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Stepan Fomichev

Publications and source records attributed to Stepan Fomichev.

18 recordsLinked to original sources
arXiv2026

Practical Estimation of Trotter Error for Hamiltonian Simulation

Trotter product formulas are a leading approach for Hamiltonian simulation on quantum computers, yet their practical performance has remained difficult to assess due to the challenge of accurately estimating the Trotter error. In this work, we develop new theoretical results, algorithms, and software tools that advance the state-of-the-art in Trotter error estimation by orders of magnitude in both scale and accuracy. On the theoretical side, we prove that in the asymptotic limit the error of a product formula depends on the diagonal elements of the Baker-Campbell-Hausdorff (BCH) error operator in the eigenbasis of the Hamiltonian, rather than its full spectral norm -- yielding an improved scaling for Hamiltonian simulation using product formulas. On the algorithmic side, we introduce a compact representation of the BCH expansion that reduces the number of commutators from $\mathcal{O}(n^3)$ to $\mathcal{O}(n)$ for second-order, and from $\mathcal{O}(n^5)$ to $\mathcal{O}(n^2)$ for fourth-order formulas on $n$ fragments, complemented by an importance sampling scheme to further reduce the computational cost. We provide implementations of these techniques in software and demonstrate their power on two applications: (i) X-ray absorption spectroscopy of an electronic Hamiltonian (Li$_4$Mn$_2$O) at up to 56 qubits using tensor networks; and (ii) vibronic dynamics of naphthalene at over 100 qubits using ML-MCTDH, where we find that naive analytical bounds overestimate the required number of Trotter steps by nearly five orders of magnitude. Our framework enables, for the first time, the accurate estimation of Trotter error at practically relevant system sizes, providing a foundation for fair algorithmic comparisons and rational design of product formulas.

quant-ph↗
arXiv2026

Theory and practice of Trotter product formulas for quantum chemistry

Trotter product formulas are a fundamental class of methods for Hamiltonian simulation, particularly attractive due to their low qubit requirements. However, they are often overlooked for use with fault-tolerant quantum algorithms, because of their perceived higher gate counts and the difficulty of estimating Trotter error. Here, we introduce Symmetry-Protected Randomized near-Integrable Trotter (SPRINT) formulas, a framework for building optimized product formulas for electronic structure Hamiltonians widely used in quantum chemistry. SPRINT integrates a generalization of classical near-integrability, randomization, symmetry protection, use of QROM, and other techniques into a thoroughly optimized methodology for Hamiltonian simulation. When applied to concrete simulation tasks, we find SPRINT leads to substantial reduction in gate count compared to previous approaches. Alongside SPRINT, we introduce and analyze a Generalized Rank Decomposition (GRADE) of electronic Hamiltonians that generalizes previous factorization methods. We apply these techniques to the task of simulating the X-ray absorption spectrum of Li$_4$Mn$_2$O, a candidate battery cathode material, leveraging recent advances in tight Trotter error estimation to carefully identify the best version of SPRINT for this problem. Using a Trotter error estimation tool developed in the PennyLane software platform, we show that SPRINT reduces the Toffoli gate cost by a factor of $4.5$ relative to the previous state of the art for this problem, with a gate cost only $\times 2.5$ higher than qubitization, while requiring a dramatic $\times 5.5$ fewer logical qubits. These results establish well-designed Trotter product formulas as an attractive Hamiltonian simulation method for industrially relevant problems in chemistry and materials science.

