arXiv subjects

Francesco A. Evangelista

Publications and source records attributed to Francesco A. Evangelista.

At least 19 recordsLinked to original sources

arXiv2026

Reaching the thermodynamic limit of periodic CCSD cohesive energies and band gaps

The high computational cost of periodic coupled-cluster theory has limited the density of Brillouin zone sampling, yielding finite-size errors that need to be removed by extrapolation. Here we report the development and application of a distributed-memory software implementation of periodic coupled-cluster theory with single and double excitations (CCSD) that runs efficiently on up to 12 nodes with 96 cores each. This new implementation allows ground-state and excited-state calculations in which the Brillouin zone is sampled with up to $6^3=216$ $k$-points, allowing us to reliably extrapolate to the thermodynamic limit. For eight simple semiconductors and insulators, we report the cohesive energy and band gap, which are converged to 0.1 eV, providing definitive benchmark numbers for the CCSD level of theory. Compared to experimental values, average errors for the cohesive energy are 0.1-0.2 eV (typically an underestimate), and average errors for the band gap are about 0.4 eV (typically an overestimate).

physics.chem-ph↗

arXiv2026

Spin-Adapted Fermionic Unitaries: From Lie Algebras to Compact Quantum Circuits

Conservation of symmetries is crucial for reliable quantum simulations of molecular systems, yet compact circuit implementations of fully symmetry-adapted fermionic unitaries have remained elusive beyond the simplest excitation classes. Here we address this issue for the set of singlet spin-adapted generalized singles and doubles operators (saGSD). Using the Wei--Norman approach, we derive exact product formulas that express spin-adapted fermionic unitaries as products of elementary spin-orbital unitaries. To obtain closed-form parameters in the more challenging 28- and 84-dimensional dynamical Lie algebras, we develop a computational discovery-and-verification protocol combining numerical optimization, parameter-structure identification, closed-form inference, and exact validation against reduced Wei--Norman equations. We also introduce an algorithm for constructing closed-form fermionic unitary transformations on Krylov subspaces and extend the fermionic-excitation-based circuit formalism to generators consisting of an anti-Hermitian fermionic string multiplied by arbitrary linear combinations of number-operator products. Together, these developments yield the most compact circuits to date for exact implementation of saGSD unitaries. Finally, for non fully spin-polarized systems, we identify a compact universal symmetry-adapted subset of saGSD that further reduces the quantum resources required for chemically relevant simulations.

quant-ph↗

arXiv2026

Witnessing Spin-Orbital Entanglement using Resonant Inelastic X-Ray Scattering

Entanglement plays a central role in quantum technologies, yet its characterization and control in materials remain challenging. Recent developments in spectrum-based entanglement witnesses have enabled new strategies for quantifying many-body entanglement in macroscopic materials. Here, we develop a protocol for detecting spin-orbital entanglement using experiment-accessible resonant inelastic x-ray scattering (RIXS). Central to our approach is the construction of a Hermitian generator from experimentally measurable spectra, which allows us to compute the quantum Fisher information (QFI) available in spin--orbital systems. The resulting QFI provides upper bounds for $k$-producible states and thus serves as a robust witness of spin-orbital entanglement. To account for realistic experimental limitations, we further extend our framework to include relaxed QFI bounds applicable to measurements lacking full polarization resolution.

quant-ph↗

arXiv2026

One-Step Relativistic Driven Similarity Renormalization Group Multireference Perturbation Theory

We present an efficient implementation of a one-step relativistic second-order multireference perturbation theory based on the multireference driven similarity renormalization group (MR-DSRG) using the exact two-component (X2C) Hamiltonian, which we denote X2C-DSRG-MRPT2. We show that the X2C-DSRG-MRPT2 method can accurately capture spin--orbit coupling (SOC) effects in the electronic structure of strongly correlated systems containing elements across the periodic table. We further demonstrate that the X2C-DSRG-MRPT2 method, through its variational treatment of SOC effects, can yield spin--orbit splittings with mean absolute percentage errors consistently below 7% with respect to experimental values for systems containing up to sixth row elements. With its modest computational scaling (fifth power in system size) and high accuracy, X2C-DSRG-MRPT2 provides a promising avenue for the routine treatment of relativistic effects in strongly correlated molecular systems.

physics.chem-ph↗

arXiv2026

The Python Simulations of Chemistry Framework: 10 years of an open-source quantum chemistry project

Over the past decade, the Python-based Simulations of Chemistry Framework (PySCF) has developed into a widely used open-source platform for electronic structure theory and quantum chemical method development. This article reviews the major advances since the previous overview in 2020, covering new modules and methodology, infrastructure changes, and performance benchmarks.

