arXiv subjects

Gunhee Park

Publications and source records attributed to Gunhee Park.

14 recordsLinked to original sources

arXiv2026

Statistical mechanics in continuous space with tensor network methods

Tensor network (TN) methods are well established for computing partition functions in statistical mechanics, though this use has traditionally been limited to lattice models. We extend the scope of TN methodology to interacting particle systems in continuous space. Through a real-space discretization combined with a cell-based coarse-graining scheme, we formulate an effective lattice model that explicitly preserves spatial locality. The partition function of this model is represented as a TN, and the thermodynamic quantities are computed via boundary contraction. We apply this framework to the two-dimensional hard-disk problem and demonstrate the strengths of the TN formulation compared to existing Monte Carlo simulations.

cond-mat.stat-mech↗

arXiv2025

Tensor Network Loop Cluster Expansions for Quantum Many-Body Problems

We analyze the tensor network loop cluster expansion, introduced in [G. Park, J. Gray, and G. K.-L. Chan, Phys. Rev. B 112, 174310 (2025)] as a systematic correction to belief propagation, in the context of general quantum many-body problems. We provide numerical examples of the accuracy and practical applicability of the approach for the computation of ground-state observables for high bond dimension tensor networks, in two- and three-dimensions, with open and periodic boundary conditions, and for spin and fermion problems. We find that the contraction error converges approximately exponentially with cluster size, enabling accurate local observable and energy estimates for many systems where standard contraction methods are otherwise impractical.

quant-ph↗

arXiv2025

Coupled Lindblad pseudomode theory for simulating open quantum systems

Coupled Lindblad pseudomode theory is a promising approach for simulating non-Markovian quantum dynamics on both classical and quantum platforms, with dynamics that can be realized as a quantum channel. We provide theoretical evidence that the number of coupled pseudomodes only needs to scale as $\mathrm{polylog}(T/\varepsilon)$ in the simulation time $T$ and precision $\varepsilon$. Inspired by the realization problem in control theory, we also develop a robust numerical algorithm for constructing the coupled modes that avoids the non-convex optimization required by existing approaches. We demonstrate the effectiveness of our method by computing population dynamics and absorption spectra for the spin-boson model. This work provides a significant theoretical and computational improvement to the coupled Lindblad framework, which impacts a broad range of applications from classical simulations of quantum impurity problems to quantum simulations on near-term quantum platforms.

quant-ph↗

arXiv2025

Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation

Describing nonequilibrium quantum dynamics remains a significant computational challenge due to the growth of spatial entanglement. The tensor network influence functional (TN-IF) approach mitigates this problem for computing the time evolution of local observables by encoding the subsystem's influence functional path integral as a matrix product state (MPS), thereby shifting the resource governing computational cost from spatial entanglement to temporal entanglement. We extend the applicability of the TN-IF method to two-dimensional lattices by demonstrating its construction on tree lattices and proposing a belief propagation (BP) algorithm for the TN-IF, termed influence functional BP (IF-BP), to simulate local observable dynamics on arbitrary graphs. Even though the BP algorithm introduces uncontrolled approximation errors on arbitrary graphs, it provides an accurate description for locally tree-like lattices. Numerical simulations of the kicked Ising model on a heavy-hex lattice, motivated by a recent quantum experiment, highlight the effectiveness of the IF-BP method, which demonstrates superior performance in capturing long-time dynamics where traditional tensor network state-based methods struggle. Our results further reveal that the temporal entanglement entropy (TEE) only grows logarithmically with time for this model, resulting in a polynomial computational cost for the whole method. We further construct a cluster expansion of IF-BP to introduce loop correlations beyond the BP approximation, providing a systematic correction to the IF-BP estimate. We demonstrate the power of the cluster expansion of the IF-BP in simulating the quantum quench dynamics of the 2D transverse field Ising model, obtaining numerical results that improve on the state-of-the-art.