quant-ph↗
arXiv2026

Quantum Simulations for Extreme Ultraviolet Photolithography

A key challenge of extreme ultraviolet (EUV) lithography in semiconductor fabrication is the line edge roughness or "blur" produced by the electron cascades following absorption of a high-energy photon. Here we present quantum algorithms to compute EUV absorption and photoelectron emission spectra, which are key to predicting blur. The first is a time-domain algorithm resolving absorption at a given frequency; the second is a first-quantized plane-wave algorithm computing the photoemission spectrum via real-time dynamics that treats bound and continuum states on equal footing. For a model photoresist monomer IMePh, 92 eV absorption requires $200$ logical qubits and $10^{9}$ non-Clifford gates per circuit with $10^3$ shots, while the photoemission spectrum needs $\geq 10^{14}$ gates, $10^4$ shots, and several thousand logical qubits. These results establish high-fidelity quantum simulations as a key component to parameterize the multi-scale macroscopic models required to overcome the electron blur bottleneck in semiconductor miniaturization.

quant-ph↗
arXiv2026

Quantum algorithm for simulating resonant inelastic X-ray scattering in battery materials

Resonant inelastic X-ray scattering (RIXS) is the workhorse experimental technique for probing the structural degradation of higher-capacity cathode materials. However, the interpretation of experimental spectra is challenging due to the lack of accurate simulations. In this work, we propose a quantum algorithm for simulating the RIXS spectrum of molecular clusters hypothesized to form in Li-excess cathodes. The algorithm uses quantum phase estimation to sample the spectrum from a state encoding the scattering transition amplitudes of the cluster valence excitations. We prepare this state in the quantum computer using a block-encoding of the dipole operator and quantum signal processing to implement the Green's function propagator over intermediate core-excited states. To showcase the algorithm, we use a model cluster proposed in recent experimental works consisting of an oxygen dimer bonded to a manganese atom. Using the PennyLane software platform, we report resource estimation for simulating RIXS spectra for chemically motivated active spaces of increasing sizes. For a classically challenging active space with 20 orbitals, the algorithm requires $2.0 \times 10^{10}$ Toffoli gates and $414$ logical qubits.

quant-ph↗
arXiv2025

Quantum Algorithms for Photoreactivity in Cancer-Targeted Photosensitizers

Photodynamic therapy (PDT) is a targeted cancer treatment that uses light-activated photosensitizers to generate reactive oxygen species that selectively destroy tumor cells, generally causing less collateral damage than conventional treatments. However, its clinical success hinges on the availability of photosensitizers with strong optical sensitivity and high efficiency in generating reactive oxygen species. While classical computational methods have provided useful insights into photosensitizer design, they struggle to scale and often lack the accuracy needed for these simulations. In this work, we show how fault-tolerant quantum algorithms can be used to identify promising photosensitizer candidates for PDT. To predict photosensitizer performance, we assess two computational properties. First, we quantify light sensitivity by calculating the cumulative absorption in the therapeutic window with a threshold projection algorithm. Second, we determine the efficiency of reactive oxygen generation by estimating intersystem crossing (ISC) rates using the evolution-proxy approach, complemented by a vibronic dynamic treatment where appropriate. We apply these algorithms to a clinically relevant and actively pursued class of photosensitizers, BODIPY derivatives, including heavy-atom and transition-metal-substituted systems that are challenging for classical methods. Our resource estimates, obtained with PennyLane, suggest that systems with active spaces ranging from 11 to 45 spatial orbitals can be simulated using $180$-$350$ logical qubits and Toffoli gate depths between $10^7$ and $10^9$, placing our algorithms within reach of realistic fault-tolerant quantum devices. This paves the way to an efficient quantum-based workflow for designing photosensitizers that can accelerate the discovery of new PDT agents.

quant-ph↗
arXiv2025

Filtered Quantum Phase Estimation

Accurate state preparation is a critical bottleneck in many quantum algorithms, particularly those for ground-state energy estimation. Even in fault-tolerant quantum computing, preparing a quantum state with sufficient overlap with the desired eigenstate remains a major challenge. To address this, we develop a unified cost-aware framework for filtered-state preparation that enhances the overlap of a given input state through spectral filtering. The framework covers polynomial and trigonometric realizations of filters and makes explicit the trade-off among overlap amplification, preparation success probability, and filter-implementation cost. As representative examples, we analyze Gaussian filters and introduce a modified Krylov-subspace-based filter that improves the success-probability/overlap trade-off relevant to filtered state preparation. Within this framework, we study a filtered variant of quantum phase estimation (FQPE) that mitigates the unfavorable dependence on the initial overlap present in standard QPE. Numerical experiments on Fermi-Hubbard models show that FQPE reduces the total runtime by more than two orders of magnitude in the high-precision regime, with overlap amplification exceeding a factor of one hundred.

