arXiv subjects

Markus Reiher

Publications and source records attributed to Markus Reiher.

At least 19 recordsLinked to original sources

arXiv2026

Quantum algorithm for weakly correlated molecular electronic ground states with sub-quintic scaling in the system size

Weakly correlated electronic structures are predominant among molecules, and are routinely solved with heuristic classical methods such as the ``gold standard'' CCSD(T) coupled cluster model, incurring a formal time complexity $O(n^7)$ in the number of molecular orbitals and with no guarantee of energy error $\varepsilon$ at or below chemical accuracy. In this work, a quantum algorithm is presented for ground state energy estimation of weakly correlated molecules using Trotterized time evolution, with an end-to-end quantum operations cost that scales as $\tilde{O}(n^{4.8}/\varepsilon^2)$ in the limit of high-order product formulae when run as a low-depth, shot-noise limited algorithm, or $\tilde{O}(n^{4.8} + n^{3.8}/\varepsilon)$ when scaling the simulation time $T\propto 1/\varepsilon$. The algorithm combines adiabatic state preparation using a smoothed Gevrey schedule with eigenstate filtering via quantum prolate diagonalization (QPD). Both steps of the algorithm rely on a size-independent spectral gap assumption, which is validated by numerical studies on alanine chains with up to 64 monomers. We benchmark the performance of our eigenstate filtering algorithm on a set of 28 molecules to compare our approach against prior phase estimation algorithms, finding that QPD achieves state-of-the-art cost tradeoffs for $\varepsilon$-accurate results. Physical quantum resource estimates are obtained for running Trotter step circuits with up to 40 spin-orbitals, providing a clear path for scaling up quantum simulation of chemistry on early fault-tolerant hardware.

quant-ph↗

arXiv2026

eCAS: An Orbital Embedding Method for Quantum Computing

Future fault-tolerant quantum computers will allow us to calculate electronic structures of atomistic systems. However, these systems will be intrinsically limited in size, requiring embedding theories for many systems because of the unfavorable scaling of the number of terms describing the electron-electron interaction in the second-quantized electronic Hamiltonian. Quantum embedding theories address this challenge by partitioning a quantum system into a region of interest, the impurity, and its (larger) complement, the environment. However, currently available quantum embedding methods place restrictive demands on near-future quantum computers, such as the need to measure reduced density matrices or the need for repeated evaluations. Here, we introduce the new orbital embedding method eCAS that steers clear of these pitfalls by constructing a multi-CAS problem, the active spaces of which are localized and can be solved independently of each other with any quantum algorithm. This also allows for the development of comparatively simple gradient expressions. eCAS leverages the Schmidt decomposition to construct initial impurity and bath orbitals and augments them with localized environment orbitals, based on a mutual correlation criterion. The mutual correlation criterion makes eCAS systematically improvable without the need for any iteratively determined quantities.

quant-ph↗

arXiv2026

A Hybrid Message-Passing and Electric-Field Representation for Electrostatic QM/MM Embedding with Machine Learning Interatomic Potentials

Within a hybrid quantum mechanics/molecular mechanics approach a small region of a large atomistic system is described quantum mechanically, while the rest of the system is represented by a classical force field. Despite this, the computational cost of the quantum calculation severely limits the accessible simulation and sampling time. Replacing the quantum calculation with a machine learning interatomic potential (MLIP) trained on quantum reference data can greatly increase the accessible simulation time. However, the accuracy and efficiency strongly depend on the specific way in which the MLIP incorporates information about the classical (electrostatic) environment. Here, we demonstrate that existing strategies based purely on features derived from an external electric field fail to distinguish certain environments, ultimately limiting their accuracy. As a solution, we propose an extension to the equivariant TensorNet architecture that mitigates this shortcoming by incorporating classical atoms close to the quantum region into the message-passing scheme, combined with features derived from the electric field for describing the environment farther away. We show that this combination achieves higher accuracy than either approach alone.

