technology. They consist of controllable quantum devices with a system-specific mapping onto a quantum system of interest, such as a molecule. I will present our recent work on the development of an analog quantum toolkit for the simulation of vibronic coupling Hamiltonians, including the prediction of vibronic spectra. I will show the theoretical capabilities and limits of our approach, and show proof-of-principle experimental results from collaborators. Finally, I will discuss what is next in the exciting world of analog quantum simulation.

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In this work, we present a linear optical implementation for analog quantum simulation of molecular vibronic spectra, incorporating the non-Condon scattering operation with a quadratically small truncation error. To date, analog and digital quantum algorithms for achieving quantum speedup have been suggested only in the Condon regime, which refers to a transition dipole moment that is independent of nuclear coordinates. For analog quantum optical simulation beyond the Condon regime (i.e., non-Condon transitions), the resulting nonunitary scattering operations must be handled appropriately in a linear optical network. In this paper, we consider the first- and second-order Herzberg–Teller expansions of the transition dipole moment operator for the non-Condon effect for implementation on linear optical quantum hardware. We believe that the method opens a new way to approximate arbitrary nonunitary operations in analog and digital quantum simulations. We report in silico simulations of the vibronic spectra for naphthalene, phenanthrene, and benzene to support our findings.
Although molecular vibronic spectra generation is pivotal for chemical analysis, tackling such exponentially complex tasks on classical computers remains inefficient. Quantum simulation, though theoretically promising, faces technological challenges in experimentally extracting vibronic spectra for molecules with multiple modes. Here, we propose a nontrivial algorithm to generate the vibronic spectra using states with zero displacements (squeezed vacuum states) coupled to a linear optical network, offering ease of experimental implementation. We also fabricate an integrated quantum photonic microprocessor chip as a versatile simulation platform containing 16 modes of single-mode squeezed vacuum states and a fully programmable interferometer network. Molecular vibronic spectra of formic acid and thymine under the Condon approximation are simulated using the quantum microprocessor chip with high reconstructed fidelity ( > 92%). Furthermore, vibronic spectra of naphthalene, phenanthrene, and benzene under the non-Condon approximation are also experimentally simulated. Such demonstrations could pave the way for solving complicated quantum chemistry problems involving vibronic spectra and computational tasks beyond the reach of classical computers.
Spectroscopy is one of the most accurate probes of the molecular world. However, predicting molecular spectra accurately is computationally difficult because of the presence of entanglement between electronic and nuclear degrees of freedom. Although quantum computers promise to reduce this computational cost, existing quantum approaches rely on combining signals from individual eigenstates, an approach that is difficult to scale because the number of eigenstates grows exponentially with molecule size. Here, we introduce a method for scalable analog quantum simulation of molecular spectroscopy, by performing simulations in the time domain. Our approach can treat more complicated molecular models than previous ones, requires fewer approximations, and can be extended to open quantum systems with minimal overhead. We present a direct mapping of the underlying problem of time-domain simulation of molecular spectra to the degrees of freedom and control fields available in a trapped-ion quantum simulator. We experimentally demonstrate our algorithm on a trapped-ion device, exploiting both intrinsic electronic and motional degrees of freedom, showing excellent quantitative agreement for a single-mode vibronic photoelectron spectrum of SO2_22​.
Molecular vibronic spectra can be used to derive the structural properties of molecules. Although there is no known efficient classical algorithm for calculating these spectra, it has recently been shown that an ideal quantum optics simulator can in principle be used to efficiently perform this calculation. In this work, we demonstrate that imperfect quantum simulators can also yield approximations of these spectra, and illustrate our findings using a proof of principle experimental simulation of the partial vibronic spectrum of tropolone. Specifically, we demonstrate a method for designing an experiment in the presence of imperfections, show that the error on the resulting estimations of vibronic spectra can be efficiently bounded, and show that such experiments can outperform a classicality criterion. Our findings provide a roadmap for future simulations of large molecules beyond the reach of current classical computers.
In this work, we develop an extended dissipaton theory that generalizes the environmental couplings beyond the conventional linear and quadratic forms, enabling the treatment of arbitrary order of bath couplings. Applying this theoretical framework to the condensed-phase non-Condon spectroscopy, we demonstrate the interplay of anharmonicity, non-Condon and solvent effects on optical spectra. Precise simulations are carried out with high efficiency on linear absorption spectra involving the above mentioned correlated effects. We exhibit how an anharmonic potential modulates the vibronic feature, offering insights into the role of nonlinear environmental couplings in spectroscopic signatures and exemplifying the success of the extended dissipaton formalism as an exact and efficient method for higher-order bath couplings.
We present a digital quantum simulation framework for ultrafast optical spectroscopy of semiconductor materials. The framework is based on Brillouin-zone discretization and is designed as a quantum alternative to classical simulations based on the semiconductor Bloch equations. Its current capabilities include quantum simulations of linear absorption and optical gain, incorporating Lorentzian broadening, finite-temperature band-filling effects, and reduced-dimensionality effects. Comparison with classical simulations of GaAs within the single-particle approximation demonstrates quantitative agreement in the noiseless limit. The inclusion of realistic hardware noise characteristic of NISQ-era quantum computers effectively manifests as an additional source of scattering, resulting in increased spectral broadening. We also show that the linear optical response, including many-body interactions treated within the Hartree-Fock approximation, can be mapped onto a system of coupled classical oscillators. Under certain assumptions about the query complexity of the oscillator couplings, this system exhibits a provable quantum advantage, as demonstrated in [Phys. Rev. X 13, 041041 (2023)]. Beyond the Hartree-Fock approximation, classical simulations based on many-body quantum kinetic equations face the so-called hierarchy problem, whereas the algorithmic complexity of the quantum simulations remains unchanged, offering a promising approach to overcoming this challenge.
For roughly a century, spectroscopy has been our window into the molecular domain. It has served as a benchmark for the development of new theoretical methods in quantum chemistry, which in turn have aided the assignment and characterization of molecular spectra. The advent of quantum computing is no exception. Quantum computers have the potential to greatly increase the scale and accuracy of simulated molecular systems. However, current "digital" quantum computers will remain limited in size and number of operations in the near future due to environmental noise. Conversely, analog quantum computers may be used to simulate realistic molecular systems with current technology. They consist of controllable quantum devices with a system-specific mapping onto a quantum system of interest, such as a molecule. I will present our recent work on the development of an analog quantum toolkit for the simulation of vibronic coupling Hamiltonians, including the prediction of vibronic spectra. I will show the theoretical capabilities and limits of our approach, and show proof-of-principle experimental results from collaborators. Finally, I will discuss what is next in the exciting world of analog quantum simulation.