Hyeongjin Kim

I am an incoming applied scientist at Amazon’s Center for Quantum Computing based in San Francisco.

My interests are in numerical simulations of many-body systems, quantum computing, and tensor network algorithms.

I received my Ph.D. in physics at Boston University, advised by Professor Anatoli Polkovnikov, and my B.A. in physics at Williams College, advised by Professor Frederick Strauch.

For a more detailed summary, please check out my cv!

Publications

2026

Quantum Signal Processing for Linear PDEs: Circuit Design and Experimental Validation

Hyeongjin Kim, Revathi Jambunathan, Jan Balewski, and 1 more author

arXiv preprint arXiv:2606.00368, May 2026

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Quantum algorithms offer new avenues for solving partial differential equations (PDEs). While the potential for end-to-end quantum advantage is at present not well understood, recent literature presents explicit circuit constructions for solving certain classes of linear PDEs in the frequency domain and thus offers concrete examples to study. In this work, we develop end-to-end implementations of these quantum circuits compiled to machine-level instructions and benchmark them in both numerical simulations and IBMQ hardware experiments. We focus on the advection, wave, and Poisson equations and study quantum circuits that propagate the dynamics in frequency space via the quantum Fourier transform using approximate methods based on a first-order approximation which offer compact representations with uncontrollable approximation error, and polynomial approximation methods based on quantum signal processing (QSP) leading to deeper circuits with tunable algorithmic error. In addition, we experimentally demonstrate that the QSP-augmented algorithm can provide accurate solutions under realistic hardware constraints. Finally, we extend our method to address non-homogeneous Dirichlet boundary conditions and verify it numerically for a Poisson equation with source term obtained from high-fidelity physics simulations of a capacitively coupled plasma.
@article{kim2026quantumsignalprocessinglinear, title = {Quantum Signal Processing for Linear PDEs: Circuit Design and Experimental Validation}, author = {Kim, Hyeongjin and Jambunathan, Revathi and Balewski, Jan and Camps, Daan}, year = {2026}, month = may, journal = {arXiv preprint arXiv:2606.00368}, }
Defining classical and quantum chaos through adiabatic transformations

Hyeongjin Kim, Cedric Lim, Kirill Matirko, and 2 more authors

Journal of Physics A: Mathematical and Theoretical, Feb 2026

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We propose a formalism which defines chaos in both quantum and classical systems in an equivalent manner by means of \textitadiabatic transformations. The complexity of adiabatic transformations which preserve classical time-averaged trajectories (quantum eigenstates) in response to Hamiltonian deformations serves as a measure of chaos. This complexity is quantified by the (properly regularized) fidelity susceptibility. Physically this measure quantifies long time instabilities of physical observables due to small changes in the Hamiltonian of the system. Our exposition clearly showcases the common structures underlying quantum and classical chaos and allows us to distinguish integrable, chaotic but non-thermalizing, and ergodic/mixing regimes. We apply the fidelity susceptibility to a model of two coupled spins and demonstrate that it successfully predicts the universal onset of chaos, both for finite spin S and in the classical limit S →∞. Interestingly, we find that finite S effects are anomalously large close to integrability.
@article{kim2026definingclassicalquantumchaos, title = {Defining classical and quantum chaos through adiabatic transformations}, author = {Kim, Hyeongjin and Lim, Cedric and Matirko, Kirill and Polkovnikov, Anatoli and Flynn, Michael O.}, year = {2026}, month = feb, journal = {Journal of Physics A: Mathematical and Theoretical}, }

2025

Quantum Computing Technology Roadmaps and Capability Assessment for Scientific Computing – An analysis of use cases from the NERSC workload

Daan Camps, Ermal Rrapaj, Katherine Klymko, and 6 more authors

arXiv preprint arXiv:2509.09882, Sep 2025

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The National Energy Research Scientific Computing Center (NERSC), as the high-performance computing (HPC) facility for the Department of Energy’s Office of Science, recognizes the essential role of quantum computing in its future mission. In this report, we analyze the NERSC workload and identify materials science, quantum chemistry, and high-energy physics as the science domains and application areas that stand to benefit most from quantum computers. These domains jointly make up over 50% of the current NERSC production workload, which is illustrative of the impact quantum computing could have on NERSC’s mission going forward. We perform an extensive literature review and determine the quantum resources required to solve classically intractable problems within these science domains. This review also shows that the quantum resources required have consistently decreased over time due to algorithmic improvements and a deeper understanding of the problems. At the same time, public technology roadmaps from a collection of ten quantum computing companies predict a dramatic increase in capabilities over the next five to ten years. Our analysis reveals a significant overlap emerging in this time frame between the technological capabilities and the algorithmic requirements in these three scientific domains. We anticipate that the execution time of large-scale quantum workflows will become a major performance parameter and propose a simple metric, the Sustained Quantum System Performance (SQSP), to compare system-level performance and throughput for a heterogeneous workload.
@article{camps2025quantum, title = {Quantum Computing Technology Roadmaps and Capability Assessment for Scientific Computing -- An analysis of use cases from the NERSC workload}, author = {Camps, Daan and Rrapaj, Ermal and Klymko, Katherine and Kim, Hyeongjin and Gott, Kevin and Darbha, Siva and Balewski, Jan and Austin, Brian and Wright, Nicholas J.}, year = {2025}, month = sep, journal = {arXiv preprint arXiv:2509.09882}, }
Confined and deconfined chaos in classical spin systems

