arXiv subjects

David A. Mazziotti

Publications and source records attributed to David A. Mazziotti.

At least 37 records · Page 2Linked to original sources

arXiv2024

Molecular Origins of Exciton Condensation in Van der Waals Heterostructure Bilayers

Recent experiments have realized exciton condensation in bilayer materials such as graphene double layers and the van der Waals heterostructure MoSe$_2$-WSe$_2$ with the potential for nearly frictionless energy transport. Here we computationally observe the microscopic beginnings of exciton condensation in a molecular-scale fragment of MoSe$_2$-WSe$_2$, using advanced electronic structure methods based on reduced density matrices. We establish a connection between the signature of exciton condensation -- the presence of a large eigenvalue in the particle-hole reduced density matrix -- and experimental evidence of exciton condensation in the material. The presence of a "critical seed" of exciton condensation in a molecular-scale fragment of a heterostructure bilayer provides insight into how local short-range strongly correlated effects may give rise to macroscopic exciton condensation. We find that molecular-scale properties such as layer alignment and interlayer distance can impact the formation of nonclassical long-range order in heterostructure bilayers, demonstrating the importance of geometric considerations for the rational design of exciton condensate material. Mechanistic insights into the microscopic origins of exciton condensation have potential implications for the design and development of new materials with enhanced energy transport properties.

cond-mat.mes-hall↗

arXiv2024

Enhancing Density Functional Theory for Static Correlation in Large Molecules

A critical challenge for density functional theory (DFT) in practice is its limited ability to treat static electron correlation, leading to errors in its prediction of charges, multiradicals, and reaction barriers. Recently, we combined one- and two-electron reduced density matrix theories with DFT to obtain a universal $O(N^3)$ generalization of DFT for static correlation. In this Letter, we enhance the theory's treatment of large molecules by renormalizing the trace of the two-electron identity matrix in the correction using Cauchy-Schwarz inequalities of the electron-electron repulsion matrix. We apply the resulting functional theory to linear hydrogen chains as well as the prediction of the singlet-triplet gap and equilibrium geometries of a series of acenes. This renormalization of the generalized DFT retains the $O(N^{3})$ computational scaling of DFT while enabling the accurate treatment of static correlation for a broad range of molecules and materials.

physics.chem-ph↗

arXiv2024

Characterizing conical intersections of nucleobases on quantum computers

Hybrid quantum-classical computing algorithms offer significant potential for accelerating the calculation of the electronic structure of strongly correlated molecules. In this work, we present the first quantum simulation of conical intersections (CIs) in a biomolecule, cytosine, using a superconducting quantum computer. We apply the Contracted Quantum Eigensolver (CQE) -- with comparisons to conventional Variational Quantum Deflation (VQD) -- to compute the near-degenerate ground and excited states associated with the conical intersection, a key feature governing the photostability of DNA and RNA. The CQE is based on an exact ansatz for many-electron molecules in the absence of noise -- a critically important property for resolving strongly correlated states at CIs. Both methods demonstrate promising accuracy when compared with exact diagonalization, even on noisy intermediate-scale quantum computers, highlighting their potential for advancing the understanding of photochemical and photobiological processes. The ability to simulate these intersections is critical for advancing our knowledge of biological processes like DNA repair and mutation, with potential implications for molecular biology and medical research.

quant-ph↗

arXiv2024

Enhanced Shadow Tomography of Molecular Excited States from Enforcing $N$-representability Conditions by Semidefinite Programming

Excited-state properties of highly correlated systems are key to understanding photosynthesis, luminescence, and the development of novel optical materials, but accurately capturing their interactions is computationally costly. We present an algorithm that combines classical shadow tomography with physical constraints on the two-electron reduced density matrix (2-RDM) to treat excited states. The method reduces the number of measurements of the many-electron 2-RDM on quantum computers by (i) approximating the quantum state through a random sampling technique called shadow tomography and (ii) ensuring that the 2-RDM represents an $N$-electron system through imposing $N$-representability constraints by semidefinite programming. This generalizes recent work on the $N$-representability-enhanced shadow tomography of ground-state 2-RDMs. We compute excited-state energies and 2-RDMs of the H$_4$ chain and analyze the critical points along the photoexcited reaction pathway from gauche-1,3-butadiene to bicyclobutane via a conical intersection. The results show that the generalized shadow tomography retains critical multireference correlation effects while significantly reducing the number of required measurements, offering a promising avenue for the efficient treatment of electronically excited states on quantum devices.

