arXiv subjects

Matthew Otten

Publications and source records attributed to Matthew Otten.

At least 19 recordsLinked to original sources

arXiv2026

Preservation of Positive-Definiteness by Bernstein Operators on the Circle

We prove that, for every $n\ge1$, the degree-$n$ Bernstein operator on $[0,\pi]$ preserves positive-definiteness on the circle $S^1$. Equivalently, if a continuous function on $[0,\pi]$ defines a positive-definite isotropic kernel on $S^1$, then its Bernstein polynomial approximation of any fixed degree does as well. The proof reduces the problem to the nonnegativity of the cosine coefficients of the Bernstein images $Q_{n,m}=B_n[\cos(mx)]$, which we prove using an explicit coefficient formula and a two-regime positivity argument. We also discuss the higher-dimensional sphere analogue and show that the naive affine Bernstein operator fails to preserve the positive-definite cone already on $S^2$.

math.CA↗

arXiv2026

Absorbing Many-Body Correlations into Core-Optimized Orbitals

The cost of simulating quantum many-body systems - on classical or quantum hardware - scales with the number of variational parameters, so progress at fixed computational budget hinges on more parameter-efficient ans\"atze. Configuration Interaction (CI) is widely dismissed as parameter-heavy; we show this verdict is an artifact of the orbital basis. Co-optimizing the orbital basis with a sparse CI wavefunction - a method we call Core-Optimized Orbitals (COO) - absorbs a large fraction of the dynamical correlation directly into the single-particle basis, cutting the determinant count by several orders of magnitude beyond the already compact TrimCI ansatz on which it builds. On [Fe$_4$S$_4$] (54e, 36o), a billion-determinant TrimCI+COO wavefunction reaches accuracy that would require $3\!\times\!10^{14}$ determinants in a localized basis. At matched accuracy, it is $8\times$ more compact than the largest unrestricted-DMRG benchmark ($25\times$ with PT2). Across the iron-sulfur series - from [Fe$_2$S$_2$] (30e,20o) to the P-cluster (114e,73o) - TrimCI+COO is $10$-$100\times$ more compact than SU(2)-adapted DMRG with entanglement-minimized orbitals at matched accuracy. A tunable Hubbard-on-graph model factorizes the advantage into an orbital-basis gain and an ansatz gain, the latter capturing multi-center entanglement that resists MPS localization. COO therefore changes the picture of CI efficiency: sparse CI with optimized orbitals can outperform state-of-the-art tensor networks on strongly correlated multi-center systems.

quant-ph↗

arXiv2026

CANOE: Classically Assisted Non-Orthogonal Eigensolver

In the early fault-tolerant regime, where quantum resources remain limited, hybrid quantum-classical strategies offer one possible route toward quantum advantage. We introduce CANOE, the Classically Assisted Non-Orthogonal Eigensolver, as such an approach, distributing Rayleigh-Ritz basis states between quantum and classical hardware. This approach leverages the expressive power of quantum states, which are costly to reproduce classically, while augmenting them with a large pool of classically generated basis states that can be incorporated at negligible computational cost. We validate this through numerical simulations of a 76-qubit chromium atom system, quantifying how each additional quantum basis state enhances ground-state representability and how the inclusion of classical states further amplifies this improvement. Such a hybrid basis framework necessarily requires an efficient protocol on quantum hardware for evaluating overlaps between quantum and classical states in the resulting generalized eigenvalue formulation. We address this by introducing a histogram-based protocol and demonstrate through numerical simulations that it can approach chemical accuracy at moderate sampling cost. To solve the resulting generalized eigenvalue problem stably, CANOE incorporates a Schur-complement-based stabilization procedure that mitigates ill-conditioning caused by linear dependencies in the hybrid basis. Taken together, these results position CANOE as a practical framework for combining limited quantum resources with expansive classical resources for early fault-tolerant quantum simulations.