Hyeongjin Kim, Robin Schaefer, David M. Long, and 2 more authors

arXiv preprint arXiv:2507.07168, Aug 2025

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Weakly perturbed integrable many-body systems are typically chaotic and thermal at late times. However, there are distinct relationships between the timescales for thermalization and chaos. The typical relationship is confined chaos: when trajectories are still confined to regions in phase space with constant conserved quantities (actions), the conjugate angle variables are already unstable. Confined chaos thus far precedes thermalization. In a different relationship, which we term deconfined chaos, chaotic instabilities and thermalization occur on the same timescale. We investigate these two qualitatively distinct scenarios through numerical and analytical studies of two perturbed integrable classical spin models: the Ishimori spin chain (confined chaos), and the central spin model with XX interactions (deconfined chaos). We analytically establish (super)-integrability in the latter model in a microcanonical shell. Deconfined chaos emerges through the separation of phase space into large quasi-integrable regions and a thin chaotic manifold. The latter causes chaos and thermalization on the fastest possible timescale, which is proportional to the inverse perturbation strength. This behavior is reminiscent of the quantum SYK models and strange metals.
@article{kim2025confined, title = {Confined and deconfined chaos in classical spin systems}, author = {Kim, Hyeongjin and Schaefer, Robin and Long, David M. and Polkovnikov, Anatoli and Chandran, Anushya}, year = {2025}, journal = {arXiv preprint arXiv:2507.07168}, month = aug, }

2024

Variational Adiabatic Transport of Tensor Networks

Hyeongjin Kim, Matthew Fishman, and Dries Sels

PRX Quantum, Jun 2024

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We discuss a tensor network method for constructing the adiabatic gauge potential—the generator of adiabatic transformations—as a matrix product operator, which allows us to adiabatically transport matrix product states. Adiabatic evolution of tensor networks offers a wide range of applications, of which two are explored in this paper: improving tensor network optimization and scanning phase diagrams. By efficiently transporting eigenstates to quantum criticality and performing intermediary density-matrix renormalization group (DMRG) optimizations along the way, we demonstrate that we can compute ground and low-lying excited states faster and more reliably than a standard DMRG method at or near quantum criticality. We demonstrate a simple automated step size adjustment and detection of the critical point based on the norm of the adiabatic gauge potential. Remarkably, we are able to reliably transport states through the critical point of the models we study.
@article{PRXQuantum.5.020361, title = {Variational Adiabatic Transport of Tensor Networks}, author = {Kim, Hyeongjin and Fishman, Matthew and Sels, Dries}, journal = {PRX Quantum}, volume = {5}, issue = {2}, pages = {020361}, numpages = {13}, year = {2024}, month = jun, publisher = {American Physical Society}, doi = {10.1103/PRXQuantum.5.020361}, }
Integrability as an attractor of adiabatic flows

Hyeongjin Kim, and Anatoli Polkovnikov

Phys. Rev. B, May 2024

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The interplay between quantum chaos and integrability has been extensively studied in the past decades. We approach this topic from the point of view of geometry encoded in the quantum geometric tensor, which describes the complexity of adiabatic transformations. In particular, we consider two generic models of spin chains that are parameterized by two independent couplings. In one, the integrability breaking perturbation is global while, in the other, integrability is broken only at the boundary. In both cases, the shortest paths in the coupling space lead towards integrable regions and we argue that this behavior is generic. These regions thus act as attractors of adiabatic flows similar to river basins in nature. Physically, the directions towards integrable regions are characterized by faster relaxation dynamics than those parallel to integrability, and the anisotropy between them diverges in the thermodynamic limit as the system approaches the integrable point. We also provide evidence that the transition from integrable to chaotic behavior is universal for both models, similar to continuous phase transitions, and that the model with local integrability breaking quickly becomes chaotic but avoids ergodicity.
@article{PhysRevB.109.195162, title = {Integrability as an attractor of adiabatic flows}, author = {Kim, Hyeongjin and Polkovnikov, Anatoli}, journal = {Phys. Rev. B}, volume = {109}, issue = {19}, pages = {195162}, numpages = {16}, year = {2024}, month = may, publisher = {American Physical Society}, doi = {10.1103/PhysRevB.109.195162}, }