physics.chem-ph↗

arXiv2025

Symmetry Dilemmas in Quantum Computing for Chemistry: A Comprehensive Analysis

Symmetry adaptation, universality, and gate efficiency are central but often competing requirements in quantum algorithms for electronic structure and many-body physics. For example, fully symmetry-adapted universal operator pools typically generate long and deep quantum circuits, gate-efficient universal operator pools generally break symmetries, and gate-efficient fully symmetry-adapted operator pools may not be universal. In this work, we analyze such symmetry dilemmas both theoretically and numerically. On the theory side, we prove that the popular, gate-efficient operator pool consisting of singlet spin-adapted singles and perfect-pairing doubles is not universal when spatial symmetry is enforced. To demonstrate the strengths and weaknesses of the three types of pools, we perform numerical simulations using an adaptive algorithm paired with operator pools that are (i) fully symmetry-adapted and universal, (ii) fully symmetry-adapted and non-universal, and (iii) breaking a single symmetry and are universal. Our numerical simulations encompass three physically relevant scenarios in which the target state is (i) the global ground state, (ii) the ground state crossed by a state differing in multiple symmetry properties, and (iii) the ground state crossed by a state differing in a single symmetry property. Our results show when symmetry-breaking but universal pools can be used safely, when enforcing at least one distinguishing symmetry suffices, and when a particular symmetry must be rigorously preserved to avoid variational collapse. Together, the formal and numerical analysis provides a practical guide for designing and benchmarking symmetry-adapted operator pools that balance universality, resource requirements, and robust state targeting in quantum simulations for chemistry.

quant-ph↗

arXiv2025

Clifford Transformations for Fermionic Quantum Systems: From Paulis to Majoranas to Fermions

Clifford gates and transformations, which map products of elementary Pauli or Majorana operators to other such products, are foundational in quantum computing, underpinning the stabilizer formalism, error-correcting codes, magic state distillation, quantum communication and cryptography, and qubit tapering. Moreover, circuits composed entirely of Clifford gates are classically simulatable, highlighting their computational significance. In this work, we extend the concept of Clifford transformations to fermionic systems. We demonstrate that fermionic Clifford transformations are generated by half-body and pair operators, providing a systematic framework for their characterization. Additionally, we establish connections with fermionic mean-field theories and applications in qubit tapering, offering insights into their broader implications in quantum computing.

quant-ph↗

arXiv2025

Multireference equation-of-motion driven similarity renormalization group for X-ray photoelectron spectra

We formulate and implement the core-valence separated multireference equation-of-motion driven similarity renormalization group method (CVS-IP-EOM-DSRG) for simulating X-ray photoelectron spectra (XPS) of strongly correlated molecular systems. This method is numerically robust and computationally efficient, delivering accurate core-ionization energies with O(N^4) scaling relative to basis set size N in the EOM step. To ensure rigorous core intensivity, we propose a simple modification of the ground-state MR-DSRG formalism. We develop and compare three variants of the theory based on different approximations of the effective Hamiltonian: two derived from low-order perturbative methods (DSRG-MRPT2 and DSRG-MRPT3), and one from a non-perturbative scheme truncated to 1- and 2-body operators [MR-LDSRG(2)]. We benchmark the CVS-IP-EOM-DSRG methods by computing vertical core-ionization energies for a representative molecular test set and comparing results against established single-reference and multireference methods. To demonstrate the applicability of CVS-IP-EOM-DSRG to strongly correlated systems, we compute the potential energy curves and vibrationally resolved XPS of N2 and CO and the XPS of ozone. Comparison with experimental data and other high-level theoretical results shows that all three CVS-IP-EOM-DSRG variants accurately predict vertical ionization energies, but only DSRG-MRPT3 and MR-LDSRG(2) levels of theory reliably capture the full dissociation behavior and reproduce the experimental vibrational structure.

physics.chem-ph↗

arXiv2025

Multireference equation-of-motion driven similarity renormalization group: theoretical foundations and applications to ionized states

