arXiv subjects

Artur F. Izmaylov

Publications and source records attributed to Artur F. Izmaylov.

At least 19 recordsLinked to original sources

arXiv2026

Classical Active-Space Hybrid Quantum Subspace Expansion (CASH-QSE): Quantum Corrections without Remeasuring the Classically Calculable Energy

The wave function prepared by a variational quantum eigensolver (VQE) can contain a substantial classically tractable component, yet its energy contribution is sampled on the quantum device. Representing the wave function as a combination of a classical reference and separately prepared quantum states allows the reference energy to be evaluated without quantum sampling. However, near-linear dependence among these components can amplify measurement errors and destabilize the resulting energy estimate. We introduce Classical Active-Space Hybrid Quantum Subspace Expansion (CASH-QSE), which retains a complete-active-space self-consistent field (CASSCF) reference classically and uses occupation structure to construct quantum states exactly orthogonal to the reference and to one another. The energy follows from an ordinary Hermitian eigenvalue problem without overlap measurements, while the same occupation constraints simplify the measured operators. Using full configuration interaction to guide component selection, we test CASH-QSE along H$_2$O and N$_2$ bond-stretching coordinates spanning weakly to strongly correlated regimes. The benchmarks use STO--3G for both molecules and a restricted cc-pVDZ orbital space for H$_2$O. CASH-QSE reaches chemical accuracy while limiting the largest complete measurement circuits to a few hundred all-to-all logical controlled-NOT gates. In favorable cases, it also reduces the idealized final-energy sampling cost by several orders of magnitude relative to VQE with an adaptive derivative-assembled pseudo-Trotter ansatz (ADAPT-VQE).

quant-ph↗

arXiv2026

Resource-efficient energy-based operator selection in fermionic ADAPT-VQE via exact Hamiltonian transformation

The energy-based approach to operator selection in ADAPT-VQE relies on reconstructing the one-parameter energy landscape for each operator in the pool. In fermionic implementations, the cost of reconstructing this energy landscape often becomes a bottleneck. We address this issue through an exact Hamiltonian transformation that reformulates the one-parameter energy landscape according to a generator-dependent fragmentation of the transformed Hamiltonian. While our method is mathematically identical to standard fermionic Rotoselect, it effectively reduces its cost by about a factor of two, bringing it close to that of gradient-based ADAPT-VQE. We use this formulation to benchmark the gradient-based and energy-based selection approaches in combination with two ansatz-optimization strategies -- "last", where only the appended operator is optimized, and "full", where the full ansatz is re-optimized -- and with both fixed-orbital and orbital-optimized formulations. The benchmark comprises $\text{LiH}$, $\text{BeH}_2$, and $\text{H}_2\text{O}$ at both equilibrium and stretched geometries. In the most weakly correlated system, pairing energy-based selection with "last" optimization enables the efficient construction of an accurate ansatz, which avoids any VQE optimization. As correlation increases, full ansatz re-optimization and orbital optimization become the main factors governing convergence and overall resource cost. This study shows how exact Hamiltonian transformations provide an effective route to reducing the measurement overhead of fermionic energy-based ADAPT-VQE. Moreover, the benchmark clarifies the relative role of operator scoring approach, re-optimization strategy, and orbital treatment in the performance of ADAPT-VQE.

quant-ph↗

arXiv2026

Bounding Eigenstate Overlap from Hamiltonian Moments: Success Probability Guarantees for Quantum Phase Estimation

Estimating the overlap between a prepared state and a target eigenstate is crucial for the efficiency of quantum phase estimation (QPE), since QPE succeeds with probability equal to this overlap. We present a systematically improvable method to compute certified upper and lower bounds on such overlaps using a finite set of Hamiltonian moments. Our approach constructs optimal polynomial upper/lower bounds on an energy-window indicator and evaluates them through linear and semidefinite programs, yielding the tightest bounds consistent with the available moment and spectral-interval information. We demonstrate the method on strongly correlated molecular Hamiltonians and study the impact of approximate moments obtained from tensor-network contractions. The resulting bounds provide a practical pre-QPE screening tool for selecting initial states and can be implemented with either classical moment computation or quantum expectation estimation.