quant-ph↗
arXiv2025

Quantum Simulation of Electron Energy Loss Spectroscopy for Battery Materials

The dynamic structure factor (DSF) is a central quantity for interpreting a vast array of inelastic scattering experiments in chemistry and materials science, but its accurate simulation is a considerable challenge for classical computational methods. In this work, we present a quantum algorithm and an end-to-end simulation framework to compute the DSF, providing a general approach for simulating momentum-resolved spectroscopies. We apply this approach to the simulation of electron energy loss spectroscopy (EELS) in the core-level electronic excitation regime, a spectroscopic technique offering sub-nanometer spatial resolution and capable of resolving element-specific information, crucial for analyzing battery materials. We derive a quantum algorithm for computing the DSF for EELS by evaluating the off-diagonal terms of the time-domain Green's function, enabling the simulation of momentum-resolved spectroscopies. To showcase the algorithm, we study the oxygen K-edge EELS spectrum of lithium manganese oxide ($Li_2MnO_3$), a prototypical cathode material for investigating the mechanisms of oxygen redox in battery materials. For a representative model of an oxygen-centered cluster of $Li_2MnO_3$ with an active space of 18 active orbitals, the algorithm requires a circuit depth of $3.25\times10^{8}$ T gates, 100 logical qubits, and roughly $10^4$ shots.

quant-ph↗
arXiv2025

Quantum algorithms to detect ODMR-active defects for quantum sensing applications

Spin defects in two-dimensional materials are a promising platform for quantum sensing. Simulating the defect's optical response and optically detected magnetic resonance (ODMR) contrast is key to identifying suitable candidates. However, existing simulation methods are typically unable to supply the required accuracy. Here, we propose two quantum algorithms to detect an imbalance in the triplet-to-singlet intersystem crossing (ISC) rates between excited states with the same and different spin projections -- a necessary condition for nonzero ODMR response. The lowest-cost approach evaluates whether the evolution of an $S=0$ state under the spin-orbit coupling induces ISC to $S=1$, and also whether there is an imbalance in its intensity depending on the final state spin projection. The second approach works by comparing the emission spectrum of a spin defect with and without the spin-orbit coupling operator, inferring ISC intensity for different spin transition channels from spectrum intensity changes. Additionally, we present an improved scheme to evaluate the defect's optical response, building upon previous work. We study these quantum algorithms in the context of the negatively charged boron vacancy in hexagonal boron nitride. We generate an embedded active space of 18 spatial orbitals using quantum defect embedding theory (QDET) and show that the ISC rate imbalance can be detected with as few as 105 logical qubits and $4.41 \times 10^8$ Toffoli gates. By avoiding direct and costly rate calculations, our methods enable faster screening of candidate defects for ODMR activity, advancing the prospect of using quantum simulations to aid the development of high-performing sensing devices.

