Response functions are a fundamental aspect of physics; they represent the link between experimental observations and the underlying quantum many-body state. However, this link is often under-appreciated, as the Lehmann formalism for obtaining response functions in linear response has no direct link to experiment. Within the context of quantum computing, and by using a linear response framework, we restore this link by making the experiment an inextricable part of the quantum simulation. This method can be frequency- and momentum-selective, avoids limitations on operators that can be directly measured, and is ancilla-free. As prototypical examples of response functions, we demonstrate that both bosonic and fermionic Green's functions can be obtained, and apply these ideas to the study of a charge-density-wave material on ibm_auckland. The linear response method provides a robust framework for using quantum computers to study systems in physics and chemistry. It also provides new paradigms for computing response functions on classical computers.Response functions are a fundamental aspect of physics; they represent the link between experimental observations and the underlying quantum many-body state. However, this link is often under-appreciated, as the Lehmann formalism for obtaining response functions in linear response has no direct link to experiment. Within the context of quantum computing, and by using a linear response framework, we restore this link by making the experiment an inextricable part of the quantum simulation. This method can be frequency- and momentum-selective, avoids limitations on operators that can be directly measured, and is ancilla-free. As prototypical examples of response functions, we demonstrate that both bosonic and fermionic Green's functions can be obtained, and apply these ideas to the study of a charge-density-wave material on ibm_auckland. The linear response method provides a robust framework for using quantum computers to study systems in physics and chemistry. It also provides new paradigms for computing response functions on classical computers.

arXiv:2302.10219Feb 20, 20231 citation

Quantum Simulation of Non-Hermitian Linear Response via Schrödingerization

Jeongbin Jo

Linear response theory and Green's functions provide a universal framework for understanding dynamical correlations in strongly correlated open quantum systems. While the theoretical foundation for non-Hermitian linear response has been recently established to describe dissipation and fluctuation-dissipation relations (FDR), generalizing these predictions onto practical quantum computers remains a formidable algorithmic challenge due to the intrinsically non-unitary nature of the dynamics. In this work, we present a systematic algorithmic framework that seamlessly transforms non-unitary multi-time correlation functions into a unitary form viable for digital quantum hardware. By mapping the vectorization of the Lindblad master equation into an expanded continuous-variable Liouville space, we employ the Schrödingerization technique to deterministically evaluate the non-Hermitian response. Furthermore, through hardware-aware simulations utilizing a 133-qubit device noise model, we demonstrate that our unitary framework robustly preserves the fundamental spectral information -- specifically the phase and oscillatory frequency -- against realistic depolarizing channels. By bypassing explicit non-unitary mid-circuit measurements, this approach intrinsically supports the integration of standard quantum error mitigation protocols, providing a scalable algorithmic blueprint for probing open-system universality on near-term hardware.Linear response theory and Green's functions provide a universal framework for understanding dynamical correlations in strongly correlated open quantum systems. While the theoretical foundation for non-Hermitian linear response has been recently established to describe dissipation and fluctuation-dissipation relations (FDR), generalizing these predictions onto practical quantum computers remains a formidable algorithmic challenge due to the intrinsically non-unitary nature of the dynamics. In this work, we present a systematic algorithmic framework that seamlessly transforms non-unitary multi-time correlation functions into a unitary form viable for digital quantum hardware. By mapping the vectorization of the Lindblad master equation into an expanded continuous-variable Liouville space, we employ the Schrödingerization technique to deterministically evaluate the non-Hermitian response. Furthermore, through hardware-aware simulations utilizing a 133-qubit device noise model, we demonstrate that our unitary framework robustly preserves the fundamental spectral information -- specifically the phase and oscillatory frequency -- against realistic depolarizing channels. By bypassing explicit non-unitary mid-circuit measurements, this approach intrinsically supports the integration of standard quantum error mitigation protocols, providing a scalable algorithmic blueprint for probing open-system universality on near-term hardware.

quant-pharXiv:2603.17342Mar 19, 20260 citations

Efficient Quantum Algorithm for Computing n -time Correlation Functions

Julen Simon Pedernales, Roberto Di Candia, I. L. Egusquiza +2 more

We propose a method for computing n-time correlation functions of arbitrary spinorial, fermionic, and bosonic operators, consisting of an efficient quantum algorithm that encodes these correlations in an initially added ancillary qubit for probe and control tasks. For spinorial and fermionic systems, the reconstruction of arbitrary n-time correlation functions requires the measurement of two ancilla observables, while for bosonic variables time derivatives of the same observables are needed. Finally, we provide examples applicable to different quantum platforms in the frame of the linear response theory.We propose a method for computing n-time correlation functions of arbitrary spinorial, fermionic, and bosonic operators, consisting of an efficient quantum algorithm that encodes these correlations in an initially added ancillary qubit for probe and control tasks. For spinorial and fermionic systems, the reconstruction of arbitrary n-time correlation functions requires the measurement of two ancilla observables, while for bosonic variables time derivatives of the same observables are needed. Finally, we provide examples applicable to different quantum platforms in the frame of the linear response theory.

