arXiv subjects

Samuel J. Elman

Publications and source records attributed to Samuel J. Elman.

11 recordsLinked to original sources

arXiv2026

Expanding the Class of Free Fermions via Twin-Collapse Methods

We present a novel graph-theoretic approach to simplifying generic many-body Hamiltonians. Our primary result introduces a recursive twin-collapse algorithm, leveraging the identification and elimination of symmetric vertex pairs (twins), as well as line-graph modules, within the frustration graph of the Hamiltonian. This method systematically block-diagonalizes Hamiltonians, significantly reducing complexity while preserving the energetic spectrum. Importantly, our approach expands the class of models that can be mapped to non-interacting fermionic Hamiltonians (free-fermion solutions), thereby broadening the applicability of classical solvability methods. Through numerical simulations on spin Hamiltonians arranged in periodic lattice configurations and Majorana Hamiltonians, we demonstrate that the twin-collapse increases the identification of simplicial and claw-free graph structures, which characterize free-fermion solvability. Finally, we extend our framework by presenting a generalized discrete Stone-von Neumann theorem. This comprehensive framework provides new insights into Hamiltonian simplification techniques, free-fermion solutions, and group-theoretical characterizations relevant for quantum chemistry, condensed matter physics, and quantum computation.

quant-ph↗

arXiv2026

Dissipative continuation for ground-state preparation at chemical transition states

Simulating chemical reactions exhibits a pronounced unevenness in computational difficulty: while equilibrium reactant and product geometries are often tractable, transition-state (TS) geometries frequently display strong multi-reference character that challenges both classical solvers and coherent quantum state-preparation methods. We introduce a dissipative continuation protocol for preparing electronic ground states near TS geometries within a hybrid classical--quantum workflow. In the intended setting, classical electronic-structure methods supply an approximate TS geometry, a computationally motivated continuation path, and a locally compatible active-space representation along that path. Starting from a warm start at a tractable geometry on the same aligned path, the quantum routine transports the state toward the TS using orbital-gauge-aligned Hamiltonians and engineered dissipative cooling primitives that repeatedly contract population into the instantaneous low-energy sector. We prove that, for continuation paths satisfying a Lipschitz smoothness condition and a localized Eigenstate Thermalization Hypothesis (ETH)-motivated downward-drift condition within the relevant energy window, the ground state at the target geometry can be prepared to total energy error $\epsilon_E$ with total ideal cooling-step complexity $\widetilde{O}(C_{\mathrm{DK}}^2 N_o^2 / \epsilon_E)$. Here $C_{\mathrm{DK}}$ quantifies ground-state rotation along the aligned path. The corresponding logical gate count is obtained by multiplying this primitive count by the cost of implementing one dissipative step, which is polynomial in the block-encoding size of the Lindbladian under standard Lindblad-simulation algorithms. This identifies a structured regime in which dissipative continuation provides a conditional route to ground-state preparation at strongly correlated TS geometries.

quant-ph↗

arXiv2025

End-to-End Complexity Analysis for Quantum Simulation of the Extended Jaynes-Cummings Models

The extended Jaynes-Cummings model (eJCM) is a foundational framework for describing multi-mode light-matter interactions, with direct applications in quantum technologies such as photon addition and quasi-noiseless amplification. However, the model's complexity makes classical simulation intractable for large systems that could be of practical interest. In this work, we present a comprehensive, end-to-end framework for the quantum simulation of the eJCM. We develop explicit quantum algorithms and circuits for simulating the system's time evolution using first and second-order product formulas, analyzing the dynamics in both the Schrodinger and interaction pictures. Our analysis includes rigorous, closed-form error bounds that guide the choice of simulation parameters, and we extend the methodology to efficiently handle both pure and mixed quantum states. Furthermore, we validate our theoretical cost models with numerical simulations and provide a detailed fault-tolerant resource analysis, compiling the simulation circuits for a surface-code architecture to yield concrete estimates for physical qubit counts and execution times. This work establishes a complete roadmap for simulating the eJCM on future quantum computers.

quant-ph↗

arXiv2025

A Graph-Theoretic Framework for Free-Parafermion Solvability

We present a graph-theoretic characterisation of when a quantum spin model admits an exact solution via a mapping to free parafermions. Our characterisation is based on the concept of a frustration graph, which represents the commutation relations between Weyl operators of a Hamiltonian. We show that a quantum spin system has an exact free-parafermion solution if its frustration graph is an oriented indifference graph. Further, we show that if the frustration graph of a model can be dipath oriented via switching operations, then the model is integrable in the sense that there is a family of commuting independent set charges. Additionally, we establish an efficient algorithm for deciding whether this is possible. Our characterisation extends that given for free-fermion solvability. Finally, we apply our results to solve three qudit spin models.