We present a formulation and implementation of an equation-of-motion (EOM) extension of the multireference driven similarity renormalization group (MR-DSRG) formalism for ionization potentials (IP-EOM-DSRG). The IP-EOM-DSRG formalism results in a Hermitian generalized eigenvalue problem, delivering accurate ionization potentials for systems with strongly correlated ground and excited states. The EOM step scales as $O(N^5)$ with the basis set size $N$, allowing for efficient calculation of spectroscopic properties, such as transition energies and intensities. The IP-EOM-DSRG formalism is combined with three truncation schemes of the parent MR-DSRG theory: an iterative nonperturbative method with up to two-body excitations [MR-LDSRG(2)] and second- and third-order perturbative approximations [DSRG-MRPT2/3]. We benchmark these variants by computing 1) the vertical valence ionization potentials of a series of small molecules at both equilibrium and stretched geometries; 2) the spectroscopic constants of several low-lying electronic states of the OH, CN, N2+, and CO+ radicals; and 3) the binding curves of low-lying electronic states of the CN radical. A comparison with experimental data and theoretical results shows that all three IP-EOM-DSRG methods accurately reproduce the vertical ionization potentials and spectroscopic constants of these systems. Notably, the DSRG-MRPT3 and MR-LDSRG(2) versions outperform several state-of-the-art multireference methods of comparable or higher cost.

physics.chem-ph↗

arXiv2025

Mutual Correlation

Quantifying correlation and complexity in quantum many-body states is central to advancing theoretical and computational chemistry, physics, and quantum information science. This work introduces a novel framework, mutual correlation, based on the Frobenius norm squared of the two-body reduced density matrix cumulant. Through systematic partitioning of the cumulant norm, mutual correlation quantifies nonadditive correlations among interacting subsystems. Benchmark studies on model systems, including H$_{10}$, N$_{2}$, and p-benzyne, demonstrate its efficacy and computational advantage compared to entropy-based metrics such as orbital mutual information. Maximally correlated orbitals, obtained by maximizing a nonlinear cost function of the mutual correlation, are also considered to identify a basis-independent partitioning of correlation. This study suggests that mutual correlation is a broadly applicable metric, useful in active space selection and the interpretation of electronic states.

physics.chem-ph↗

arXiv2025

Closed-Form Expressions for Unitaries of Spin-Adapted Fermionic Operators

One of the open challenges in quantum computing simulations of problems of chemical interest is the proper enforcement of spin symmetry. Efficient quantum circuits implementing unitaries generated by spin-adapted operators remain elusive, while naïve Trotterization schemes break spin symmetry. In this work, we analyze the mathematical structure of spin-adapted operators and derive closed-form expressions for unitaries generated by singlet spin-adapted generalized single and double excitations. These results represent significant progress toward the economical enforcement of spin symmetry in quantum simulations.

quant-ph↗

arXiv2025

Exact closed-form unitary transformations of fermionic operators

Unitary transformations play a fundamental role in many-body physics, and except for special cases, they are not expressible in closed form. We present closed-form expressions for unitary transformations generated by a single fermionic operator for Hermitian and anti-Hermitian generators. We demonstrate the usefulness of these expressions in formal analyses of unitary transformations and numerical applications involving block-diagonalization and Heisenberg dynamics. This work paves the way for new analytical treatments of unitary transformations and numerical many-body methods for fermions.

quant-ph↗

arXiv2025

Equation-of-motion internally contracted multireference unitary coupled-cluster theory

The accurate computation of excited states remains a challenge in electronic structure theory, especially for systems with a ground state that requires a multireference treatment. In this work, we introduce a novel equation-of-motion (EOM) extension of the internally contracted multireference unitary coupled-cluster framework (ic-MRUCC), termed EOM-ic-MRUCC. EOM-ic-MRUCC follows the transform-then-diagonalize approach, in analogy to its non-unitary counterpart [Datta and Nooijen, J. Chem. Phys. 137, 204107 (2012)]. By employing a projective approach to optimize the ground state, the method retains additive separability and proper scaling with system size. We show that excitation energies are size intensive if the EOM operator satisfies the "killer" and the projective conditions. Furthermore, we propose to represent changes in reference state upon electron excitation via projected many-body operators that span active orbitals and show that the EOM equations formulated in this way are invariant with respect to active orbital rotations. We test the EOM-ic-MRUCC method truncated to single and double excitations by computing the potential energy curves for several excited states of a BeH$_2$ model system, the HF molecule, and water undergoing symmetric dissociation. Across these systems, our method delivers accurate excitation energies and potential energy curves within 5 m$E_\mathrm{h}$ (ca. 0.14 eV) from full configuration interaction. We find that truncating the Baker-Campbell-Hausdorff series to four-fold commutators contributes negligible errors (on the order of $10^{-5}$ $E_\mathrm{h}$ or less), offering a practical route to highly accurate excited-state calculations with reduced computational overhead.

physics.chem-ph↗

arXiv2025

Challenging Excited States from Adaptive Quantum Eigensolvers: Subspace Expansions vs. State-Averaged Strategies