quant-ph↗

arXiv2025

Hardware Efficient Quantum Kernels Using Multimode Bulk Acoustic Resonators

The kernel trick is a widely applicable technique in machine learning domains that maps datasets that are difficult to classify into a computationally friendly feature space. As the dimension of the dataset scales, these kernel calculations can quickly become computationally intractable or data inefficient. In this work, we extend prior efforts in quantum kernel design for Kerr nonlinear devices by implementing time-dependent simulations of a Kerr-qubit coupled to acoustic resonators. For experimentally feasible parameters, we demonstrate that the Kerr nonlinearity directly induces non-classical behavior in the multimode system, which we use to define and analyze a quantum-enhanced kernel. Finally, we present a brief scaling characterization that demonstrates the computational intractability of classically simulating the kernel as the number of resonators scales.

quant-ph↗

arXiv2025

Energy-Scaled Zero-Noise Extrapolation for Gottesman-Kitaev-Preskill Code

The performance of Gottesman-Kitaev-Preskill (GKP) codes, an approach to hardware-efficient quantum error correction, is limited by the finite squeezing capabilities of current experimental platforms. To circumvent this hardware demand, we introduce Energy-Scaled Zero-Noise Extrapolation (ES-ZNE), a quantum error mitigation protocol that uses the mean photon number of the GKP code as a tunable effective noise parameter. The protocol measures logical observables at a series of accessible finite energies and extrapolates the results to the ideal, infinite-energy limit using an ansatz based on the code's asymptotic error scaling. Through simulating a GKP qubit under a pure-loss channel, we demonstrate that ES-ZNE successfully mitigates finite-energy errors, recovering the ideal expectation values (within numerical uncertainty) in the shallow-noise regime. Furthermore, by computationally removing artifacts arising from the finite-energy encoding, our method characterizes the intrinsic performance of the ideal GKP code, revealing a sharp error threshold beyond which the code's corrective power diminishes. These results establish ES-ZNE as a practical, software-based strategy for enhancing the performance of near-term bosonic quantum processors, trading sampling overhead for demanding physical resources like high squeezing.

quant-ph↗

arXiv2025

First ionization potentials of Cr, Mo, and W calculated with SHCI

The design and performance of future fusion power plants will depend on accurate atomic data for plasma-facing material and plasma impurity species. A leading candidate for the plasma-facing material is tungsten due to its high melting point, however, the energy levels and wavefunctions of high-Z atoms with many electrons (e.g. 30 or more), including tungsten, are difficult to calculate with high accuracy. Gaps and large uncertainties in atomic data for tungsten introduce design and performance uncertainties for a fusion power plant. Specifically, improved atomic data for ionization potential, excited state energies, and collisional excitation rates are needed for the low charge states of atomic tungsten. We aim to address these shortcomings by using the semistochastic heat-bath configuration interaction (SHCI) method, which nearly exactly calculates the energies that can be determined at higher cost with the full configuration interaction. Adding well-motivated approximations to SHCI, including orbital optimization and effective core potentials, we demonstrate good agreement between our calculated first ionization potentials and the best available experimental values for chromium, molybdenum, and tungsten. The efficiency and accuracy achieved in calculating these ionization potentials demonstrates that our SHCI workflow can yield improved electron structure data for ions with many electrons, suggesting that the method could also be useful for collisional processes, such as state-selective charge exchange reactions and electron impact ionization.

physics.atom-ph↗

arXiv2025

From Random Determinants to the Ground State

Accurate quantum many-body calculations often depend on reliable reference states or good human-designed ans\"atze, yet these sources of knowledge can become unreliable in hard problems like strongly correlated systems. We introduce the Trimmed Configuration Interaction (TrimCI) method, a prior-knowledge-free algorithm that builds accurate ground states directly from random Slater determinants. TrimCI iteratively expands the variational space and trims away unimportant states, allowing a random initial core to self-refine into an accurate approximation of exact ground state. Across challenging benchmarks, TrimCI achieves state-of-the-art accuracy with strikingly efficiency gains of several orders of magnitude. For [4Fe-4S] cluster, it matches recent quantum computing results with $10^6$-fold fewer determinants and CPU-hours. For the nitrogenase P-cluster, it matches selected-CI accuracy using $10^5$-fold fewer determinants. For $8\times8$ Hubbard model, it recovers over $99\%$ of the ground-state energy using only $10^{-28}$ of the Hilbert space. In some regimes, TrimCI attains orders-of-magnitude higher accuracy than AFQMC method. These results demonstrate that high-accuracy many-body ground states can be discovered directly from random determinants, establishing TrimCI as a prior-knowledge-free, accurate and highly efficient framework for quantum many-body systems. The compact explicit wavefunctions it produces further enable direct and rapid evaluation of observables.