quant-ph↗

arXiv2025

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↗

arXiv2025

Optimal Scheduling of Graph States via Path Decompositions

We study the optimal scheduling of graph states in measurement-based quantum computation, establishing an equivalence between measurement schedules and path decompositions of graphs. We define the spatial cost of a measurement schedule based on the number of simultaneously active qubits and prove that an optimal measurement schedule corresponds to a path decomposition of minimal width. Our analysis shows that approximating the spatial cost of a graph is $\textsf{NP}$-hard, while for graphs with bounded spatial cost, we establish an efficient algorithm for computing an optimal measurement schedule.

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↗

arXiv2023

A Unified Graph-Theoretic Framework for Free-Fermion Solvability

We show that a quantum spin system has an exact description by non-interacting fermions if its frustration graph is claw-free and contains a simplicial clique. The frustration graph of a spin model captures the pairwise anticommutation relations between Pauli terms of its Hamiltonian in a given basis. This result captures a vast family of known free-fermion solutions. In previous work, it was shown that a free-fermion solution exists if the frustration graph is either a line graph, or (even-hole, claw)-free. The former case generalizes the celebrated Jordan-Wigner transformation and includes the exact solution to the Kitaev honeycomb model. The latter case generalizes a non-local solution to the four-fermion model given by Fendley. Our characterization unifies these two approaches, extending generalized Jordan-Wigner solutions to the non-local setting and generalizing the four-fermion solution to models of arbitrary spatial dimension. Our key technical insight is the identification of a class of cycle symmetries for all models with claw-free frustration graphs. We prove that these symmetries commute, and this allows us to apply Fendley's solution method to each symmetric subspace independently. Finally, we give a physical description of the fermion modes in terms of operators generated by repeated commutation with the Hamiltonian. This connects our framework to the developing body of work on operator Krylov subspaces. Our results deepen the connection between many-body physics and the mathematical theory of claw-free graphs.

quant-ph↗

arXiv2021

Free fermions behind the disguise

An invaluable method for probing the physics of a quantum many-body spin system is a mapping to noninteracting effective fermions. We find such mappings using only the frustration graph $G$ of a Hamiltonian $H$, i.e., the network of anticommutation relations between the Pauli terms in $H$ in a given basis. Specifically, when $G$ is (even-hole, claw)-free, we construct an explicit free-fermion solution for $H$ using only this structure of $G$, even when no Jordan-Wigner transformation exists. The solution method is generic in that it applies for any values of the couplings. This mapping generalizes both the classic Lieb-Schultz-Mattis solution of the XY model and an exact solution of a spin chain recently given by Fendley, dubbed "free fermions in disguise." Like Fendley's original example, the free-fermion operators that solve the model are generally highly nonlinear and nonlocal, but can nonetheless be found explicitly using a transfer operator defined in terms of the independent sets of $G$. The associated single-particle energies are calculated using the roots of the independence polynomial of $G$, which are guaranteed to be real by a result of Chudnovsky and Seymour. Furthermore, recognizing (even-hole, claw)-free graphs can be done in polynomial time, so recognizing when a spin model is solvable in this way is efficient. We give several example families of solvable models for which no Jordan-Wigner solution exists, and we give a detailed analysis of such a spin chain having 4-body couplings using this method.

quant-ph↗

arXiv2021

Boundary topological entanglement entropy in two and three dimensions

The topological entanglement entropy is used to measure long-range quantum correlations in the ground state of topological phases. Here we obtain closed form expressions for topological entropy of (2+1)- and (3+1)-dimensional loop gas models, both in the bulk and at their boundaries, in terms of the data of their input fusion categories and algebra objects. Central to the formulation of our results are generalized $\mathcal{S}$-matrices. We conjecture a general property of these $\mathcal{S}$-matrices, with proofs provided in many special cases. This includes constructive proofs for categories up to rank 5.

quant-ph↗

arXiv2017

Long-range entanglement for spin qubits via quantum Hall edge modes

We propose and analyse a scheme for performing a long-range entangling gate for qubits encoded in electron spins trapped in semiconductor quantum dots. Our coupling makes use of an electrostatic interaction between the state-dependent charge configurations of a singlet-triplet qubit and the edge modes of a quantum Hall droplet. We show that distant singlet-triplet qubits can be selectively coupled, with gate times that can be much shorter than qubit dephasing times and faster than decoherence due to coupling to the edge modes. Based on parameters from recent experiments, we argue that fidelities above 99% could in principle be achieved for a two-qubit entangling gate taking as little as 20 ns.

cond-mat.mes-hall↗