quant-ph↗

arXiv2026

Exact Factorization of Unitary Transformations with Spin-Adapted Generators

Preserving spin symmetry in variational quantum algorithms is essential for producing physically meaningful electronic wavefunctions. Implementing spin-adapted transformations on quantum hardware, however, is challenging because the corresponding fermionic generators translate into noncommuting Pauli operators. In this work, we introduce an exact and computationally efficient factorization of spin-adapted unitaries derived from fermionic double excitation and deexcitation rotations. These unitaries are expressed as ordered products of exponentials of Pauli operators. Our method exploits the fact that the elementary operators in these generators form small Lie algebras. By working in the adjoint representation of these algebras, we reformulate the factorization problem as a low-dimensional nonlinear optimization over matrix exponentials. This approach enables precise numerical reparametrization of the unitaries without relying on symbolic manipulations. The proposed factorization provides a practical strategy for constructing symmetry-conserving quantum circuits within variational algorithms. It preserves spin symmetry by design, reduces implementation cost, and ensures the accurate representation of electronic states in quantum simulations of molecular systems.

quant-ph↗

arXiv2026

Accuracy and resource advantages of quantum eigenvalue estimation with non-Hermitian transcorrelated electronic Hamiltonians

In electronic structure calculations, the transcorrelated method consists in transforming the Hamiltonian so as to remove the Coulomb cusp in its eigenfunctions. As a result, the wavefunction can be described more accurately without increasing the size of the basis set. However, the transcorrelated Hamiltonian is non-Hermitian and non-normal, which makes many common quantum algorithms inapplicable. Recently, a quantum eigenvalue estimation algorithm (QEVE) was proposed for non-Hermitian Hamiltonians with real spectra [FOCS 65, 1051 (2024)]. Although the asymptotic scaling of this algorithm with the desired accuracy is shown to be optimal, the constant factor in its complexity scaling has not been analyzed. Here we investigate the cost of QEVE applied to transcorrelated electronic Hamiltonians of second-row atoms and compare it to the cost of applying standard qubitization to non-transcorrelated Hamiltonians. We find that, with the xTC approximation, the T gate count of QEVE in the minimal STO-6G basis is between those of standard qubitization in the cc-pVTZ and cc-pVQZ bases. The accuracy of the transcorrelated energy differs between systems: for Li and Be, it is more accurate than the cc-pVQZ energy, while for larger atoms, the error gradually increases, exceeding the cc-pVDZ level for O, F, and Ne.

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↗

arXiv2026

Multistate iterative qubit coupled cluster (MS-iQCC): a quantum-inspired, state-averaged approach to ground- and excited-state energies

We introduce the multistate iterative qubit coupled cluster (MS-iQCC) method, a quantum-inspired algorithm that runs efficiently on classical hardware and is designed to predict both ground and excited electronic states of molecules. Accurate excited-state energetics are essential for interpreting spectroscopy and chemical reactivity, but standard electronic structure methods are either too computationally expensive for larger systems or lose reliability in the presence of strong electron correlation. MS-iQCC addresses this challenge by simultaneously optimizing multiple electronic states in a single, state-averaged procedure that treats ground and excited states on equal footing. This removes the energetic bias that is introduced when excited states are computed one at a time and constrained to remain orthogonal to previously optimized states. The approach supports multireference electronic structure by allowing multideterminantal initial guesses and by adaptively building a compact exponential ansatz from a pool of qubit excitation generators. We apply MS-iQCC to H$_4$, H$_2$O, N$_2$, and C$_2$, including strongly correlated geometries, and observe robust convergence of all targeted state energies to chemically meaningful accuracy across their potential energy surfaces.

physics.chem-ph↗

arXiv2025

Quantum Seniority-based Subspace Expansion: Linear Combinations of Short-Circuit Unitary Transformations for the Electronic Structure Problem