physics.chem-ph↗

arXiv2026

Lanthanide Crystal Field Theory in the J-Mixing Regime: $f^n$ Configurations

The low-energy sector of the lanthanide $f^n$ shell is to first approximation governed by the interplay of three interactions: Coulomb repulsion, spin-same-orbit coupling and the ligand crystal field potential. To rationalize the energy landscape in different chemical environments, it is desirable to extract the phenomenological crystal field parameters from experimental data; however, in practice, high-dimensional fitting procedures complicate their routine determination. Here, we present a computational extraction procedure based on real tensorial sets and the $U(7)$ canonical chain that, unlike existing operator equivalent methods, takes all $J$ multiplets of the lowest-energy $LS$ term into account, ensuring meaningful results even in the presence of considerable $J$-mixing. Two series of lanthanide compounds, [Ln(III)(C$_8$H$_8$)$_2$]$^-$} and doped Ln(III):Y$_2$O$_3$} (Ln $\in$ {Ce, Pr, Nd, Sm, Eu}) serve as examples for high- ($D_{8h}$) and low-symmetry ($C_2$) scenarios. Consequences for the generalisation toward actinides are briefly discussed.

physics.chem-ph↗

arXiv2026

Propagating sparsely supported states with time-dependent neural quantum states

Neural quantum states (NQSs) have emerged as a powerful ansatz for quantum dynamics. Their high entanglement capacity promises to overcome the entanglement barrier. However, existing time-dependent NQS methods are ill-equipped to propagate sparsely supported initial states due to the inherent mismatch between the supports of such states and their time derivatives. To address this issue, we introduce the interpolation sampling method as a novel form of importance sampling, where samples are drawn from a distribution that interpolates between the wave function and its time derivative. Combined with a global-in-time variational principle, we demonstrate with the example of the two-dimensional transverse-field Ising model that interpolation sampling allows for accurate propagation of extremely peaked states that standard wave function sampling could not tackle. We further improve sampling efficiency by introducing (i) a configuration-time joint sampling scheme where spin configurations and time are both treated as random variables, and (ii) a hybrid strategy for sample proposal that incorporates the knowledge of a Krylov subspace. Our work extends the scope of time-dependent NQS methods to a wider range of physically relevant scenarios, while challenging the prevailing reliance on the Born distribution and its close variants as the default basis for sampling.

quant-ph↗

arXiv2026

OrbGNN: A Wave function-based Machine Learning Interelectronic Representation

Machine learning interatomic potentials (MLIPs) have become emerging tools in molecular modeling and computational chemistry. By learning high-dimensional potential energy surfaces from quantum chemical data, MLIPs enable accurate and efficient predictions of structural, thermodynamic, and dynamical properties. However, such models have limitations in predictions of electronic properties and the effects of static electron correlation due to their lack of electronic structure information. This work presents OrbGNN, an electronic structure graph architecture analogous to molecular graph and MLIP frameworks, where pair-orbital interactions constitute the graph representation, while orbital entanglement encodes the connectivity between them. By embedding information derived from orbital correlation metrics directly into the graph topology, OrbGNN provides a compact representation of a molecule s orbital landscape and electron correlation patterns. Analysis of the behavior of the feature space in an orbital graph are shown to demonstrate model robustness. The model is evaluated for the dissociation of nitrogen and for a larger dataset of diatomic molecules. Finally, the OrbGNN model is applied to a set of octahedral iron(II) complexes to predict spin-state energy gaps.

physics.chem-ph↗

arXiv2026

General Symmetry-Based Potential Energy Surface Grid Reduction in Normal Coordinates

The construction of a grid-based potential energy surface (PES) can be prohibitively expensive as the number of grid points grows exponentially with molecular size. Molecular symmetry can reduce this cost by eliminating symmetry-equivalent points. We present an algebraic symmetry-based grid reduction method, ASyBGR, that is capable of handling non-Abelian and higher-order cyclic symmetry groups. Non-coordinate-mixing operations are encoded into a vector space bit-string, where Gaussian elimination and closure can identify all symmetry-valid sign change patterns and the coordinate axes whose grids can be halved about the origin. In the presence of degenerate subspaces, we optimize the coordinate basis to maximize reduction. The method was validated by comparing vibrational configuration interaction (VCI) energies calculated using the full and symmetry-reduced fourth-order HDMR PESs for molecules spanning a broad range of symmetries. The number of grid points required to construct the PES was reduced by as much as 81\%, while VCI energies deviated below 1 1/cm for all test cases on average. The relative root-mean-square deviation (RRMSD) between the full and symmetry-reduced potential energy and dipole moment surfaces were at most on the order of 10$^{-3}$ and 10$^{-2}$, respectively.

