arXiv subjects

Woo-Ram Lee

Publications and source records attributed to Woo-Ram Lee.

13 recordsLinked to original sources

arXiv2025

Noise-resilient and resource-efficient hybrid algorithm for robust quantum gap estimation

We present a hybrid quantum algorithm for estimating gaps in many-body energy spectra, supported by an analytic proof of its inherent resilience to state preparation and measurement errors, as well as mid-circuit multi-qubit depolarizing noise. Our analysis extends to a broader class of Markovian noise, employing error mitigation strategies that optimize the utilization of quantum resources. By integrating trial-state optimization and classical signal processing into the algorithm, we amplify the signal peak corresponding to the exact target gap beyond the error threshold, thereby significantly reducing gap estimate errors. The algorithm's robustness is demonstrated through noisy simulations on the Qiskit Aer simulator and demonstrations on IBM Quantum processors. These results underscore the potential to enable accurate quantum simulations on near-term noisy quantum devices without resource-intensive error correction.

quant-ph↗

arXiv2024

Hybrid quantum gap estimation algorithm using a filtered time series

Quantum simulation advantage over classical memory limitations would allow compact quantum circuits to yield insight into intractable quantum many-body problems, but the interrelated obstacles of large circuit depth in quantum time evolution and noise seem to rule out unbiased quantum simulation in the near term. We prove that classical post-processing, i.e., long-time filtering of an offline time series, exponentially improves the circuit depth needed for quantum time evolution. We apply the filtering method to the construction of a hybrid quantum-classical algorithm to estimate energy gap, an important observable not governed by the variational theorem. We demonstrate, within an operating range of filtering, the success of the algorithm in proof-of-concept simulation for finite-size scaling of a minimal spin model. Our findings set the stage for unbiased quantum simulation to offer memory advantage in the near term.

quant-ph↗

arXiv2022

Measurement-Based Time Evolution for Quantum Simulation of Fermionic Systems

Quantum simulation using time evolution in phase estimation-based quantum algorithms can yield unbiased solutions of classically intractable models. However, long runtimes open such algorithms to decoherence. We show how measurement-based quantum simulation uses effective time evolution via measurement to allow runtime advantages over conventional circuit-based algorithms that use real-time evolution with quantum gates. We construct a hybrid algorithm to find energy eigenvalues in fermionic models using only measurements on graph states. We apply the algorithm to the Kitaev and Hubbard chains. Resource estimates show a runtime advantage if measurements can be performed faster than gates, and graph states compactification is fully used. In this letter, we set the stage to allow advances in measurement precision to improve quantum simulation.

quant-ph↗

arXiv2021

Quantifying Entanglement in Cluster States Built with Error-Prone Interactions

Measurement-based quantum computing is an alternative paradigm to the circuit-based model. This approach can be advantageous in certain scenarios, such as when read-out is fast and accurate, but two-qubit gates realized via inter-particle interactions are slow and can be parallelized to efficiently create a cluster state. However, understanding how two-qubit errors impact algorithm accuracy and developing experimentally viable approaches to characterize cluster-state fidelity are outstanding challenges. Here, we consider one-dimensional cluster states built from controlled phase, Ising, and XY interactions with slow two-qubit error in the interaction strength, consistent with error models of interactions found in a variety of qubit architectures. We detail an experimentally viable teleportation fidelity that offers a measure of the impact of these errors on the cluster state. Our fidelity calculations show that the error has a distinctly different impact depending on the underlying interaction used for the two-qubit entangling gate. In particular, the Ising and XY interactions can allow perfect teleportation through the cluster state even with large errors, but the controlled phase interaction does not. Nonetheless, we find that teleportation through cluster state chains of size $N$ has a maximum two-qubit error for teleportation along a quantum channel that decreases as $N^{-1/2}$. To enable construction of larger cluster states, we design lowest-order refocusing pulses for correcting these slow errors in the interaction strength. Our work generalizes to higher-dimensional cluster states and sets the stage for experiments to monitor the growth of entanglement in cluster states built from error-prone interactions.

quant-ph↗

arXiv2021

Lorenz ratio of an impure compensated metal in the degenerate Fermi liquid regime