quant-ph↗

arXiv2025

Digital quantum magnetism on a trapped-ion quantum computer

Digital quantum matter -- realized when discrete quantum gates approximate continuous time evolution -- is susceptible to heating into chaotic, structureless states. If digitization errors are adequately suppressed, a long-lived transient regime of approximately energy-conserving dynamics can be observed on gate-based quantum computers. Conservation of energy, in turn, enables the exploration of a wide variety of complex behaviors observed in equilibrium systems, ranging from the nontrivial microscopic origins of thermalization itself to the stabilization of effective models hosting exotic emergent properties. Here, we use Quantinuum's system model H2 quantum computer to simulate digitized dynamics of the quantum Ising model, suppressing digitization errors well enough to observe thermalization on timescales that severely challenge classical simulation methods. Relaxation of an inhomogeneous state reveals an emergent hydrodynamics due to approximate energy conservation, and we compute the associated diffusion constant. By reprogramming our simulations to take place on a triangular lattice with periodic boundary conditions, we observe thermalization consistent with emergent gauge and topological constraints resulting from lattice frustration. Our results were enabled by continued advances in two-qubit gate quality (native partial entangler fidelities of $99.94(1)\%$), and establish digital quantum computers as powerful tools for studying (effectively) continuous-time dynamics.

quant-ph↗

arXiv2024

Unified error bounds for perturbations of non-Markovian open quantum systems in Gaussian environments

We present perturbative error bounds for the non-Markovian dynamics of observables in open quantum systems interacting with Gaussian environments, governed by a general Liouville dynamics. This extends the work of [Mascherpa et al., Phys. Rev. Lett. 118, 100401, 2017], which demonstrated qualitatively tighter bounds over the standard Gr\"onwall-type inequality for unitary system-bath evolution. Our results apply to systems with both bosonic and fermionic environments. Our approach utilizes a superoperator formalism, which avoids the need for formal coherent state path integral calculations, or the dilation of Lindblad dynamics into an equivalent unitary framework with infinitely many degrees of freedom. This enables a unified treatment of a wide range of open quantum systems. These findings provide a solid theoretical basis for various recently developed pseudomode methods in simulating open quantum system dynamics.

quant-ph↗

arXiv2024

Fermionic tensor network contraction for arbitrary geometries

We describe our implementation of fermionic tensor network contraction on arbitrary lattices within both a globally ordered and locally ordered formalism. We provide a pedagogical description of these two conventions as implemented for the quimb library. Using hyperoptimized approximate contraction strategies, we present benchmark fermionic projected entangled pair states simulations of finite Hubbard models defined on the three-dimensional diamond lattice and random regular graphs.

quant-ph↗

arXiv2024

Quasi-Lindblad pseudomode theory for open quantum systems

We introduce a new framework to study the dynamics of open quantum systems with linearly coupled Gaussian baths. Our approach replaces the continuous bath with an auxiliary discrete set of pseudomodes with dissipative dynamics, but we further relax the complete positivity requirement in the Lindblad master equation and formulate a quasi-Lindblad pseudomode theory. We show that this quasi-Lindblad pseudomode formulation directly leads to a representation of the bath correlation function in terms of a complex weighted sum of complex exponentials, an expansion that is known to be rapidly convergent in practice and thus leads to a compact set of pseudomodes. The pseudomode representation is not unique and can differ by a gauge choice. When the global dynamics can be simulated exactly, the system dynamics is unique and independent of the specific pseudomode representation. However, the gauge choice may affect the stability of the global dynamics, and we provide an analysis of why and when the global dynamics can retain stability despite losing positivity. We showcase the performance of this formulation across various spectral densities in both bosonic and fermionic problems, finding significant improvements over conventional pseudomode formulations.

quant-ph↗

arXiv2024

Correlation Functions From Tensor Network Influence Functionals: The Case of the Spin-Boson Model

We investigate the application of matrix product state (MPS) representations of the influence functionals (IF) for the calculation of real-time equilibrium correlation functions in open quantum systems. Focusing specifically on the unbiased spin-boson model, we explore the use of IF-MPSs for complex time propagation, as well as IF-MPSs for constructing correlation functions in the steady state. We examine three different IF approaches: one based on the Kadanoff-Baym contour targeting correlation functions at all times, one based on a complex contour targeting the correlation function at a single time, and a steady state formulation which avoids imaginary or complex times, while providing access to correlation functions at all times. We show that within the IF language, the steady state formulation provides a powerful approach to evaluate equilibrium correlation functions.

physics.chem-ph↗

arXiv2024

Tensor network influence functionals in the continuous-time limit: connections to quantum embedding, bath discretization, and higher-order time propagation