physics.chem-ph↗

arXiv2026

phase2: Full-State Vector Simulation of Quantum Time Evolution at Scale

Classical simulation of quantum computers is essential for designing and benchmarking quantum algorithms. Here we present phase2, a full-state-vector simulator optimised for sequences of many-qubit Pauli rotations on distributed CPU and GPU clusters. Exploiting the common-suffix structure of Pauli-rotation circuits, the implementation reduces inter-node communication and achieves two orders of magnitude speedup for grouped rotations. We demonstrate weak and strong scaling to 40 qubits across 512 NVIDIA H100 GPUs using 32 TB of distributed memory. Applying the simulator to Hamiltonian time evolution of ruthenium-ligand active spaces up to 40 qubits, we find that the empirical Trotter error lies more than two orders of magnitude below the rigorous analytic upper bound for every active space in which the fit converged (up to 32 qubits). Practical circuit depths and simulation costs are therefore substantially smaller than the conservative estimates suggest.

quant-ph↗

arXiv2026

Ground and excited-state energies with analytic errors and short time evolution on a quantum computer

Accurately solving the Schrödinger equation remains a central challenge in computational physics, chemistry, and materials science. Here, we propose an alternative eigenvalue problem based on a system's autocorrelation function, avoiding direct reference to a wave function. In particular, we develop a rigorous approximation framework that enables precise frequency estimation from a finite number of signal samples. Our analysis builds on new results involving prolate spheroidal wave functions and yields error bounds that reveal a sharp accuracy transition governed by the observation time and spectral density of the signal. These results are very general and thus carry far. As one important example application we consider the quantum computation for molecular systems. By combining our spectral method with a quantum subroutine for signal generation, we define quantum prolate diagonalization (QPD) - a hybrid classical-quantum algorithm. QPD simultaneously estimates ground and excited state energies within chemical accuracy at the Heisenberg limit. An analysis of different input states demonstrates the robustness of the method, showing that high precision can be retained even under imperfect state preparation.

quant-ph↗

arXiv2026

After 100 Years of Quantum Mechanics: Toward a Constructive Observation-Centered Perspective

Quantum mechanics owes much of its extraordinary success to a Hilbertian program of mathematical formalization. Yet, the formalism remains poorly aligned with the practical limitations of computations in finite dimensions and under finite accuracy. In this perspective, we argue that this mismatch points to the need for a new mathematical program: a rigorous constructive theory for effective descriptions to identify essential degrees of freedom. We propose an observation-centered point of view in which signals are treated as the primary objects of analysis, while wave functions and Hamiltonians are reconstructed as auxiliary structures to rationalize the observed data. Our starting point is a signal-based spectral equation that reformulates frequency analysis as an operator problem. We connect this point of view to results on prolate Fourier theory, spectral analysis with finite observation time, and short-time quantum simulation. We highlight a sharp accuracy transition relating necessary observation time to the effective spectral density of a signal for achieving accurate resolution. The resulting framework integrates approximation as a fundamental necessity more directly into the foundations of quantum mechanics and points toward a broader program for the effective description of complex quantum systems, such as those found in the molecular sciences.

quant-ph↗

arXiv2026

A New Paradigm for Computational Chemistry

Computational chemistry has become an indispensable tool for generating data and insights, pervading all branches of experimental chemistry. Its most central concept is the potential energy hypersurface, key to all chemistry and materials science, as it assigns an energy to a molecular structure, the necessary ingredient for reaction mechanism elucidation and reaction rate calculation. Density functional theory (DFT) has been the most important method in practice for obtaining such energies, which is mirrored in the use of high-performance computing hardware. In the last two decades, a new class of surrogate potential energy functions has been evolving with remarkable properties: quantum accuracy combined with force-field speed. Until very recently, their application was hampered by the fact that they needed to be trained on truly large system-specific data sets, generated before a computational chemistry study could be started (in sharp contrast to DFT, which, as a first-principles method, works out of the box, but at a far higher price of computational cost). Very recently, this roadblock has been overcome by so-called foundation machine learning interatomic potentials, which are poised to completely change the way we do computational chemistry, likely prompting us to abandon DFT as the prime method of choice for this purpose in less than a decade.