The Lorenz ratio serves as a measure to compare thermal and electric conductivities of metals. Recent experiments observed small Lorenz ratios in the compensated metal WP$_2$, indicating that charge flow is strongly favored over heat conduction. Motivated by these findings, we study transport properties of compensated metals in the presence of electron-electron collisions and electron-impurity scattering. We focus on intermediate temperatures, where the phonon contributions to transport are weak and elastic and inelastic scattering rates are comparable. Our exact solution for the kinetic equation in the presence of general Fermi-liquid interactions is used to extract the Lorenz ratio for short and long range interactions. We find that the Lorenz ratio develops a temperature dependence and gets enhanced as a consequence of disorder scattering. For collisions mediated by the Coulomb interaction, impurities give rise to a non-monotonic dependence of the Lorenz ratio on the screening wave number with a minimum for intermediate screening strength. To help future experimental efforts, we establish a scheme to connect the exact results with the solution of the Boltzmann equation under the relaxation time approximation for all collision integrals. Our recipe provides simple phenomenological expressions for the transport coefficients and it allows for a physically transparent interpretation of the results.

cond-mat.str-el↗

arXiv2021

Electric Quantum Oscillation in Weyl Semimetals

Electronic transport in Weyl semimetals is quite extraordinary due to the topological property of the chiral anomaly generating the charge pumping between two distant Weyl nodes with opposite chiralities under parallel electric and magnetic fields. Here, we develop a full nonequilibrium quantum transport theory of the chiral anomaly, based on the fact that the chiral charge pumping is essentially nothing but the Bloch oscillation. Specifically, by using the Keldysh nonequilibrium Green function method, it is shown that there is a rich structure in the chiral anomaly transport, including the negative magnetoresistance, the non-Ohmic behavior, the Esaki-Tsu peak, and finally the resonant oscillation of the DC electric current as a function of electric field, called the electric quantum oscillation. We argue that, going beyond the usual behavior of linear response, the non-Ohmic behavior observed in BiSb alloys can be regarded as a precursor to the occurrence of electric quantum oscillation, which is both topologically and energetically protected in Weyl semimetals.

cond-mat.str-el↗

arXiv2020

The role of electron-electron collisions for magnetotransport at intermediate temperatures

We discuss galvanomagnetic and thermomagnetic effects in disordered electronic systems focusing on intermediate temperatures, for which electron-electron scattering and electron-impurity scattering occur at similar rates, while phonon-related effects can be neglected. In particular, we explore how electric and thermal currents driven either by an electric field or by a temperature gradient are affected by the interplay of momentum-dependent electron-impurity scattering, electron-electron scattering, and the presence of a magnetic field. We find that the electric resistance, the Seebeck coefficient and the Nernst coefficient are particularly sensitive to the momentum dependence of the electron-impurity scattering rate at intermediate temperatures. A sufficiently strong momentum dependence of the electron-impurity scattering rate can induce a sign change of the Seebeck coefficient. This sign change can be suppressed by a perpendicular magnetic field. The temperature and magnetic field dependence of the Seebeck coefficient can be used for measuring the magnitude of the electron-impurity and electron-electron scattering rates. The Nernst coefficient vanishes for momentum-independent electron-impurity scattering, but displays a maximum at finite temperatures once the momentum dependence is accounted for. By contrast, the Hall coefficient and the Righi-Leduc coefficient display only a weak dependence on the momentum dependence of the electron-impurity scattering at intermediate temperatures.

cond-mat.str-el↗

arXiv2019

The role of electron-electron collisions for charge and heat transport at intermediate temperatures

Electric, thermal and thermoelectric transport in correlated electron systems probe different aspects of the many-body dynamics, and thus provide complementary information. These are well studied in the low- and high-temperature limits, while the experimentally important intermediate regime, in which elastic and inelastic scattering are both important, is less understood. To fill this gap, we provide comprehensive solutions of the Boltzmann equation in the presence of an electric field and a temperature gradient for two different cases: First, when electron-electron collisions are treated within the relaxation-time approximation while the full momentum dependence of electron-impurity scattering is included and, second, when the electron-impurity scattering is momentum-independent, but the electron-electron collisions give rise to a momentum-dependent inelastic scattering rate of the Fermi-liquid type. We find that for Fermi-liquid as well as for Coulomb interactions, both methods give the same results for the leading temperature dependence of the transport coefficients. Moreover, the inelastic relaxation rate enters the electric conductivity and the Seebeck coefficient only when the momentum dependence of the electron-impurity collisions, analytical or non-analytical, is included. Specifically, we show that inelastic processes only mildly affect the electric conductivity, but can generate a non-monotonic dependence of the Seebeck coefficient on temperature and even a change of sign. Thermal conductivity, by contrast, always depends on the inelastic scattering rate even for a constant elastic relaxation rate.

cond-mat.str-el↗

arXiv2018

Photon-Induced Suppression of Interlayer Tunneling in Van Der Waals Heterostructures

