arXiv subjects

Juan Miguel Arrazola

Publications and source records attributed to Juan Miguel Arrazola.

At least 19 recordsLinked to original sources

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.

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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.

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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.

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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.

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arXiv2026

Quantum algorithm for simulating non-adiabatic dynamics at metallic surfaces

Non-adiabatic dynamics at molecule-metal interfaces govern diverse and technologically important phenomena, from heterogeneous catalysis to dye-sensitized solar energy conversion and charge transport across molecular junctions. Realistic modeling of such dynamics necessitates taking into account various charge and energy transfer channels involving the coupling of nuclear motion with a very large number of electronic states, leading to prohibitive cost using classical computational methods. In this work we introduce a generalization of the Anderson-Newns Hamiltonian and develop a highly optimized quantum algorithm for simulating the non-adiabatic dynamics of realistic molecule-metal interfaces. Using the PennyLane software platform, we perform resource estimations of our algorithm, showing its remarkably low implementation cost for model systems representative of various scientifically and industrially relevant molecule-metal systems. Specifically, we find that time evolution for models including $100$ metal orbitals, $8$ molecular orbitals, and $20$ nuclear degrees of freedom, requires only $271$ qubits and $7.9 \times 10^7$ Toffoli gates for $1000$ Trotter steps, suggesting non-adiabatic molecule-metal dynamics as a fruitful application of first-generation fault-tolerant quantum computers.

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arXiv2026

Efficient Simulation of Pre-Born-Oppenheimer Dynamics on a Quantum Computer

In this work, we present a quantum algorithm for direct first-principles simulation of electron-nuclear dynamics on a first-quantized real-space grid. Our algorithm achieves best-in-class efficiency for block-encoding the pre-Born-Oppenheimer molecular Hamiltonian by harnessing the linear scaling of swap networks for implementing the quadratic number of particle interactions, while using a novel alternating sign implementation of the Coulomb interaction that exploits highly optimized arithmetic routines. We benchmark our approach for a series of scientifically and industrially relevant chemical reactions. We demonstrate over an order-of-magnitude reduction in costs compared to previous state-of-the-art for the $\rm NH_3+BF_3$ reaction, achieving a Toffoli cost of $8.7\times10^{9}$ per femtosecond using $1362$ logical qubits (system + ancillas). Our results significantly lower the resources required for fault-tolerant simulations of photochemical reactions, while providing a suite of algorithmic primitives that are expected to serve as foundational building blocks for a broader class of quantum algorithms.

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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.

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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.

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arXiv2025

Quantum compilation framework for data loading

Efficient encoding of classical data into quantum circuits is a critical challenge that directly impacts the scalability of quantum algorithms. In this work, we present an automated compilation framework for resource-aware quantum data loading tailored to a given input vector and target error tolerance. By explicitly exploiting the trade-off between exact and approximate state preparation, our approach systematically partitions the total error budget between precision and approximation errors, thereby minimizing quantum resource costs. The framework supports a comprehensive suite of state-of-the-art methods, including multiplexer-based loaders, quantum read-only memory (QROM) constructions, sparse encodings, matrix product states (MPS), Fourier series loaders (FSL), and Walsh transform-based diagonal operators. We demonstrate the effectiveness of our framework across several applications, where it consistently uncovers non-obvious, resource-efficient strategies enabled by controlled approximation. In particular, we analyze a computational fluid dynamics workflow where the automated selection of MPS state preparation and Walsh transform-based encoding, combined with a novel Walsh-based measurement technique, leads to resource reductions of over four orders of magnitude compared to previous approaches. We also introduce two independent advances developed through the framework: a more efficient circuit for d-diagonal matrices, and an optimized block encoding for kinetic energy operators. Our results underscore the indispensable role of automated, approximation-aware compilation in making large-scale quantum algorithms feasible on resource-constrained hardware.

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arXiv2025

Quantum Algorithm for Vibronic Dynamics: Case Study on Singlet Fission Solar Cell Design

Vibronic interactions between nuclear motion and electronic states are critical for the accurate modeling of photochemistry. However, accurate simulations of fully quantum non-adiabatic dynamics are often prohibitively expensive for classical methods beyond small systems. In this work, we present a quantum algorithm based on product formulas for simulating time evolution under a general vibronic Hamiltonian in real space, capable of handling an arbitrary number of electronic states and vibrational modes. We develop the first trotterization scheme for vibronic Hamiltonians beyond two electronic states and introduce an array of optimization techniques for the exponentiation of each fragment in the product formula, resulting in a remarkably low cost of implementation. To demonstrate practical relevance, we outline a proof-of-principle integration of our algorithm into a materials discovery pipeline for designing more efficient singlet fission-based organic solar cells. We estimate that $100$ fs of propagation using a second-order Trotter product formula for a $6$-state, $21$-mode model of exciton transport at an anthracene dimer requires $154$ qubits and $2.76 \times 10^6$ Toffoli gates. While a $4$-state, $246$-mode model describing charge transfer at an anthracene-fullerene interface requires $1053$ qubits and $2.66 \times 10^7$ Toffoli gates.