quant-ph↗
arXiv2025

Trotter simulation of vibrational Hamiltonians on a quantum computer

Simulating vibrational dynamics is essential for understanding molecular structure, unlocking useful applications such as vibrational spectroscopy for high-fidelity chemical detection. Quantum algorithms for vibrational dynamics are emerging as a promising alternative to resource-demanding classical approaches, but this domain is largely underdeveloped compared to quantum simulations of electronic structure. In this work, we describe in detail three distinct forms of the vibrational Hamiltonian: canonical bosonic quantization, real space representation, and the Christiansen second-quantized form. Leveraging Lie algebraic properties of each, we develop efficient fragmentation schemes to enable the use of Trotter product formulas for simulating time evolution. We introduce circuits required to implement time evolution in each form, and highlight factors that contribute to the simulation cost, including the choice of vibrational coordinates. Using a perturbative approach for the Trotter error, we obtain tight estimates of T gate cost for the simulation of time evolution in each form, enabling their quantitative comparison. Combining tight Trotter error estimates and efficient fragmentation schemes, we find that for the medium-sized CH$_4$ molecule with 9 vibrational modes, time evolution for approximately 1.8 ps may be simulated using as little as 36 qubits and approximately $3 \times 10^{8}$ T gates -- an order-of-magnitude speedup over prior-art algorithms. Finally, we present calculations of vibrational spectra using each form to demonstrate the fidelity of our algorithms. This work presents a unified and highly optimized framework that makes simulating vibrational dynamics an attractive use case for quantum computers.

quant-ph↗
arXiv2025

Fast simulations of X-ray absorption spectroscopy for battery materials on a quantum computer

X-ray absorption spectroscopy (XAS) is a leading technique for understanding structural changes in advanced battery materials such as lithium-excess cathodes. However, extracting critical information like oxidation states from the experimental spectra requires expensive and time-consuming simulations. Building upon a recent proposal to simulate XAS using quantum computers, this work proposes a highly-optimized implementation of the time-domain algorithm for X-ray absorption. Among a host of improvements to Hamiltonian representation, circuit implementation, and measurement strategies, three optimizations are key to the efficiency of the algorithm. The first is the use of product formulas with the compressed double factorized form of the Hamiltonian. The second is recognizing that for spectroscopy applications, it is sufficient to control the error in the eigenvalues of the (approximate) Hamiltonian being implemented by the product formula, rather than the generic error on the full time evolution operator. Using perturbation theory to estimate this eigenvalue error, we find that significantly fewer Trotter steps are needed than expected from the time evolution error bound. The third is the choice of an optimized distribution of samples that takes advantage of the exponentially decaying Lorentzian kernel. Through constant factor resource estimates, we show that a challenging model Li$_4$Mn$_2$O cluster system with 18 spatial orbitals and 22 electrons in the active space can be simulated with 100 logical qubits and less than $4 \times 10^8$ T gates per circuit. Finally, the algorithm is implemented on a simulator, and the reconstructed spectrum is verified against a classical computational reference. The low cost of our algorithm makes it attractive to use on fault-tolerant quantum devices to accelerate the development and commercialization of high-capacity battery cathodes.

quant-ph↗
arXiv2025

Simulating near-infrared spectroscopy on a quantum computer for enhanced chemical detection

Near-infrared (NIR) spectroscopy is a non-invasive, low-cost, reagent-less, and rapid technique to measure chemical concentrations in a wide variety of sample types. However, extracting concentration information from the NIR spectrum requires training a statistical model on a large collection of measurements, which can be impractical, expensive, or dangerous. In this work, we propose a method for simulating NIR spectra on a quantum computer, as part of a larger workflow to improve NIR-based chemical detection. The quantum algorithm is highly optimized, exhibiting a cost reduction of many orders of magnitude relative to prior approaches. The main optimizations include the localization of vibrational modes, an efficient real-space-based representation of the Hamiltonian with a quantum arithmetic-based implementation of the time-evolution, optimal Trotter step size determination, and specific targeting of the NIR region. Overall, our algorithm achieves a O(M^2) scaling, compared with the O(M^12) coming from equivalent high-accuracy classical methods. As a concrete application, we show that simulating the spectrum of azidoacetylene (HC2N3), a highly explosive molecule with strong anharmonicities consisting of M = 12 vibrational modes, requires circuits with a maximum 8.47 x 10^8 T gates and 173 logical qubits. By enhancing the training datasets of detection models, the full potential of vibrational spectroscopy for chemical detection could be unlocked across a range of applications, including pharmaceuticals, agriculture, environmental monitoring, and medical sensing.