We develop a theory for interlayer tunneling in van der Waals heterostructures driven under a strong electromagnetic field, using graphene/{\it h}-BN/graphene as a paradigmatic example. Our theory predicts that strong anti-resonances appear at bias voltage values equal to an integer multiple of the light frequency. These features are found to originate from photon-assisted resonant tunneling transitions between Floquet sidebands of different graphene layers, and are unique to two-band systems due to the interplay of both intraband and interband tunneling transitions. Our results point to the possibility of tunneling localization in van der Waals heterostructures using strong electromagnetic fields.

cond-mat.mes-hall↗

arXiv2017

Dynamical Quantum Anomalous Hall Effect in Strong Optical Fields

Topological insulators (TIs) are characterized by the quantum anomalous Hall effect (QAHE) on the topological surface states under time-reversal symmetry breaking. Motivated by recent experiments on the magneto-optical effects induced by the QAHE, we develop a theory for the dynamical Hall conductivity for subgap optical frequency and intense optical fields using the Keldysh-Floquet Green's function formalism. Our theory reveals a nonlinear regime in which the Hall conductivity remains close to $e^2/2h$ at low frequencies. At higher optical fields, we find that the subsequent collapse of the half quantization is accompanied by coherent oscillations of the dynamical Hall conductivity as a function of field strength, triggered by the formation of Floquet subbands and the concomitant inter-subband transitions.

cond-mat.str-el↗

arXiv2016

Weyl nodes as topological defects of the Wannier-Stark ladder: From surface to bulk Fermi arcs

A hallmark of Weyl semimetal is the existence of surface Fermi arcs connecting two surface-projected Weyl nodes with opposite chiralities. An intriguing question is what determines the connectivity of surface Fermi arcs, when multiple pairs of Weyl nodes are present. To answer this question, we first show that the locations of surface Fermi arcs are predominantly determined by the condition that the Zak phase integrated along the normal direction to the surface is $π$. More importantly, the Zak phase can reveal the peculiar topological structure of Weyl semimetal directly in the bulk. Here, we show that the non-trivial winding of the Zak phase around each projected Weyl node manifests itself as a topological defect of the Wannier-Stark ladder, the energy eigenstates emerging under an electric field. Remarkably, this structure leads to "bulk Fermi arcs," i.e., open line segments in the bulk momentum spectra. It is argued that bulk Fermi arcs should exist in conjunction with the surface counterparts to conserve the Weyl fermion number under an electric field, which is supported by explicit numerical evidence.

cond-mat.str-el↗

arXiv2015

Direct manifestation of band topology in the winding number of the Wannier-Stark ladder

Topological quantum phases of matter have been a topic of intense interest in contemporary condensed matter physics. Extensive efforts are devoted to investigate various exotic properties of topological matters including topological insulators, topological superconductors, and topological semimetals. For topological insulators, the dissipationless transport via gapless helical edge or surface states is supposed to play a defining role, which unfortunately has proved difficult to realize in experiments due to inevitable backscattering induced in the sample boundary. Motivated by the fundamental connection between topological invariants and the Zak phase, here, we show that the non-trivial band topologies of both two and three-dimensional topological insulators, characterized by the Chern numbers and the $\mathbb{Z}_2$ invariants, respectively, are directly manifested in the winding numbers of the Wannier-Stark ladder (WSL) emerging under an electric field. We use the Floquet Green's function formalism to show that the winding number of the WSL is robust against interband interference as well as non-magnetic impurity scattering.

cond-mat.str-el↗

arXiv2014

Nonequilibrium steady states of the electric-field-driven Mott insulator: Thermalization, emergent Wannier-Stark ladder, and dielectric breakdown

In this work, we explore the possibility of emergent nonequilibrium steady states arising from the electric-field-driven Mott insulator via the Keldysh-Floquet dynamical mean field theory (DMFT), which can determine the fully-interacting, nonequilibrium steady-state Green's functions with the noninteracting counterparts as an input to the DMFT self-consistency loop. Unlike the retarded component, obtaining the lesser Green's function for the noninteracting system presents an important obstacle since the thermalization of the noninteracting system still requires a precise understanding of the dissipation mechanism. A crucial breakthrough in this work is that the noninteracting lesser Green's function can be determined in terms of the Wannier-Stark ladder (WSL) eigenstates, which are thermalized via the standard canonical ensemble according to the Markovian quantum master equation. As a result, it is shown that the intricate interplay between strong correlation and large electric field can generate a sequence of two dielectric breakdowns with the first induced by a coherent reconstruction of the mid-gap state within the Mott gap and the second by an incoherent tunneling through the biased Hubbard bands. It is predicted that the reconstructed mid-gap state generates its own emergent WSL structure with a reduced effective electric field. The two dielectric breakdowns are mediated by a reentrant insulating phase, which is characterized by the population inversion, causing instability toward inhomogeneous current density states at weak electron-impurity scattering.

cond-mat.str-el↗