Nonlinear Spectroscopy via Generalized Quantum Phase Estimation
arXiv:2405.13885 · doi:10.22331/q-2025-08-07-1822
Abstract
Response theory has a successful history of connecting experimental observations with theoretical predictions. Of particular interest is the optical response of matter, from which spectroscopy experiments can be modelled. However, the calculation of response properties for quantum systems is often prohibitively expensive, especially for nonlinear spectroscopy, as it requires access to either the time evolution of the system or to excited states. In this work, we introduce a generalized quantum phase estimation framework designed for multi-variate phase estimation. This allows the treatment of general correlation functions enabling the recovery of response properties of arbitrary orders. The generalized quantum phase estimation circuit has an intuitive construction that is linked with a physical process of interest, and can directly sample frequencies from the distribution that would be obtained experimentally. In addition, we provide a single-ancilla modification of the new framework for early fault-tolerant quantum computers. Overall, our framework enables the efficient simulation of spectroscopy experiments beyond the linear regime, such as Raman spectroscopy, having that the circuit cost grows linearly with respect to the order of the target nonlinear response. This opens up an exciting new field of applications for quantum computers with potential technological impact.
19 pages, 5 figures, 1 table
References in corpus (33)
- Quantum Simulation
- Quantum Thermodynamics
- Optimal Hamiltonian Simulation by Quantum Signal Processing
- Tutorial: A Beginner's Guide to Interpreting Magnetic Susceptibility Data with the Curie-Weiss Law
- Polynomial-time quantum algorithm for the simulation of chemical dynamics
- Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
- Quantum Algorithms for Fermionic Simulations
- Sampling from the thermal quantum Gibbs state and evaluating partition functions with a quantum computer
- Heisenberg-limited ground state energy estimation for early fault-tolerant quantum computers
- Quantum theory of the nonlinear Hall effect
- Vibrational Heat Transport in Molecular Junctions
- Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators
- Quantum Algorithm for Spectral Measurement with Lower Gate Count
- Linear Response on a Quantum Computer
- Thermodynamic uncertainty relation in thermal transport
- Quantum algorithm for calculating molecular vibronic spectra
- Quantum algorithm for ground state energy estimation using circuit depth with exponentially improved dependence on precision
- Role of Exchange Interactions in the Magnetic Response and Intermolecular Recognition of Chiral Molecules
- Initial state preparation for quantum chemistry on quantum computers
- Reducing molecular electronic Hamiltonian simulation cost for Linear Combination of Unitaries approaches
- Strong coupling effects in quantum thermal transport with the reaction coordinate method
- Analyzing Prospects for Quantum Advantage in Topological Data Analysis
- Two-Unitary Decomposition Algorithm and Open Quantum System Simulation
- Mapping Electronic Decoherence Pathways in Molecules
- Efficient simulation of sparse Markovian quantum dynamics
- Superdiffusive quantum stochastic walk definable of arbitrary directed graph
- Quantum Theory of Nonlinear Thermal Response
- A quantum algorithm for solving open system dynamics on quantum computers using noise
- Magnetic susceptibility of topological semimetals
- Subspace methods for the simulation of molecular response properties on a quantum computer
- Quantum generative model for sampling many-body spectral functions
- Entanglement-assisted phase estimation algorithm for calculating dynamical response functions
- Nonlinear optical responses in superconductors under magnetic fields: quantum geometry and topological superconductivity