quant-ph↗
arXiv2024

Simulating X-ray absorption spectroscopy of battery materials on a quantum computer

X-ray absorption spectroscopy is a crucial experimental technique for elucidating the mechanisms of structural degradation in battery materials. However, extracting information from the measured spectrum is challenging without high-quality simulations. In this work, we propose simulating near-edge X-ray absorption spectra as a promising application for quantum computing. It is attractive due to the ultralocal nature of X-ray absorption that significantly reduces the sizes of problems to be simulated, and because of the classical hardness of simulating spectra. We describe three quantum algorithms to compute the X-ray absorption spectrum and provide their asymptotic cost. One of these is a Monte-Carlo based time-domain algorithm, which is cost-friendly to early fault-tolerant quantum computers. We then apply the framework to an industrially relevant example, a CAS(22e,18o) active space for an O-Mn cluster in a Li-excess battery cathode, showing that practically useful simulations could be obtained with much fewer qubits and gates than ground-state energy estimation of the same material.

quant-ph↗
arXiv2023

Initial state preparation for quantum chemistry on quantum computers

Quantum algorithms for ground-state energy estimation of chemical systems require a high-quality initial state. However, initial state preparation is commonly either neglected entirely, or assumed to be solved by a simple product state like Hartree-Fock. Even if a nontrivial state is prepared, strong correlations render ground state overlap inadequate for quality assessment. In this work, we address the initial state preparation problem with an end-to-end algorithm that prepares and quantifies the quality of initial states, accomplishing the latter with a new metric -- the energy distribution. To be able to prepare more complicated initial states, we introduce an implementation technique for states in the form of a sum of Slater determinants that exhibits significantly better scaling than all prior approaches. We also propose low-precision quantum phase estimation (QPE) for further state quality refinement. The complete algorithm is capable of generating high-quality states for energy estimation, and is shown in select cases to lower the overall estimation cost by several orders of magnitude when compared with the best single product state ansatz. More broadly, the energy distribution picture suggests that the goal of QPE should be reinterpreted as generating improvements compared to the energy of the initial state and other classical estimates, which can still be achieved even if QPE does not project directly onto the ground state. Finally, we show how the energy distribution can help in identifying potential quantum advantage.

quant-ph↗
arXiv2023

Exciton dissociation mediated by phonons in organic photovoltaics

It is well known that phonons can overscreen the bare Coulomb electron-electron repulsion, turning it into the effective attraction that binds the Cooper pairs responsible for BCS superconductivity. Here, we use a simple lattice model to prove that the counterpart of this is also possible, whereby phonons overscreen the bare electron-hole attraction and may turn it repulsive at short distances, driving exciton dissociation in certain regions of the parameter space. We argue that this phonon-mediated short-range screening plays an important role in the physics of organic solar cell materials (and other materials with strong electron-phonon coupling) and could point the way to new strategies for optimizing their efficiencies.

cond-mat.str-el↗
arXiv2022

The Generalized Green's function Cluster Expansion: A Python package for simulating polarons

We present an efficient implementation of the Generalized Green's function Cluster Expansion (GGCE), which is a new method for computing the ground-state properties and dynamics of polarons (single electrons coupled to lattice vibrations) in model electron-phonon systems. The GGCE works at arbitrary temperature and is well suited for a variety of electron-phonon couplings, including, but not limited to, site and bond Holstein and Peierls (Su-Schrieffer-Heeger) couplings, and couplings to multiple phonon modes with different energy scales and coupling strengths. Quick calculations can be performed efficiently on a laptop using solvers from NumPy and SciPy, or in parallel at scale using the PETSc sparse linear solver engine.

physics.comp-ph↗
arXiv2021

Effects of reduced dimensionality, crystal field, electron-lattice coupling, and strain on the ground-state of a rare-earth nickelates monolayer

