arXiv subjects

Kabgyun Jeong

Publications and source records attributed to Kabgyun Jeong.

At least 37 records · Page 2Linked to original sources

arXiv2025

Collapses in quantum-classical probabilistically checkable proofs and the quantum polynomial hierarchy

We investigate the structure of quantum proof systems by establishing collapse results that reveal simplifications in their complexity landscape. By extending classical theorems such as the Karp-Lipton theorem to quantum settings and analyzing uniqueness in quantum-classical PCPs, we clarify how various constraints influence computational power. Our main contributions are: (1) We show that restricting quantum-classical PCPs to unique proofs does not reduce their power: $\mathsf{UniqueQCPCP} = \mathsf{QCPCP}$ under $\mathsf{BQ}$-operator and randomized reductions. This parallels the known $\mathsf{UniqueQCMA} = \mathsf{QCMA}$ result, indicating robustness of uniqueness even in quantum PCP-type systems. (2) We prove a non-uniform quantum analogue of the Karp-Lipton theorem: if $\mathsf{QMA} \subseteq \mathsf{BQP}/\mathsf{qpoly}$, then $\mathsf{QPH} \subseteq \mathsf{QΣ}_2/\mathsf{qpoly}$. This conditional collapse suggests limits on quantum advice for $\mathsf{QMA}$-complete problems. (3) We define a bounded-entanglement version of the quantum polynomial hierarchy, $\mathsf{BEQPH}$, and prove that it collapses above the fourth level. We also introduce the separable hierarchy $\mathsf{SepQPH}$ (zero entanglement), for which the same collapse result holds. These collapses stem not from entanglement, as in prior work, but from the convex structure of the protocols, which renders higher levels tractable. Collectively, these results offer new insights into the structure of quantum proof systems and the role of entanglement, uniqueness, and advice in defining their complexity.

quant-ph↗

arXiv2025

Reducing Circuit Depth in Quantum State Preparation for Quantum Simulation Using Measurements and Feedforward

Reducing circuit depth and identifying an optimal trade-off between circuit depth and width is crucial for successful quantum computation. In this context, midcircuit measurement and feedforward have been shown to significantly reduce the depth of quantum circuits, particularly in implementing logical gates. By leveraging these techniques, we propose several parallelization strategies that reduce quantum circuit depth at the expense of increasing width in preparing various quantum states relevant to quantum simulation. With measurements and feedforward, we demonstrate that utilizing unary encoding as a bridge between two quantum states substantially reduces the circuit depth required for preparing quantum states, such as sparse quantum states and sums of Slater determinants within the first quantization framework, while maintaining an efficient circuit width. Additionally, we show that a Bethe wave function, characterized by its high degree of freedom in its phase, can be probabilistically prepared in a constant-depth quantum circuit using measurements and feedforward. We anticipate that our study will contribute to the reduction of circuit depth in initial state preparation, particularly for quantum simulation, which is a critical step toward achieving quantum advantage.

quant-ph↗

arXiv2025

Hidden quantum-classical correspondence in chaotic billiards revealed by mutual information

Avoided level crossings, commonly associated with quantum chaos, are typically interpreted as signatures of eigenstate hybridization and spatial delocalization, often viewed as ergodic spreading. We show that, contrary to this expectation, increasing chaos in quantum billiards enhances mutual information between conjugate phase space variables, revealing nontrivial correlations. Using an information-theoretic decomposition of eigenstate entropy, we demonstrate that spatial delocalization may coincide with increased mutual information between position and momentum. These correlations track classical invariant structures in phase space and persist beyond the semiclassical regime, suggesting a robust information-theoretic manifestation of quantum-classical correspondence.

nlin.CD↗

arXiv2025

Topological Switching via Exceptional Point Pairs in an Optical Microcavity Laser