quant-ph↗

arXiv2025

A Versatile Variational Quantum Kernel Framework for Non-Trivial Classification

Quantum kernel methods are a promising branch of quantum machine learning, yet their effectiveness on diverse, high-dimensional, real-world data remains unverified. Current research has largely been limited to low-dimensional or synthetic datasets, preventing a thorough evaluation of their potential. To address this gap, we developed an algorithmic framework for variational quantum kernels utilizing resource-efficient ans\"atze for complex classification tasks and introduced a parameter scaling technique to accelerate convergence. We conducted a comprehensive benchmark of this framework on eight challenging, real-world and high-dimensional datasets covering tabular, image, time series, and graph data. Our results show that the proposed quantum kernels demonstrate competitive classification accuracy compared to standard classical kernels in classical simulation, such as the radial basis function (RBF) kernel. This work demonstrates that properly designed quantum kernels can function as versatile, high-performance tools, laying a foundation for quantum-enhanced applications in real-world machine learning. Further research is needed to fully assess the practical performance of quantum methods.

cs.LG↗

arXiv2025

Physics-Informed Neural Networks for Gate Design using Quantum Optimal Control

Implementing quantum gates on quantum computers can require the application of carefully shaped pulses for high-fidelity operations. We explore the use of physics-informed neural networks (PINNs) for quantum optimal control to assess their usefulness in predicting such pulses. Our PINN is a feedforward neural network that utilizes an unsupervised learning approach, whose loss function includes terms that enforce the equations that govern the evolution of a quantum system, measure how close the learned unitary is to the target unitary operation, and ensure state normalization. We use a sinusoidal activation function and adopt variance-type weight initialization, tailored to our activation function. By analyzing the model's performance with important machine learning metrics, we demonstrate that the choice of our architecture is well-suited for this type of problem. We ensure that our network avoids the vanishing and exploding gradients with our relevant choices. We build two different PINNs, one based on the Schr\"odinger equation and another one based on the Lindblad equation. Our PINNs are able to discover high-fidelity two-qubit gate pulses for a variety of quantum operations, demonstrating its flexibility and robustness. We build two different PINNs, one based on the Schr\"odinger equation and another one based on the Lindblad equation. Our PINNs are able to discover high-fidelity two-qubit gate pulses for a variety of quantum operations, demonstrating its flexibility and robustness.

quant-ph↗

arXiv2025

Achieving Utility-Scale Applications through Full Stack Co-Design of Fault Tolerant Quantum Computers

Quantum computing promises revolutionary advances in modeling materials and molecules. However, the up-to-date runtime estimates for utility-scale applications on certain quantum hardware systems are in the order of years rendering quantum computations impractical. Our work incorporates state-of-the-art innovations in all key aspects of the fault-tolerant quantum computing (FTQC) stack to show how quantum computers could realistically and practically tackle CO$_2$ utilization for green energy production. We bring down the quantum computation runtime from 22 years to just 1 day, achieving a significant 7.9e03 reduction from previous state-of-the-art work. This reduction renders the quantum computation feasible, challenges state-of-the-art classical methods and results to a predicted run-time quantum advantage. We provide a rigorous analysis of how different innovations across the stack combine to provide such reductions. Our work provides strong evidence that all layers of FTQC are crucial in the quest for quantum advantage. Our analysis can be applied to related problems on FTQC and for any type of quantum architecture. Our methodology connects quantum algorithms to applications of positive real-world impact and leads to compelling evidence of achievable quantum advantage.