We describe two developments of tensor network influence functionals (in particular, influence functional matrix product states (IF-MPS)) for quantum impurity dynamics within the fermionic setting of the Anderson impurity model. The first provides the correct extension of the IF-MPS to continuous time by introducing a related mathematical object, the boundary influence functional MPS. The second connects the dynamics described by a compressed IF-MPS to that of a quantum embedding method with a time-dependent effective bath undergoing nonunitary dynamics. Using these concepts, we implement higher-order time propagators for the quench dynamics of the Anderson impurity model within the boundary IF-MPS formalism. The calculations illustrate the ability of the current formulation to efficiently remove the time step error in standard discrete-time IF-MPS implementations as well as to interface with state vector propagation techniques. They also show the advantages of IF-MPS dynamics, with its associated highly compact effective bath dynamics, over state vector propagation with a static bath discretization.

cond-mat.str-el↗

arXiv2023

Ab initio quantum many-body description of superconducting trends in the cuprates

Using a systematic ab initio quantum many-body approach that goes beyond low-energy models, we directly compute the superconducting pairing order and estimate the pairing gap of several doped cuprate materials and structures within a purely electronic picture. We find that we can correctly capture two well-known trends: the pressure effect, where the pairing order and gap increase with intra-layer pressure, and the layer effect, where the pairing order and gap vary with the number of copper-oxygen layers. From these calculations, we observe that the strength of superexchange and the covalency at optimal doping are the best descriptors for these trends. Our microscopic analysis further identifies that strong short-range spin fluctuations and multi-orbital charge fluctuations drive the development of the pairing order. Our work illustrates the possibility of a material-specific ab initio understanding of unconventional high-temperature superconducting materials.

cond-mat.supr-con↗

arXiv2022

Real time evolution of Anderson impurity models via tensor network influence functionals

In this work we present and analyze two tensor network-based influence functional approaches for simulating the real-time dynamics of quantum impurity models such as the Anderson model. Via comparison with recent numerically exact simulations, we show that such methods accurately capture the long-time non-equilibrium quench dynamics. The two parameters that must be controlled in these tensor network influence functional approaches are a time discretization (Trotter) error and a bond dimension (tensor network truncation) error. We show that the actual numerical uncertainties are controlled by an intricate interplay of these two approximations which we demonstrate in different regimes. Our work opens the door to using these tensor network influence functional methods as general impurity solvers.

cond-mat.str-el↗

arXiv2022

Variational quantum one-class classifier

One-class classification is a fundamental problem in pattern recognition with a wide range of applications. This work presents a semi-supervised quantum machine learning algorithm for such a problem, which we call a variational quantum one-class classifier (VQOCC). The algorithm is suitable for noisy intermediate-scale quantum computing because the VQOCC trains a fully-parameterized quantum autoencoder with a normal dataset and does not require decoding. The performance of the VQOCC is compared with that of the one-class support vector machine (OC-SVM), the kernel principal component analysis (PCA), and the deep convolutional autoencoder (DCAE) using handwritten digit and Fashion-MNIST datasets. The numerical experiment examined various structures of VQOCC by varying data encoding, the number of parameterized quantum circuit layers, and the size of the latent feature space. The benchmark shows that the classification performance of VQOCC is comparable to that of OC-SVM and PCA, although the number of model parameters grows only logarithmically with the data size. The quantum algorithm outperformed DCAE in most cases under similar training conditions. Therefore, our algorithm constitutes an extremely compact and effective machine learning model for one-class classification.

quant-ph↗

arXiv2022

Ideal refocusing of an optically active spin qubit under strong hyperfine interactions

Combining highly coherent spin control with efficient light-matter coupling offers great opportunities for quantum communication and networks, as well as quantum computing. Optically active semiconductor quantum dots have unparalleled photonic properties, but also modest spin coherence limited by their resident nuclei. Here, we demonstrate that eliminating strain inhomogeneity using lattice-matched GaAs-AlGaAs quantum dot devices prolongs the electron spin coherence by nearly two orders of magnitude, beyond 0.113(3) ms. To do this, we leverage the 99.30(5)% fidelity of our optical pi-pulse gates to implement dynamical decoupling. We vary the number of decoupling pulses up to N = 81 and find a coherence time scaling of N^{0.75(2)}. This scaling manifests an ideal refocusing of strong interactions between the electron and the nuclear-spin ensemble, holding the promise of lifetime-limited spin coherence. Our findings demonstrate that the most punishing material science challenge for such quantum-dot devices has a remedy, and constitute the basis for highly coherent spin-photon interfaces.

cond-mat.mes-hall↗