Motivated by the potential for cuprate-like superconductivity in monolayer rare-earth nickelate superlattices, we study the effects of crystal field splitting, lattice distortions and strain on the charge, magnetic, and orbital order in undoped two-dimensional (2D) nickelate monolayers $R$NiO$_3$. We use a two-band Hubbard model to describe the low-energy electron states, with correlations controlled by a effective Hubbard $U$ and Hund's $J$. The electrons are coupled to the octahedral breathing-mode lattice distortions. Treating the lattice semiclassically, we apply the Hartree-Fock approximation to obtain the phase diagram for the ground-state as a function of the various parameters. We find that the 2D confinement leads to strong preference for the planar $d_{x^2-y^2}$ orbital even in the absence of a crystal-field splitting. The $d_{x^2-y^2}$ polarization is enhanced by adding a crystal field splitting, whereas coupling to breathing-mode lattice distortions weakens it. However, the former effect is stronger, leading to $d_{x^2-y^2}$ orbital and antiferromagnetic (AFM) order at reasonable values of $U,J$ and thus to the possibility to realize cuprate-like superconductivity in this 2D material upon doping. We also find that the application of tensile strain enhances the cuprate-like phase and phases with orbital polarization in general, by reducing the $t_2 / t_1$ ratio of next-nearest to nearest neighbour hopping. On the contrary, systems with compressive stress have an increased hopping ratio and consequently show a preference for ferromagnetic (FM) phases, including, unexpectedly, the out-of-plane $d_{3z^2-r^2}$ FM phase.

cond-mat.str-el↗
arXiv2021

Renormalized phonon spectrum of polyacetylene and similar materials

Motivated to understand the phonon spectrum renormalization in the ground state of the half-filled SSH model, we use the Born-Oppenheimer approximation together with the harmonic approximation to evaluate the all-to-all real-space ionic force constants generated through the electron-phonon interaction. Using these force constants, we compute the renormalized phonon spectrum and study its behaviour as a function of the Peierls distortion. For the undimerized chain we confirm the presence of a large Kohn anomaly at $2k_F$, signalling a strong lattice instability. For the dimerized chain, we find an optical branch separated by a gap from the acoustic one, while the Kohn anomaly manifests as phonon softening. To find the equilibrium dimerization, we minimize the ground state energy, crucially including the contribution of the renormalized phonon zero-point energy (ZPE). Our results show strong agreement with prior \textit{ab initio} studies for trans-polyacetylene and linear acetylenic carbon (carbyne), validating our method which is much simpler, and moreover can be easily generalized to study other problems in higher dimensions.

cond-mat.str-el↗
arXiv2019

Effect of the electron-lattice coupling on the charge and magnetic order in rare-earth nickelates

We investigate the impact of electron-lattice coupling on the stability of various magnetic orders in rare-earth nickelates. We use the Hartree-Fock approximation, at zero temperature, to study an effective, two-band model with correlations characterized by a Hubbard $U$ and a Hund's $J$. This is coupled to breathing-mode distortions of the octahedral oxygen cages, described semi-classically, with a Holstein term. We analyze the effect of the various parameters on the resulting phase diagram, in particular on the charge disproportionation and on the magnetic order. We confirm that the coupling to the lattice cooperates with Hund's coupling and thus encourages charge disproportionation. We also find that it favors the fully disproportionated, 4-site periodic magnetic order of type $\Uparrow 0 \Downarrow 0$. Other convergent magnetic phases, such as the collinear $\uparrow\uparrow\downarrow\downarrow$ and non-collinear $\uparrow\rightarrow\downarrow\leftarrow$ states, do not couple to the lattice because of their lack of charge disproportionation. Novel phases, e.g. with charge disproportionation but no magnetic order, are also found to be stabilized in specific conditions.

cond-mat.str-el↗