arXiv:1401.2430Physical Review LettersJul 10, 201472 citations

Dynamical quantum simulations as laboratories for quantum information

Su Yeon Chang, Hailey S. Murray, Brian Barch +5 more

Dynamical quantum simulations are commonly designed to access a particular response function or correlation function. Yet the underlying protocol prepares a family of many-body states that contains information well beyond the observable for which the simulation was originally designed. In this work, we explore the idea of using these states as laboratories for quantum information. As a case study, we consider the local-pulse protocols used to compute Green functions in finite XX and XXX spin chains, and we interpret opposite source rotations as encoding a classical bit into the many-body system. This allows us to follow how the resulting record propagates, how it is encoded across local subsystems, and how readily it can be accessed with different measurements. We also find a clear separation between representation and readout. While fermionic covariance data exactly reconstruct the signed response in the XX chain, simple spin measurements recover a larger fraction of the locally available information in the XXX chain. This reversed ordering persists when we move from finite-pulse discrimination to local source-angle estimation. Going beyond the source record, the same reduced states also allow us to reinterpret results in terms of Bell state recovery and quantum communication rates, as well as providing direct access to the evolving bipartite and genuine multipartite entanglement of the system. Our results show that dynamical quantum simulations developed for response calculations can naturally be used to ask a much broader set of quantum-information questions about the many-body states they already prepare.Dynamical quantum simulations are commonly designed to access a particular response function or correlation function. Yet the underlying protocol prepares a family of many-body states that contains information well beyond the observable for which the simulation was originally designed. In this work, we explore the idea of using these states as laboratories for quantum information. As a case study, we consider the local-pulse protocols used to compute Green functions in finite XX and XXX spin chains, and we interpret opposite source rotations as encoding a classical bit into the many-body system. This allows us to follow how the resulting record propagates, how it is encoded across local subsystems, and how readily it can be accessed with different measurements. We also find a clear separation between representation and readout. While fermionic covariance data exactly reconstruct the signed response in the XX chain, simple spin measurements recover a larger fraction of the locally available information in the XXX chain. This reversed ordering persists when we move from finite-pulse discrimination to local source-angle estimation. Going beyond the source record, the same reduced states also allow us to reinterpret results in terms of Bell state recovery and quantum communication rates, as well as providing direct access to the evolving bipartite and genuine multipartite entanglement of the system. Our results show that dynamical quantum simulations developed for response calculations can naturally be used to ask a much broader set of quantum-information questions about the many-body states they already prepare.

quant-pharXiv:2610.37589Oct 28, 20260 citations

The formal framework of linear-response TDDFT

Carsten A. Ullrich

This chapter discusses the linear-response framework of time-dependent density-functional theory (TDDFT). It begins with a thorough and self-contained exposition of general linear-response theory for many-body systems. The time-dependent as well as the frequency-dependent response are discussed. Several exact representations and properties of the density-density response function are reviewed, such as the Lehmann representation and fluctuation-dissipation theorem, and the Kramers-Kronig relations. It is shown how several important spectroscopic observables are obtained from linear-response theory. Then, the TDDFT formulation of linear-response theory is derived. The key quantity in this formalism is the so-called exchange-correlation kernel. The remainder of the chapter demonstrates how this linear-response formalism can be used to calculate excitation energies in principle exactly with TDDFT. The Casida equation is derived, as well as several approximate schemes. A comparison is made with time-dependent Hartree-Fock theory.This chapter discusses the linear-response framework of time-dependent density-functional theory (TDDFT). It begins with a thorough and self-contained exposition of general linear-response theory for many-body systems. The time-dependent as well as the frequency-dependent response are discussed. Several exact representations and properties of the density-density response function are reviewed, such as the Lehmann representation and fluctuation-dissipation theorem, and the Kramers-Kronig relations. It is shown how several important spectroscopic observables are obtained from linear-response theory. Then, the TDDFT formulation of linear-response theory is derived. The key quantity in this formalism is the so-called exchange-correlation kernel. The remainder of the chapter demonstrates how this linear-response formalism can be used to calculate excitation energies in principle exactly with TDDFT. The Casida equation is derived, as well as several approximate schemes. A comparison is made with time-dependent Hartree-Fock theory.