quant-ph↗

arXiv2024

Shadow Ansatz for the Many-Fermion Wave Function in Scalable Molecular Simulations on Quantum Computing Devices

Here we show that shadow tomography can generate an efficient and exact ansatz for the many-fermion wave function on quantum devices. We derive the shadow ansatz -- a product of transformations applied to the mean-field wave function -- by exploiting a critical link between measurement and preparation. Each transformation is obtained by measuring a classical shadow of the residual of the contracted Schrödinger equation (CSE), the many-electron Schrödinger equation (SE) projected onto the space of two electrons. We show that the classical shadows of the CSE vanish if and only if the wave function satisfies the SE and, hence, that randomly sampling only the two-electron space yields an exact ansatz regardless of the total number of electrons. We demonstrate the ansatz's advantages for scalable simulations -- fewer measurements and shallower circuits -- by computing H$_{3}$ on simulators and a quantum device.

quant-ph↗

arXiv2024

Simulating Chemistry on Bosonic Quantum Devices

Bosonic quantum devices offer a novel approach to realize quantum computations, where the quantum two-level system (qubit) is replaced with the quantum (an)harmonic oscillator (qumode) as the fundamental building block of the quantum simulator. The simulation of chemical structure and dynamics can then be achieved by representing or mapping the system Hamiltonians in terms of bosonic operators. In this perspective, we review recent progress and future potential of using bosonic quantum devices for addressing a wide range of challenging chemical problems, including the calculation of molecular vibronic spectra, the simulation of gas-phase and solution-phase adiabatic and nonadiabatic chemical dynamics, the efficient solution of molecular graph theory problems, and the calculations of electronic structure.

quant-ph↗

arXiv2024

Quantum Algorithms and Applications for Open Quantum Systems

Accurate models for open quantum systems -- quantum states that have non-trivial interactions with their environment -- may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction of static and dynamic molecular properties. In recent years, quantum algorithms have been leveraged for the computation of open quantum systems as the predicted quantum advantage of quantum devices over classical ones may allow previously inaccessible applications. Accomplishing this goal will require input and expertise from different research perspectives, as well as the training of a diverse quantum workforce, making a compilation of current quantum methods for treating open quantum systems both useful and timely. In this Review, we first provide a succinct summary of the fundamental theory of open quantum systems and then delve into a discussion on recent quantum algorithms. We conclude with a discussion of pertinent applications, demonstrating the applicability of this field to realistic chemical, biological, and material systems.

quant-ph↗

arXiv2024

Unitary Dynamics for Open Quantum Systems with Density-Matrix Purification

Accurate modeling of quantum systems interacting with environments requires addressing non-unitary dynamics, which significantly complicates computational approaches. In this work, we enhance an open quantum system (OQS) theory using density-matrix purification, enabling a unitary description of dynamics by entangling the system with an environment of equal dimension. We first establish the connection between density-matrix purification and conventional OQS methods. We then demonstrate the standalone applicability of purification theory by deriving system-environment interactions from fundamental design principles. Using model systems, we show that the purification approach extends beyond the complete positivity condition and effectively models both Markovian and non-Markovian dynamics. Finally, we implement density-matrix purification on a quantum simulator, illustrating its capability to map non-unitary OQS dynamics onto a unitary framework suitable for quantum computers.

quant-ph↗

arXiv2024

Exact Ansatz of Fermion-Boson Systems for a Quantum Device

We present an exact ansatz for the eigenstate problem of mixed fermion-boson systems that can be implemented on quantum devices. Based on a generalization of the electronic contracted Schrödinger equation (CSE), our approach guides a trial wave function to the ground state of any arbitrary mixed Hamiltonian by directly measuring residuals of the mixed CSE on a quantum device. Unlike density-functional and coupled-cluster theories applied to electron-phonon or electron-photon systems, the accuracy of our approach is not limited by the unknown exchange-correlation functional or the uncontrolled form of the exponential ansatz. To test the performance of the method, we study the Tavis-Cummings model, commonly used in polaritonic quantum chemistry. Our results demonstrate that the CSE is a powerful tool in the development of quantum algorithms for solving general fermion-boson many-body problems.