physics.chem-ph↗

arXiv2026

Utility-scale quantum computational chemistry

Chemistry and materials science are widely regarded as potential killer application fields for quantum hardware. While the dream of unlocking unprecedented simulation capabilities remains compelling, quantum algorithm development must adapt to the evolving constraints of the emerging quantum hardware in order to accomplish any advantage for the computational chemistry practice. At the same time, the continuous advancement of classical wavefunction-theory methods narrows the window for a broad quantum advantage. Here, we explore potential benefits of quantum computation from the broader perspective of utility-scale applications. We argue that quantum algorithms need not only enable accurate calculations for a few challenging, that is strongly correlated, molecular structures, that might be hard to describe with traditional methods. Instead, they must also support the practical integration of quantum-accelerated computations into high-throughput pipelines for routine calculations on arbitrary molecules, ultimately delivering a tangible value to society.

quant-ph↗

arXiv2026

Trotter Error and Orbital Transformations in Quantum Phase Estimation

Quantum computation with Trotter product formulae is straightforward and requires little overhead in terms of logical qubits. The choice of the orbital basis significantly affects circuit depth, with localised orbitals yielding lowest circuit depths. However, literature results point to large Trotter errors incurred by localised orbitals. Here, we therefore investigate the effect of orbital transformations on Trotter error. We consider three strategies to reduce Trotter error by orbital transformation: (i) The a priori selection of an orbital basis that produces low Trotter error. (ii) The derivation of an orbital basis that produces a ground state energy free of Trotter error (as we observed that the Trotter error is a continuous function in the Givens-rotation parameter, from which continuity of this error upon orbital transformation can be deduced). (iii) Application of propagators that change the computational basis between Trotter steps. Our numerical results show that reliably reducing Trotter error by orbital transformations is challenging. General recipes to produce low Trotter errors cannot be easily derived, despite analytical expressions which suggest ways to decrease Trotter error. Importantly, we found that localised orbital bases do not produce large Trotter errors in molecular calculations, which is an important result for efficient QPE set-ups.

quant-ph↗

arXiv2026

Neural Quantum States Based on Selected Configurations

Neural quantum states (NQS) provide a flexible and highly expressive parameterization of wave functions for strongly correlated problems in quantum chemistry. Despite rapid advances in network architectures, the evaluation of electronic energies remains almost exclusively based on variational Monte Carlo (VMC). While VMC is effective for structured systems such as spin chains, its accuracy and efficiency for electronic Hamiltonians are hindered by sharply peaked distributions, stochastic gradient noise, and slow convergence with sample size. In this letter, we assess the capability of NQS-VMC to efficiently capture correlation in electronic ground states by comparing it to a recently developed NQS-based selected configuration (NQS-SC) approach. We set up a systematic comparison of the ground-state optimizations obtained with NQS-VMC and NQS-SC for molecular systems dominated by either static or dynamical correlation. The comparison demonstrates a clear advantage of NQS-SC over NQS-VMC in both energy accuracy and wave-function coefficients, particularly for statically correlated molecules. Moreover, NQS-SC exhibits robust systematic improvability, whereas NQS-VMC does not. These findings position NQS-SC as the new default approach over NQS-VMC for electronic structure calculations. We further observe that neither NQS-SC nor NQS-VMC can efficiently capture dynamical correlation, highlighting the need for future hybrid methods, such as multiconfigurational perturbation theories built on top of NQS solutions.

physics.chem-ph↗

arXiv2025

N-Mode Quantized Anharmonic Vibronic Hamiltonians for Matrix Product State Dynamics

Theoretical predictions of photochemical processes are essential for interpreting and understanding spectral features. Reliable quantum dynamics calculations of vibronic systems require precise modeling of anharmonic effects in the potential energy surfaces and off-diagonal nonadiabatic coupling terms. In this work, we present the n-mode quantization of all vibronic Hamiltonian terms comprised of general high-dimensional model representations. This results in a second-quantized framework for accurate vibronic calculations employing the density matrix renormalization group algorithm. We demonstrate the accuracy and reliability of this approach by calculating the excited state quantum dynamics of maleimide. We analyze convergence and the choice of parameters of the underlying time-dependent density matrix renormalization group algorithm for the n-mode vibronic Hamiltonian, demonstrating that it enables accurate calculations of complex photochemical dynamics.

physics.chem-ph↗

arXiv2025

Efficient Implementation of the Spin-Free Renormalized Internally-Contracted Multireference Coupled Cluster Theory