Oxford University Press eBooksDec 22, 20110 citations

NEW TECHNIQUES IN COMPUTATIONAL QUANTUM FIELD THEORY

Tao Wang

In quantum many-body physics, Quantum Field Theory (QFT) provides powerful tools to describe collective particle behavior. This framework employs three crucial theoretical tools: Green's functions for characterizing particle propagation and response to perturbations, Feynman diagrams for organizing perturbative expansions of quantum processes, and renormalization for improving the convergence of diagrammatic series. A key challenge in QFT is the efficient representation of finite-temperature Green's functions, particularly at low temperatures. We develop a universal framework linking the effective degrees of freedom in these functions to the rank of Lehmann eigenspace, explaining the observed compressibility in Discrete Lehmann representation (DLR). To address numerical instability of DLR in self-consistent solvers, we introduce the symmetrized discrete Lehmann representation (SDLR), which incorporates physical symmetries while maintaining computational efficiency. Applying SDLR, we study phonon-mediated superconductivity in the uniform electron gas (UEG), focusing on the Coulomb interaction effects. Our analysis reveals that the conventional Coulomb pseudopotential $\mu^*$ stems from two distinct effects: modifications to the Fermi Liquid factor and alterations of effective couplings. To extend our first-principle approach to lower electron densities and real materials, vertex corrections in higher-order Feynman diagrams must be systematically evaluated. This presents a significant challenge due to the factorial growth in diagram numbers at higher orders. We address this by transforming Feynman diagrams into computational graphs, enabling efficient computation reuse across shared sub-diagrams. Furthermore, we incorporate Taylor-mode automatic differentiation to streamline the computationally intensive diagrammatic re-expansion process. This approach reduces the computational complexity from exponential to sub-exponential scale relative to the differential order, as demonstrated through calculations of the UEG effective mass ratio. This research advances computational approaches within QFT by combining theoretical physics with advanced computational methods, establishing a foundation for future interdisciplinary studies of quantum many-body systems.In quantum many-body physics, Quantum Field Theory (QFT) provides powerful tools to describe collective particle behavior. This framework employs three crucial theoretical tools: Green's functions for characterizing particle propagation and response to perturbations, Feynman diagrams for organizing perturbative expansions of quantum processes, and renormalization for improving the convergence of diagrammatic series. A key challenge in QFT is the efficient representation of finite-temperature Green's functions, particularly at low temperatures. We develop a universal framework linking the effective degrees of freedom in these functions to the rank of Lehmann eigenspace, explaining the observed compressibility in Discrete Lehmann representation (DLR). To address numerical instability of DLR in self-consistent solvers, we introduce the symmetrized discrete Lehmann representation (SDLR), which incorporates physical symmetries while maintaining computational efficiency. Applying SDLR, we study phonon-mediated superconductivity in the uniform electron gas (UEG), focusing on the Coulomb interaction effects. Our analysis reveals that the conventional Coulomb pseudopotential $\mu^*$ stems from two distinct effects: modifications to the Fermi Liquid factor and alterations of effective couplings. To extend our first-principle approach to lower electron densities and real materials, vertex corrections in higher-order Feynman diagrams must be systematically evaluated. This presents a significant challenge due to the factorial growth in diagram numbers at higher orders. We address this by transforming Feynman diagrams into computational graphs, enabling efficient computation reuse across shared sub-diagrams. Furthermore, we incorporate Taylor-mode automatic differentiation to streamline the computationally intensive diagrammatic re-expansion process. This approach reduces the computational complexity from exponential to sub-exponential scale relative to the differential order, as demonstrated through calculations of the UEG effective mass ratio. This research advances computational approaches within QFT by combining theoretical physics with advanced computational methods, establishing a foundation for future interdisciplinary studies of quantum many-body systems.

Nov 10, 20250 citations

\mu^*

stems from two distinct effects: modifications to the Fermi Liquid factor and alterations of effective couplings. To extend our first-principle approach to lower electron densities and real materials, vertex corrections in higher-order Feynman diagrams must be systematically evaluated. This presents a significant challenge due to the factorial growth in diagram numbers at higher orders. We address this by transforming Feynman diagrams into computational graphs, enabling efficient computation reuse across shared sub-diagrams. Furthermore, we incorporate Taylor-mode automatic differentiation to streamline the computationally intensive diagrammatic re-expansion process. This approach reduces the computational complexity from exponential to sub-exponential scale relative to the differential order, as demonstrated through calculations of the UEG effective mass ratio. This research advances computational approaches within QFT by combining theoretical physics with advanced computational methods, establishing a foundation for future interdisciplinary studies of quantum many-body systems.