quant-ph↗

arXiv2024

Quantum Simulation of Conical Intersections

We explore the simulation of conical intersections (CIs) on quantum devices, setting the groundwork for potential applications in nonadiabatic quantum dynamics within molecular systems. The intersecting potential energy surfaces of H$_{3}^{+}$ are computed from a variance-based contracted quantum eigensolver. We show how the CIs can be correctly described on quantum devices using wavefunctions generated by the anti-Hermitian contracted Schr{ö}dinger equation ansatz, which is a unitary transformation of wavefunctions that preserves the topography of CIs. A hybrid quantum-classical procedure is used to locate the seam of CIs. Additionally, we discuss the quantum implementation of the adiabatic to diabatic transformation and its relation to the geometric phase effect. Results on noisy intermediate-scale quantum devices showcase the potential of quantum computers in dealing with problems in nonadiabatic chemistry.

quant-ph↗

arXiv2023

Fewer measurements from shadow tomography with $N$-representability conditions

Classical shadow tomography provides a randomized scheme for approximating the quantum state and its properties at reduced computational cost with applications in quantum computing. In this Letter we present an algorithm for realizing fewer measurements in the shadow tomography of many-body systems by imposing $N$-representability constraints. Accelerated tomography of the two-body reduced density matrix (2-RDM) is achieved by combining classical shadows with necessary constraints for the 2-RDM to represent an $N$-body system, known as $N$-representability conditions. We compute the ground-state energies and 2-RDMs of hydrogen chains and the N$_{2}$ dissociation curve. Results demonstrate a significant reduction in the number of measurements with important applications to quantum many-body simulations on near-term quantum devices.

quant-ph↗

arXiv2023

Quantum simulation of excited states from parallel contracted quantum eigensolvers

Computing excited-state properties of molecules and solids is considered one of the most important near-term applications of quantum computers. While many of the current excited-state quantum algorithms differ in circuit architecture, specific exploitation of quantum advantage, or result quality, one common feature is their rooting in the Schrödinger equation. However, through contracting (or projecting) the eigenvalue equation, more efficient strategies can be designed for near-term quantum devices. Here we demonstrate that when combined with the Rayleigh-Ritz variational principle for mixed quantum states, the ground-state contracted quantum eigensolver (CQE) can be generalized to compute any number of quantum eigenstates simultaneously. We introduce two excited-state (anti-Hermitian) CQEs that perform the excited-state calculation while inheriting many of the remarkable features of the original ground-state version of the algorithm, such as its scalability. To showcase our approach, we study several model and chemical Hamiltonians and investigate the performance of different implementations.

quant-ph↗

arXiv2023

Quantum Simulation of Bosons with the Contracted Quantum Eigensolver

Quantum computers are promising tools for simulating many-body quantum systems due to their potential scaling advantage over classical computers. While significant effort has been expended on many-fermion systems, here we simulate a model entangled many-boson system with the contracted quantum eigensolver (CQE). We generalize the CQE to many-boson systems by encoding the bosonic wavefunction on qubits. The CQE provides a compact ansatz for the bosonic wave function whose gradient is proportional to the residual of a contracted Schrödinger equation. We apply the CQE to a bosonic system, where $N$ quantum harmonic oscillators are coupled through a pairwise quadratic repulsion. The model is relevant to the study of coupled vibrations in molecular systems on quantum devices. Results demonstrate the potential efficiency of the CQE in simulating bosonic processes such as molecular vibrations with good accuracy and convergence even in the presence of noise.

quant-ph↗

arXiv2023

Electronic Excited States from a Variance-Based Contracted Quantum Eigensolver

Electronic excited states of molecules are central to many physical and chemical processes, and yet they are typically more difficult to compute than ground states. In this paper we leverage the advantages of quantum computers to develop an algorithm for the highly accurate calculation of excited states. We solve a contracted Schrödinger equation (CSE) -- a contraction (projection) of the Schrödinger equation onto the space of two electrons -- whose solutions correspond identically to the ground and excited states of the Schrödinger equation. While recent quantum algorithms for solving the CSE, known as contracted quantum eigensolvers (CQE), have focused on ground states, we develop a CQE based on the variance that is designed to optimize rapidly to a ground or excited state. We apply the algorithm in a classical simulation without noise to computing the ground and excited states of H$_{4}$ and BH.