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

A Perspective on Quantum Computing Applications in Quantum Chemistry using 25--100 Logical Qubits

The intersection of quantum computing and quantum chemistry represents a promising frontier for achieving quantum utility in domains of both scientific and societal relevance. Owing to the exponential growth of classical resource requirements for simulating quantum systems, quantum chemistry has long been recognized as a natural candidate for quantum computation. This perspective focuses on identifying scientifically meaningful use cases where early fault-tolerant quantum computers, which are considered to be equipped with approximately 25--100 logical qubits, could deliver tangible impact. While recent advances in classical computing have pushed the boundaries of tractable simulations to unprecedented scales, this logical-qubit regime represents the first window where quantum devices can pursue qualitatively distinct strategies, such as polynomial-scaling phase estimation, direct simulation of quantum dynamics, and active-space embedding, that remain challenging for classical solvers, for instance, multireference charge-transfer and conical-intersection states central to photochemistry and materials design. We highlight near-term opportunities in algorithm and software design, discuss representative chemical problems suited for quantum acceleration, and propose strategic roadmaps and collaborative pathways for advancing practical quantum utility in quantum chemistry.

quant-ph↗

arXiv2025

Efficient algorithms for quantum chemistry on modular quantum processors

Quantum chemistry is a promising application of future quantum computers, but the requirements on qubit count and other resources suggest that modular computing architectures will be required. We introduce an implementation of a quantum chemistry algorithm that is distributed across several computational modules: the distributed unitary selective coupled cluster (dUSCC). We design a packing scheme using the pseudo-commutativity of Trotterization to maximize the parallelism while optimizing the scheduling of all inter-module gates around the buffering of inter-module Bell pairs. We demonstrate dUSCC on a 3-cluster (H$_4$)$_3$ chain and show that it naturally utilizes the molecule's structure to reduce inter-module latency. We show that the run time of dUSCC is unchanged with inter-module latency up to $\sim$20$\times$ slower than intra-module gates in the (H$_4$)$_3$ while maintaining chemical accuracy. dUSCC should be "free" in the weakly entangled systems, and the existence of "free" dUSCC can be found efficiently using classical algorithms. This new compilation scheme both leverages pseudo-commutativity and considers inter-module gate scheduling, and potentially provides an efficient distributed compilation of other Trotterized algorithms.

quant-ph↗

arXiv2025

Non-unitary Variational Quantum Eigensolver with the Localized Active Space Method and Cost Mitigation

Accurately describing strongly correlated systems with affordable quantum resources remains a central challenge for quantum chemistry applications on near and intermediate-term quantum computers. The localized active space self-consistent field (LASSCF) approximates the complete active space self-consistent field (CASSCF) by generating active space-based wave functions within specific fragments while treating interfragment correlation with mean-field approach, hence is computationally less expensive. Hardware-efficient ansatzes (HEA) offer affordable and shallower circuits, yet they often fail to capture the necessary correlation. Previously, Jastrow-factor-inspired non-unitary qubit operators were proposed to use with HEA for variational quantum eigensolver (VQE) calculations (nuVQE), as they do not increase circuit depths and recover correlation beyond the mean-field level for Hartree-Fock initial states. Here, we explore running nuVQE with LASSCF as the initial state. The method, named LAS-nuVQE, is shown to recover interfragment correlations, reach chemical accuracy with a small number of gates (<70) in both H4 and square cyclobutadiene. To further address the inherent symmetry-breaking in HEA, we implemented spin-constrained LAS-nuVQE to extend the capabilities of HEA further and show spin-pure results for square cyclobutadiene. We mitigate the increased measurement overhead of nuVQE via Pauli grouping and shot-frugal sampling, reducing measurement costs by up to two orders of magnitude compared to ungrouped operator, and show that one can achieve better accuracy with a small number of shots (10^3-4) per one expectation value calculation compared to noiseless simulations with one or two orders of magnitude more shots. Finally, wall clock time estimates show that, with our measurement mitigation protocols, nuVQE becomes a cheaper and more accurate alternative than VQE with HEA.

quant-ph↗

arXiv2024

How to Build a Quantum Supercomputer: Scaling from Hundreds to Millions of Qubits

