UC Berkeley Team Develops Quantum Algorithm for Nonlinear Spectroscopy Analysis

Researchers from the University of California, Berkeley, the Simons Institute for the Theory of Computing, the Berkeley Quantum Information and Computation Center, and Azure Quantum, Microsoft, have developed a fault-tolerant quantum algorithm for computing nth order response properties.

The algorithm, which is essential for the analysis of nonlinear spectroscopies of molecular and condensed phase systems, uses a semiclassical description where the electronic degrees of freedom are treated quantum mechanically, and the light is treated as a classical field. The algorithm allows for the approximation of relevant transition dipole moments and achieves Heisenberg-limited scaling for the determination of excitation energies.

What is the Quantum Algorithm for Nonlinear Spectroscopies?

A team of researchers from the Department of Chemistry at the University of California, Berkeley, the Simons Institute for the Theory of Computing, the Berkeley Quantum Information and Computation Center, and Azure Quantum, Microsoft, have developed a fault-tolerant quantum algorithm for computing nth order response properties. These properties are essential for the analysis of nonlinear spectroscopies of molecular and condensed phase systems. The algorithm uses a semiclassical description where the electronic degrees of freedom are treated quantum mechanically, and the light is treated as a classical field.

The algorithm can be viewed as an implementation of standard perturbation theory techniques, focusing on ab initio calculation of nth order response functions. The researchers provide cost estimates in terms of the number of queries to the block encoding of the unperturbed Hamiltonian and the block encodings of the perturbing dipole operators. Using the technique of eigenstate filtering, the algorithm can extract excitation energies to resolution γ and the corresponding linear response amplitude to accuracy ϵ.

How Does the Quantum Algorithm Work?

The quantum algorithm developed by the researchers is designed to compute nth order response properties, which are necessary for the analysis of nonlinear spectroscopies of molecular and condensed phase systems. The algorithm uses a semiclassical description in which the electronic degrees of freedom are treated quantum mechanically, and the light is treated as a classical field.

The algorithm can be viewed as an implementation of standard perturbation theory techniques, focusing on ab initio calculation of nth order response functions. The researchers provide cost estimates in terms of the number of queries to the block encoding of the unperturbed Hamiltonian and the block encodings of the perturbing dipole operators.

What are the Benefits of the Quantum Algorithm?

The quantum algorithm developed by the researchers has several benefits. Firstly, it allows for the approximation of relevant transition dipole moments. These quantities, combined with sum-over-states formulation of polarizabilities, can be used to compute the nth order susceptibilities and response functions for nonlinear spectroscopies under limited assumptions.

Secondly, the algorithm achieves Heisenberg-limited scaling for the determination of excitation energies, making it near optimal for the computation of frequency-dependent response properties in the semiclassical regime.

Finally, the core subroutine of the algorithm can be iteratively repeated to compute response functions of any order. This makes it the first work to provide concrete resource estimations for the general problem of estimating linear and nonlinear response functions of arbitrary order.

What is the Significance of the Quantum Algorithm?

The quantum algorithm developed by the researchers is significant because it allows for the accurate computation of excited state properties deriving from the interaction of a many-electron system with photons in the semiclassical description. This is essential for predicting and analyzing spectroscopic features deriving from light-matter interactions.

The algorithm also allows for the determination of frequency-dependent properties of the response function by using a simple excite-and-filter approach. This approach involves applying the dipole operator and then filtering the response to eigenenergies within a particular frequency bin.

What are the Future Implications of the Quantum Algorithm?

The quantum algorithm developed by the researchers has several future implications. Firstly, it can be used to accurately compute excited state properties, which are essential for predicting and analyzing spectroscopic features deriving from light-matter interactions.

Secondly, the algorithm can be used to determine frequency-dependent properties of the response function, which allows for better predictions of material properties.

Finally, the algorithm can be used to compute nth order susceptibilities and response functions for nonlinear spectroscopies under limited assumptions. This makes it a valuable tool for researchers and scientists working in the field of quantum computing and spectroscopy.