quant-ph↗

arXiv2023

Quantum Many-body Theory from a Solution of the $N$-representability Problem

Here we present a many-body theory based on a solution of the $N$-representability problem in which the ground-state two-particle reduced density matrix (2-RDM) is determined directly without the many-particle wave function. We derive an equation that re-expresses physical constraints on higher-order RDMs to generate direct constraints on the 2-RDM, which are required for its derivation from an $N$-particle density matrix, known as $N$-representability conditions. The approach produces a complete hierarchy of 2-RDM constraints that do not depend explicitly upon the higher RDMs or the wave function. By using the two-particle part of a unitary decomposition of higher-order constraint matrices, we can solve the energy minimization by semidefinite programming in a form where the low-rank structure of these matrices can be potentially exploited. We illustrate by computing the ground-state electronic energy and properties of the H$_{8}$ ring.

quant-ph↗

arXiv2023

Verifiably Exact Solution of the Electronic Schrödinger Equation on Quantum Devices

Quantum computers have the potential for an exponential speedup of classical molecular computations. However, existing algorithms have limitations; quantum phase estimation (QPE) algorithms are intractable on current hardware while variational quantum eigensolvers (VQE) are dependent upon approximate wave functions without guaranteed convergence. In this Article we present an algorithm that yields verifiably exact solutions of the many-electron Schrödinger equation. Rather than solve the Schrödinger equation directly, we solve its contraction over all electrons except two, known as the contracted Schrödinger equation (CSE). The CSE generates an exact wave function ansatz, constructed from a product of two-body-based non-unitary transformations, that scales polynomially with molecular size and hence, provides a potentially exponential acceleration of classical molecular electronic structure calculations on ideal quantum devices. We demonstrate the algorithm on both quantum simulators and noisy quantum computers with applications to H$_{2}$ dissociation and the rectangle-to-square transition in H$_{4}$. The CSE quantum algorithm, which is a type of contracted quantum eigensolver (CQE), provides a significant step towards realizing verifiably accurate but scalable molecular simulations on quantum devices.

quant-ph↗

arXiv2022

Comparison of Density-Matrix Corrections to Density Functional Theory

Density functional theory (DFT), one of the most widely utilized methods available to computational chemistry, fails to describe systems with statically correlated electrons. To address this shortcoming, in previous work we transformed DFT into a one-electron reduced density matrix theory (1-RDMFT) via the inclusion of a quadratic one-electron reduced density matrix (1-RDM) correction. Here, we combine our 1-RDMFT approach with different DFT functionals as well as Hartree-Fock to elucidate the method's dependence on the underlying functional selection. Furthermore, we generalize the information density matrix functional theory (iDMFT), recently developed as a correction to the Hartree-Fock method, by incorporating density functionals in place of the Hartree-Fock functional. We relate iDMFT mathematically to our approach and benchmark the two with a common set of functionals and systems.

physics.chem-ph↗

arXiv2022

Interplay of Electronic and Geometric Structure Tunes Organic Biradical Character in Bimetallic Tetrathiafulvalene Tetrathiolate Complexes

The synthesis and design of organic biradicals with tunable singlet-triplet gaps has become the subject of significant research interest, owing to their possible photochemical applications and use in the development of molecular switches and conductors. Recently, tetrathiafulvalene tetrathiolate (TTFtt) has been demonstrated to exhibit such organic biradical character in doubly ionized bimetallic complexes. In this article we use high-level {\em ab initio} calculations to interrogate the electronic structure of a series of TTFtt-bridged metal complexes, resolving the factors governing their biradical character and singlet-triplet gaps. We show that the degree of biradical character correlates with a readily measured experimental predictor, the central TTFtt C-C bond length, and that it may be described by a one-parameter model, providing valuable insight for the future rational design of TTFtt based biradical compounds and materials.

cond-mat.mtrl-sci↗