Any type of spectroscopy can be efficiently simulated on a quantum computer

TL;DR

This work shows that any type of molecular spectroscopy can be efficiently simulated on a quantum computer using a time-domain correlation-function framework. By mapping double-sided Feynman diagrams to Hadamard-test quantum circuits and encoding nonunitary observables with unitary blocks $M(F_j)=e^{-i\mu F_j}$, the method yields correlation functions $Q_j^{(n)}$ from which the target response functions $R^{(n)}$ are obtained via differentiation. It extends naturally to open systems by replacing unitary evolution with $\mathcal{U}(t)$ and supports both digital and analog quantum platforms, as well as electric and magnetic interactions, including differential spectroscopies. The authors provide a detailed cost analysis showing polynomial scaling in system size for fixed spectroscopy order, implying an exponential improvement over classical frequency-domain approaches. Overall, the framework unifies time-domain spectroscopy across orders and couplings and promises practical quantum-simulation routes for predicting and interpreting molecular spectra.

Abstract

Spectroscopy is the most important method for probing the structure of molecules. However, predicting molecular spectra on classical computers is computationally expensive, with the most accurate methods having a cost that grows exponentially with molecule size. Quantum computers have been shown to simulate simple types of optical spectroscopy efficiently -- with a cost polynomial in molecule size -- using methods such as time-dependent simulations of photoinduced wavepackets. Here, we show that any type of spectroscopy can be efficiently simulated on a quantum computer using a time-domain approach, including spectroscopies of any order, any frequency range, and involving both electric and magnetic transitions. Our method works by computing any spectroscopic correlation function based on the corresponding double-sided Feynman diagram, the canonical description of spectroscopic interactions. The approach can be used to simulate spectroscopy of both closed and open molecular systems using both digital and analog quantum computers.

Figures (3)

• Figure 1: Hadamard test for a two-point correlation function of unitary operators $A$ and $B$Somma2003. $G(t) = \bra{\psi} A(t) B(0) \ket{\psi}$ can be computed from measured expectation values on the ancilla qubit, $G(t)=\langle \sigma_x \rangle+i\langle \sigma_y \rangle$.
• Figure 2: Constructing a quantum circuit for a double-sided Feynman diagram.(a) Example of a double-sided Feynman diagram corresponding to a high-order correlation function. Time increases upwards and the dipole operator acts at the specified times. Additional light-matter interactions may occur between times $t_2$ and $t_i$. Absorption is shown by arrows towards either the bra or the ket and emission by arrows away from them. The dashed arrow indicates the final dipole operator, which produces the observed signal. (b) The corresponding Hadamard test showing how the double-sided Feynman diagram maps onto a simple quantum circuit, with ket-side operators $K$ controlled off the $\ket{1}$ state of the ancilla (solid circle) and the bra-side operators $B$ controlled off $\ket{0}$ (hollow circle). $K$ and $B$ both comprise sequences of time evolution and applications of the exponentiated dipole operators, $M(F_j)=\exp(-i\mu F_j)$; here, $K=M(F_{i+1}) U(\tau_{i}) \cdots U(\tau_1) M(F_1)$ and $B=U(\tau_{i})M(F_i) \cdots M(F_2) U(\tau_1)$. (c) The expanded quantum circuit, with operations applied in the same order as in the Feynman diagram. As in \ref{['fig:simplecorrelation']}, measuring the expectation values $\langle \sigma_x \rangle$ and $\langle \sigma_y \rangle$ produces a correlation function involving $M$, which can then be differentiated to give the desired correlation function involving $\mu$.
• Figure 3: Simulating open systems.(a) The circuit elements of the closed-system simulation from \ref{['fig:dsfd']}, which can be modified to simulate open systems. (b) Modification for simulating an open system with an explicit bath, where the system and the bath are governed by global unitary time evolution and the bath is traced out at the end. (c) Modification for simulating an open system using engineered noise, where experimental noise is used to mimic the effects of open systems. With either modification, the circuits retain the property that the ancilla qubit only controls the application of $M$ and not the time evolution itself.