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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.

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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.

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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.

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arXiv2025

Nonlinear Spectroscopy via Generalized Quantum Phase Estimation

Response theory has a successful history of connecting experimental observations with theoretical predictions. Of particular interest is the optical response of matter, from which spectroscopy experiments can be modelled. However, the calculation of response properties for quantum systems is often prohibitively expensive, especially for nonlinear spectroscopy, as it requires access to either the time evolution of the system or to excited states. In this work, we introduce a generalized quantum phase estimation framework designed for multi-variate phase estimation. This allows the treatment of general correlation functions enabling the recovery of response properties of arbitrary orders. The generalized quantum phase estimation circuit has an intuitive construction that is linked with a physical process of interest, and can directly sample frequencies from the distribution that would be obtained experimentally. In addition, we provide a single-ancilla modification of the new framework for early fault-tolerant quantum computers. Overall, our framework enables the efficient simulation of spectroscopy experiments beyond the linear regime, such as Raman spectroscopy, having that the circuit cost grows linearly with respect to the order of the target nonlinear response. This opens up an exciting new field of applications for quantum computers with potential technological impact.

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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.

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arXiv2025

Early Fault-Tolerant Quantum Algorithms in Practice: Application to Ground-State Energy Estimation

We investigate the feasibility of early fault-tolerant quantum algorithms focusing on ground-state energy estimation problems. In particular, we examine the computation of the cumulative distribution function (CDF) of the spectral measure of a Hamiltonian and the identification of its discontinuities. Scaling these methods to larger system sizes reveals three key challenges: the smoothness of the CDF for large supports, the lack of tight lower bounds on the overlap with the true ground state, and the difficulty of preparing high-quality initial states. To address these challenges, we propose a signal processing approach to find these estimates automatically, in the regime where the quality of the initial state is unknown. Rather than aiming for exact ground-state energy, we advocate for improving classical estimates by targeting the low-energy support of the initial state. Additionally, we provide quantitative resource estimates, demonstrating a constant-factor improvement in the number of samples required to detect a specified change in CDF. Our numerical experiments, conducted on a 26-qubit fully connected Heisenberg model, leverage a truncated density-matrix renormalization group (DMRG) initial state with a low bond dimension. The results show that the predictions from the quantum algorithm align closely with the DMRG-converged energies at larger bond dimensions while requiring several orders of magnitude fewer samples than theoretical estimates suggest. These findings underscore that CDF-based quantum algorithms are a practical and resource-efficient alternative to quantum phase estimation, particularly in resource-constrained scenarios.

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arXiv2024

Better product formulas for quantum phase estimation

Quantum phase estimation requires simulating the evolution of the Hamiltonian, for which product formulas are attractive due to their smaller qubit cost and ease of implementation. However, the estimation of the error incurred by product formulas is usually pessimistic and task-agnostic, which poses problems for assessing their performance in practice for problems of interest. In this work, we study the error of product formulas for the specific task of quantum energy estimation. To this end, we employ the theory of Trotter error with a Magnus-based expansion of the effectively simulated Hamiltonian. The result is a generalization of previous energy estimation error analysis of gapped eigenstates to arbitrary order product formulas. As an application, we discover a 9-term second-order product formula with an energy estimation error that is quadratically better than Trotter-Suzuki. Furthermore, by leveraging recent work on low-energy dynamics of product formulas, we provide tighter bounds for energy estimation error in the low-energy subspace. We show that for Hamiltonians with some locality and positivity properties, the cost can achieve up to a quadratic asymptotic speedup in terms of the target error.

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arXiv2024

Quantum simulation of time-dependent Hamiltonians via commutator-free quasi-Magnus operators

Hamiltonian simulation is arguably the most fundamental application of quantum computers. The Magnus operator is a popular method for time-dependent Hamiltonian simulation in computational mathematics, yet its usage requires the implementation of exponentials of commutators, which has previously made it unappealing for quantum computing. The development of commutator-free quasi-Magnus operators (CFQMs) circumvents this obstacle, at the expense of a lack of provable global numeric error bounds. In this work, we establish one such error bound for CFQM-based time-dependent quantum Hamiltonian simulation by carefully estimating the error of each step involved in their definition. This allows us to compare its cost with the alternatives, and show that CFQMs are often the most efficient product-formula technique available by more than an order of magnitude. As a result, we find that CFQMs may be particularly useful to simulate time-dependent Hamiltonians on early fault-tolerant quantum computers.

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