The prediction of electronic structure for strongly correlated molecules represents a promising application for near-term quantum computers. Significant attention has been paid to ground state wavefunctions, but excited states of molecules are relatively unexplored. In this work, we consider the ADAPT-VQE algorithm, a single-reference approach for obtaining ground states, and its state-averaged generalization for computing multiple states at once. We demonstrate for both rectangular and linear H$_4$, as well as for BeH$_2$, that this approach, which we call MORE-ADAPT-VQE, can make better use of small excitation manifolds than an analagous method based on a single-reference ADAPT-VQE calculation, q-sc-EOM. In particular, MORE-ADAPT-VQE is able to accurately describe both avoided crossings and crossings between states of different symmetries. In addition to more accurate excited state energies, MORE-ADAPT-VQE can recover accurate transition dipole moments in situations where traditional ADAPT-VQE and q-sc-EOM struggle. These improvements suggest a promising direction toward the use of quantum computers for difficult excited state problems.

quant-ph↗

arXiv2024

Fermionic Mean-Field Theory as a Tool for Studying Spin Hamiltonians

The Jordan--Wigner transformation permits one to convert spin $1/2$ operators into spinless fermion ones, or vice versa. In some cases, it transforms an interacting spin Hamiltonian into a noninteracting fermionic one which is exactly solved at the mean-field level. Even when the resulting fermionic Hamiltonian is interacting, its mean-field solution can provide surprisingly accurate energies and correlation functions. Jordan--Wigner is, however, only one possible means of interconverting spin and fermionic degrees of freedom. Here, we apply several such techniques to the XXZ and $J_1\text{--}J_2$ Heisenberg models, as well as to the pairing or reduced BCS Hamiltonian, with the aim of discovering which of these mappings is most useful in applying fermionic mean-field theory to the study of spin Hamiltonians.

cond-mat.str-el↗

arXiv2024

Forte: A Suite of Advanced Multireference Quantum Chemistry Methods

Forte is an open-source library specialized in multireference electronic structure theories for molecular systems and the rapid prototyping of new methods. This paper gives an overview of the capabilities of Forte, its software architecture, and examples of applications enabled by the methods it implements.

physics.chem-ph↗

arXiv2024

Towards accurate spin-orbit splittings from relativistic multireference electronic structure theory

Most nonrelativistic electron correlation methods can be adapted to account for relativistic effects, as long as the relativistic molecular spinor integrals are available, from either a four-, two-, or one-component mean-field calculation. However, relativistic multireference correlation methods remain a relatively unexplored area, with mixed evidence regarding the improvements brought by perturbative treatments. We report, for the first time, the implementation of state-averaged four-component multireference perturbation theories to second and third order based on the driven similarity renormalization group (DSRG). With our methods, named 4c-SA-DSRG-MRPT2 and 3, we find that the dynamical correlation included on top of 4c-CASSCF references can significantly improve the spin-orbit splittings in p-block elements and potential energy surfaces when compared to 4c-CASSCF and 4c-CASPT2 results. We further show that 4c-DSRG-MRPT2 and 3 are applicable to these systems over a wide range of the flow parameter, with systematic improvement from second to third order in terms of both improved error statistics and reduced sensitivity with respect to the flow parameter.

cond-mat.str-el↗

arXiv2023

Frozen natural orbitals for the state-averaged driven similarity renormalization group

We present a reduced-cost implementation of the state-averaged driven similarity renormalization group (SA-DSRG) based on the frozen natural orbital (FNO) approach. The natural orbitals (NOs) are obtained by diagonalizing the one-body reduced density matrix from SA-DSRG second-order perturbation theory (SA-DSRG-PT2). Subsequently, the virtual NOs with occupation numbers (ONs) smaller than a user-defined threshold are excluded from the high-level electron correlation treatment beyond SA-DSRG-PT2. An additive second-order correction is applied to the SA-DSRG Hamiltonian to reintroduce the correlation effect from the discarded orbitals. The FNO SA-DSRG method is benchmarked on 35 small organic molecules in the QUEST database. When keeping 98-99% of the cumulative ONs, the mean absolute error in the vertical transition energies due to FNO is less than 0.01 eV. Using the same FNO threshold, we observe a speedup of 9 times the conventional SA-DSRG implementation for nickel carbonyl with a quadruple-$ζ$ basis set. The FNO approach enables third-order SA-DSRG perturbation theory computations on chloroiron corrole [FeCl(C$_{19}$H$_{11}$N$_4$)] with more than 1000 basis functions.

physics.chem-ph↗