Quantum SENiority-based Subspace Expansion (Q-SENSE) is a hybrid quantum-classical algorithm that interpolates between the Variational Quantum Eigensolver (VQE) and Configuration Interaction (CI) methods. It constructs Hamiltonian matrix elements on a quantum device and solves the resulting eigenvalue problem classically. Unlike other expansion-based methods -- such as Quantum Subspace Expansion (QSE), Quantum Krylov Algorithms, and the Non-Orthogonal Quantum Eigensolver -- Q-SENSE introduces seniority operators as artificial symmetries to construct orthogonal basis states. This seniority-symmetry-based approach reduces one of the primary limitations of VQE on near-term quantum hardware -- circuit depth -- at the cost of measuring additional matrix elements. The artificial symmetries also reduce the number of Hamiltonian terms that must be measured, as only a small fraction of the terms couple basis states in different seniority subspaces. With all these merits, Q-SENSE offers a scalable and resource-efficient route to quantum advantage on near-term quantum devices and in the early fault-tolerant regime.

quant-ph↗

arXiv2025

On the Feasibility of Exact Unitary Transformations for Many-body Hamiltonians

Exact unitary transformations play a central role in the analysis and simulation of many-body quantum systems, yet the conditions under which they can be carried out exactly and efficiently remain incompletely understood. We show that exact transformations arise whenever the adjoint action of a unitary's generator defines a linear map within a finite-dimensional operator space. In this regime, there exists a finite-degree polynomial that annihilates the adjoint map, rendering the Baker-Campbell-Hausdorff (BCH) expansion finite. We identify the role of Lie algebras and their modules in producing finite BCH expansions in all known cases. This perspective brings together previously disparate examples of exact transformations under a single unifying principle and clarifies how algebraic relations between generators and transformed operators determine the polynomial degree of the transformation. We illustrate this framework for previously known cases of efficient unitary transformations including unitary coupled-cluster and Pauli product generators. Using this framework, we propose a new class of fermionic generators that can be used for efficient transformations. The result establishes sufficient algebraic conditions for when exact unitary transformations are possible and provides new strategies for reducing their computational cost in quantum simulation and constructing feasible unitary transformations.

quant-ph↗

arXiv2025

Planted Solutions in Quantum Chemistry: Generating Non-Trivial Hamiltonians with Known Ground States

Generating large, non-trivial quantum chemistry test problems with known ground-state solutions remains a core challenge for benchmarking electronic structure methods. Inspired by planted-solution techniques from combinatorial optimization, we introduce four classes of Hamiltonians with embedded, retrievable ground states. These Hamiltonians mimic realistic electronic structure problems, support adjustable complexity, and are derived from reference systems. Crucially, their ground-state energies can be computed exactly, provided the construction parameters are known. To obscure this structure and control perceived complexity, we introduce techniques such as killer operators, balance operators, and random orbital rotations. We showcase this framework using examples based on homogeneous catalysts of industrial relevance and validate tunable difficulty through density matrix renormalization group (DMRG) convergence behavior. Beyond enabling scalable, ground-truth benchmark generation, our approach offers a controlled setting to explore the limitations of electronic structure methods and investigate how Hamiltonian structure influences ground state solution difficulty.

quant-ph↗

arXiv2025

Quantum Gambling: Best-Arm Strategies for Generator Selection in Adaptive Variational Algorithms

Adaptive variational algorithms suffer from prohibitively high measurement costs during the generator selection step, since energy gradients must be estimated for a large operator pool. This scaling bottleneck limits their applicability to larger molecular systems on near-term quantum devices. We address this challenge by reformulating generator selection as a Best Arm Identification (BAI) problem, where the goal is to identify the generator with the largest energy gradient using as few measurements as possible. To solve it, we employ the Successive Elimination algorithm, which adaptively allocates measurements and discards unpromising candidates early. Numerical experiments on molecular systems demonstrate that this approach substantially reduces the number of measurements required while preserving ground-state energy accuracy. By cutting measurement overhead without sacrificing performance, our method makes adaptive variational algorithms more practical for near-term quantum simulations.