In this paper, an efficient implementation of the renormalized internally-contracted multreference coupled cluster with singles and doubles (RIC-MRCCSD) into the ORCA quantum chemistry program suite is reported. To this end, Evangelista's Wick&d equation generator was combined with ORCA's native AGE code generator in order to implement the many-body residuals required for the RIC-MRCCSD method. Substantial efficiency gains are realized by deriving a spin-free formulation instead of the previously reported spin-orbital version developed by some of us. Since AGE produces parallelized code, the resulting implementation can directly be run in parallel with substantial speedups when executed on multiple cores. In terms of runtime, the cost of RIC-MRCCSD is shown to be between single-reference RHF-CCSD and UHF-CCSD, even when active space spaces as large as CAS(14,14) are considered. This achievement is largely due to the fact that no reduced density matrices (RDM) or cumulants higher than three-body enter the formalism. The scalability of the method to large systems is furthermore demonstrated by computing the ground-state of a vitamin B12 model comprised of an active space of CAS(12, 12) and 809 orbitals. In terms of accuracy, RIC-MRCCSD is carefully compared to second- and approximate fourth-order $n$-electron valence state perturbation theories (NEVPT2, NEVPT4(SD)), to the multireference zeroth-order coupled-electron pair approximation (CEPA(0)), as well as to the IC-MRCCSD from Kohn. In contrast to RIC-MRCCSD, the IC-MRCCSD equations are entirely derived by AGE using the conventional projection-based approach, which, however, leads to much higher algorithmic complexity than the former as well as the necessity to calculate up to the five-body RDMs. Remaining challenges such as the variation of the results with the flow, a free parameter that enters the RIC-MRCCSD theory, are discussed.

physics.chem-ph↗

arXiv2025

Modal Backflow Neural Quantum States for Anharmonic Vibrational Calculations

Neural quantum states (NQS) are a promising ansatz for solving many-body quantum problems due to their inherent expressiveness. Yet, this expressiveness can only be harnessed efficiently for treating identical particles if the suitable physical knowledge is hardwired into the neural network itself. For electronic structure, NQS based on backflow determinants has been shown to be a powerful ansatz for capturing strong correlation. By contrast, the analogue for bosons, backflow permanents, is unpractical due to the steep cost of computing the matrix permanent and due to the lack of particle conservation in common bosonic problems. To circumvent these obstacles, we introduce a modal backflow (MBF) NQS design and demonstrate its efficacy by solving the anharmonic vibrational problem. To accommodate the demand of high accuracy in spectroscopic calculations, we implement a selected-configuration scheme for evaluating physical observables and gradients, replacing the standard stochastic approach based on Monte Carlo sampling. A vibrational self-consistent field calculation is conveniently carried out within the MBF network, which serves as a pretraining step to accelerate and stabilize the optimization. In applications to both artificial and ab initio Hamiltonians, we find that the MBF network is capable of delivering spectroscopically accurate zero-point energies and vibrational transitions in all anharmonic regimes.

physics.chem-ph↗

arXiv2025

Automated Exploration of Radical-Molecule Chemistry: The Case of Oxirane + CH in the ISM

Quantum chemistry provides accurate and reliable methods to investigate reaction pathways of reactive molecular systems relevant to the interstellar medium. However, the exhaustive exploration of a reactive network is often a daunting task, resulting in unexplored reactive channels that affect kinetic outcomes and branching ratios. Here, an automated workflow for exploring reactive potential energy surfaces (PESs) is employed for the first time to study the oxirane (C$_2$H$_4$O) plus methylidyne ($^.$CH) reaction. The ultimate goal is to comprehensively map its PES and, subsequently, derive rate constants for the most important reaction channels. In addition to its astrochemical relevance, this reaction has been considered because it is a challenging test case, its network being very extended, with 60 exothermic bimolecular products lying below the reactant's energy. Kinetic simulations indicate that the main product of the reaction is the HCO radical plus ethene (C$_2$H$_4$), while formation of s-trans-propenal (acrolein) and 2H-oxene is also possible, but to a lesser extent. Based on the present study and other references in the literature, we suggest that the slightly higher relative abundance of s-trans-propenal compared to methyl ketene in the interstellar medium is a gas-phase kinetic effect, s-trans-propenal being a more easily accessible product on the C$_3$H$_5$O$^.$ PES.

astro-ph.GA↗