In the span of four decades, quantum computation has evolved from an intellectual curiosity to a potentially realizable technology. Today, small-scale demonstrations have become possible for quantum algorithmic primitives on hundreds of physical qubits. Nevertheless, there are significant outstanding challenges in quantum hardware, fabrication, software architecture, and algorithms on the path towards a full-stack scalable quantum computing technology. Here, we provide a comprehensive review of these scaling challenges. We show how to facilitate scaling by adopting existing semiconductor technology to build much higher-quality qubits, employing systems engineering approaches, and performing distributed heterogeneous quantum-classical computing. We provide a detailed resource and sensitivity analysis for quantum applications on surface-code error-corrected quantum computers given current, target, and desired hardware specifications based on superconducting qubits, accounting for a realistic distribution of errors. We provide comprehensive resource estimates for several utility-scale applications including quantum chemistry calculations, catalyst design, NMR spectroscopy, and Fermi-Hubbard simulation. We show that orders of magnitude enhancement in performance could be obtained by a combination of hardware improvements and tight quantum-HPC integration. Furthermore, we introduce high-performance architectures for quantum-probabilistic computing with custom-designed accelerators to tackle today's industry-scale classical optimization, machine learning, and quantum simulation tasks in a cost-effective manner.

quant-ph↗

arXiv2024

Prospects for Quantum Computation in Propellant Design: Assessing the Stability of Cyclic Ozone in Nanoscale Confinement

Cyclic ozone additives have the potential to markedly increase the specific impulse of rocket fuel. This would translate to greater efficiency and reduced costs for space lift by granting more payload per rocket. While practical efforts to capture this isomer have been unsuccessful, it is possible that cyclic ozone would be stabilized in confined geometries. The required synthetic methods are nonetheless difficult to design and require theory-driven inputs that lie beyond the scope of classical methods. Quantum computation has the potential to enable these calculations, though the underlying hardware requirements remain unclear for many practical applications. We present an end-to-end analysis of how quantum methods could support efforts to isolate cyclic ozone via fullerene encapsulation. Our discussion extends beyond asymptotic complexity, reporting both logical- and physical-level resource estimates for ground-state energy determination via quantum phase estimation (QPE), computed using multiple independent resource estimation stacks - Azure Quantum Resource Estimator (AzureQRE), PennyLane's resource estimation framework, and MIT Lincoln Lab's pyLIQTR toolkit - to cross-check resource estimates and bracket realistic overheads. Taken collectively, these data delineate a plausible scale for realistic, computationally-aided molecular design efforts using fault-tolerant quantum computation.

quant-ph↗

arXiv2024

Quantum Resources Required for Binding Affinity Calculations of Amyloid beta

Amyloid beta, an intrinsically disordered protein, plays a seemingly important but not well-understood role in neurodegenerative diseases like Alzheimer's disease. A key feature of amyloid beta, which could lead to potential therapeutic intervention pathways, is its binding affinity to certain metal centers, like iron and copper. Numerically calculating such binding affinities is a computationally challenging task, involving strongly correlated metal centers. A key bottleneck in understanding the binding affinity is obtaining estimates of the ground state energy. Quantum computers have the potential to accelerate such calculations but it is important to understand the quantum resources required. In this work, we detail a computational workflow for binding affinity calculations for amyloid beta utilizing quantum algorithms, providing estimated quantum resources required, at both the logical and hardware level.

quant-ph↗

arXiv2024

Quantum computing for corrosion-resistant materials and anti-corrosive coatings design

Corrosion is a pervasive issue that impacts the structural integrity and performance of materials across various industries, imposing a significant economic impact globally. In fields like aerospace and defense, developing corrosion-resistant materials is critical, but progress is often hindered by the complexities of material-environment interactions. While computational methods have advanced in designing corrosion inhibitors and corrosion-resistant materials, they fall short in understanding the fundamental corrosion mechanisms due to the highly correlated nature of the systems involved. This paper explores the potential of leveraging quantum computing to accelerate the design of corrosion inhibitors and corrosion-resistant materials, with a particular focus on magnesium and niobium alloys. We investigate the quantum computing resources required for high-fidelity electronic ground-state energy estimation (GSEE), which will be used in our hybrid classical-quantum workflow. Representative computational models for magnesium and niobium alloys show that 2292 to 38598 logical qubits and $(1.04$ to $1962) \times 10^{13}$ T-gates are required for simulating the ground-state energy of these systems under the first quantization encoding using plane waves basis.

quant-ph↗