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

QB Ground State Energy Estimation Benchmark

Ground State Energy Estimation (GSEE) is a central problem in quantum chemistry and condensed matter physics, demanding efficient algorithms to solve complex electronic structure calculations. This work introduces a structured benchmarking framework for evaluating the performance of both classical and quantum solvers on diverse GSEE problem instances. We assess three prominent methods -- Semistochastic Heat-Bath Configuration Interaction (SHCI), Density Matrix Renormalization Group (DMRG), and Double-Factorized Quantum Phase Estimation (DF QPE) -- ighlighting their respective strengths and limitations. Our results show that fully optimized SHCI achieves near-universal solvability on the benchmark set, DMRG excels for low-entanglement systems, and DF QPE is currently constrained by hardware and algorithmic limitations. However, we observe that many benchmark Hamiltonians are drawn from datasets tailored to SHCI and related approaches, introducing a bias that favors classical solvers. To mitigate this, we propose expanding the benchmark suite to include more challenging, strongly correlated systems to enable a more balanced and forward-looking evaluation of solver capabilities. As quantum hardware and algorithms improve, this benchmarking framework will serve as a vital tool for tracking progress and identifying domains where quantum methods may surpass classical techniques. The QB-GSEE benchmark repository is openly available at https://github.com/isi-usc-edu/qb-gsee-benchmark [1]. By maintaining a scalable and open resource, we aim to accelerate innovation in computational quantum chemistry and quantum computing.

quant-ph↗

arXiv2025

Estimating Trotter Approximation Errors to Optimize Hamiltonian Partitioning for Lower Eigenvalue Errors

Trotter approximation in conjunction with Quantum Phase Estimation can be used to extract eigen-energies of a many-body Hamiltonian on a quantum computer. There were several ways proposed to assess the quality of this approximation based on estimating the norm of the difference between the exact and approximate evolution operators. Here, we explore how different error estimators correlate with the true error in the ground state energy due to Trotter approximation. For a set of small molecules we calculate these exact error in ground-state electronic energies due to the second-order Trotter approximation. Comparison of these errors with previously used upper bounds show correlation less than 0.4 across various Hamiltonian partitionings. On the other and, building the Trotter approximation error estimation based on perturbation theory up to a second order in the time-step for eigenvalues provides estimates with very good correlations with the exact Trotter approximation errors. These findings highlight the non-faithful character of norm-based estimations for prediction of a Trotter-based eigenvalue estimation performance and the need of alternative estimators. The developed perturbative estimates can be used for practical time-step and Hamiltonian partitioning selection protocols, which are needed for an accurate assessment of quantum resources.

physics.chem-ph↗

arXiv2025

Quantum Measurement for Quantum Chemistry on a Quantum Computer

Quantum chemistry is among the most promising applications of quantum computing, offering the potential to solve complex electronic structure problems more efficiently than classical approaches. A critical component of any quantum algorithm is the measurement step, where the desired properties are extracted from a quantum computer. This review focuses on recent advancements in quantum measurement techniques tailored for quantum chemistry, particularly within the second quantized framework suitable for current and near-term quantum hardware. We provide a comprehensive overview of measurement strategies developed primarily for the Variational Quantum Eigensolver (VQE) and its derivatives. These strategies address the inherent challenges posed by complexity of the electronic Hamiltonian operator. Additionally, we examine methods for estimating excited states and one- and two-electron properties, extending the applicability of quantum algorithms to broader chemical phenomena. Key aspects of the review include approaches for constructing measurement operators with reduced classical preprocessing and quantum implementation costs, techniques to minimize the number of measurements required for a given accuracy, and error mitigation strategies that leverage symmetries and other properties of the measurement operators. Furthermore, we explore measurement schemes rooted in Quantum Phase Estimation (QPE), which are expected to become viable with the advent of fault-tolerant quantum computing. This review emphasizes foundational concepts and methodologies rather than numerical benchmarks, serving as a resource for researchers aiming to enhance the efficiency and accuracy of quantum measurements in quantum chemistry.

quant-ph↗

arXiv2025

Efficient Strategies for Reducing Sampling Error in Quantum Krylov Subspace Diagonalization

Within the realm of early fault-tolerant quantum computing (EFTQC), quantum Krylov subspace diagonalization (QKSD) has emerged as a promising quantum algorithm for the approximate Hamiltonian diagonalization via projection onto the quantum Krylov subspace. However, the algorithm often requires solving an ill-conditioned generalized eigenvalue problem (GEVP) involving erroneous matrix pairs, which can significantly distort the solution. Since EFTQC assumes limited-scale error correction, finite sampling error becomes a dominant source of error in these matrices. This work focuses on quantifying sampling errors during the measurement of matrix element in the projected Hamiltonian examining two measurement approaches based on the Hamiltonian decompositions: the linear combination of unitaries and diagonalizable fragments. To reduce sampling error within a fixed budget of quantum circuit repetitions, we propose two measurement strategies: the shifting technique and coefficient splitting. The shifting technique eliminates redundant Hamiltonian components that annihilate either the bra or ket states, while coefficient splitting optimizes the measurement of common terms across different circuits. Numerical experiments with electronic structures of small molecules demonstrate the effectiveness of these strategies, reducing sampling costs by a factor of 20-500.

quant-ph↗

arXiv2025

Quantum computer formulation of the FKP-operator eigenvalue problem for probabilistic learning on manifolds

We present a quantum computing formulation to address a challenging problem in the development of probabilistic learning on manifolds (PLoM). It involves solving the spectral problem of the high-dimensional Fokker-Planck (FKP) operator, which remains beyond the reach of classical computing. Our ultimate goal is to develop an efficient approach for practical computations on quantum computers. For now, we focus on an adapted formulation tailored to quantum computing. The methodological aspects covered in this work include the construction of the FKP equation, where the invariant probability measure is derived from a training dataset, and the formulation of the eigenvalue problem for the FKP operator. The eigen equation is transformed into a Schrödinger equation with a potential V, a non-algebraic function that is neither simple nor a polynomial representation. To address this, we propose a methodology for constructing a multivariate polynomial approximation of V, leveraging polynomial chaos expansion within the Gaussian Sobolev space. This approach preserves the algebraic properties of the potential and adapts it for quantum algorithms. The quantum computing formulation employs a finite basis representation, incorporating second quantization with creation and annihilation operators. Explicit formulas for the Laplacian and potential are derived and mapped onto qubits using Pauli matrix expressions. Additionally, we outline the design of quantum circuits and the implementation of measurements to construct and observe specific quantum states. Information is extracted through quantum measurements, with eigenstates constructed and overlap measurements evaluated using universal quantum gates.

quant-ph↗

arXiv2025

Global Minimization of Electronic Hamiltonian 1-Norm via Linear Programming in the Block Invariant Symmetry Shift (BLISS) Method

The cost of encoding a system Hamiltonian in a digital quantum computer as a linear combination of unitaries (LCU) grows with the 1-norm of the LCU expansion. The Block Invariant Symmetry Shift (BLISS) technique reduces this 1-norm by modifying the Hamiltonian action on only the undesired electron-number subspaces. Previously, BLISS required a computationally expensive nonlinear optimization that was not guaranteed to find the global minimum. Here, we introduce various reformulations of this optimization as a linear programming problem, which guarantees optimality and significantly reduces the computational cost. We apply BLISS to industrially-relevant homogeneous catalysts in active spaces of up to 76 orbitals, finding substantial reductions in both the spectral range of the modified Hamiltonian and the 1-norms of Pauli and fermionic LCUs. Our linear programming techniques for obtaining the BLISS operator enable more efficient Hamiltonian simulation and, by reducing the Hamiltonian's spectral range, offer opportunities for improved LCU groupings to further reduce the 1-norm.

quant-ph↗