Conventional mode switching mechanisms, which rely on dynamically encircling exceptional points (EPs) through non-adiabatic transitions (NATs), suffer from intrinsic nonlinear dynamics that hinder precise control and reproducibility in experimental settings. Additionally, these methods exhibit low transmission efficiencies due to path-dependent attenuation, limiting their effectiveness in optical switching and logic gate applications. To overcome these limitations, we propose a novel mode switching approach that leverages a pair of EPs configuration in an optical microcavity, characterized by superradiance and subradiance. This mechanism exploits the topological structure of the Riemann surface to enable robust mode switching control and tunable Q-factor through purely adiabatic encircling. Furthermore, topological protection validated via braid isotopy ensures robustness against noise and parametric perturbations, facilitating a compact, robust, and adaptive non-Hermitian system.

physics.optics↗

arXiv2025

Designing Minimalistic Variational Quantum Ansatz Inspired by Algorithmic Cooling

This study introduces a novel minimalistic variational quantum ansatz inspired by algorithmic cooling principles. The proposed Heat Exchange algorithmic cooling ansatz (HE ansatz) facilitates efficient population redistribution without requiring bath resets, simplifying implementation on noisy intermediate-scale quantum (NISQ) devices. The HE ansatz achieves superior approximation ratios with the complete network \textsc{Maxcut} optimization problem compared to the conventional Hardware efficient and QAOA ansatz. We also proposed a new variational algorithm that utilize HE ansatz to compute the ground state of impure dissipative-system variational quantum eigensolver (dVQE) which achieved a sub-$1\%$ error in ground-state energy calculations of the 1D Heisenberg chain with impurity and successfully simulates the edge effect of impure spin chain, highlighting its potential for applications in quantum many-body physics. These results underscore the compatibility of the ansatz with hardware-efficient implementations, offering a scalable approach for solving complex quantum problems in disordered and open quantum systems.

quant-ph↗

arXiv2025

Disentangling quantum neural networks for unified estimation of quantum entropies and distance measures

The estimation of quantum entropies and distance measures, such as von Neumann entropy, Rényi entropy, Tsallis entropy, trace distance, and fidelity-induced distances such as the Bures distance, has been a key area of research in quantum information science. In our study, we introduce the disentangling quantum neural network (DEQNN), designed to efficiently estimate various physical quantities in quantum information. Estimation algorithms for these quantities are generally tied to the size of the Hilbert space of the quantum state to be estimated. Our proposed DEQNN offers a unified dimensionality reduction methodology that can significantly reduce the size of the Hilbert space while preserving the values of diverse physical quantities. We provide an in-depth discussion of the physical scenarios and limitations in which our algorithm is applicable, as well as the learnability of the proposed quantum neural network.

quant-ph↗

arXiv2024

Approximating maximum independent set on Rydberg atom arrays using local detunings

Rydberg atom arrays operated by a quantum adiabatic principle are among the most promising quantum simulating platforms due to their scalability and long coherence time. From the perspective of combinatorial optimization, they offer an efficient solution for an intrinsic maximum independent set problem because of the resemblance between the Rydberg Hamiltonian and the cost function of the maximum independent set problem. In this study, a strategy is suggested to approximate maximum independent sets by adjusting local detunings on the Rydberg Hamiltonian according to each vertex's vertex support, which is a quantity that represents connectivity between vertices. By doing so, the strategy successfully reduces the error rate three times for the checkerboard graphs with defects when the adiabaticity is sufficient. In addition, the strategy decreases the error rate for random graphs even when the adiabaticity is relatively insufficient. Moreover, it is shown that the strategy helps to prepare a quantum many-body ground state by raising the fidelity between the evolved quantum state and a 2D cat state on a square lattice. Finally, the strategy is combined with the non-abelian adiabatic mixing and this approach is highly successful in finding maximum independent sets compared to the conventional adiabatic evolution with local detunings.

quant-ph↗

arXiv2024

Asymptotic teleportation schemes bridging between standard and port-based teleportation

Various modified quantum teleportation schemes are proposed to overcome experimental constraints or to meet specific application requirements for quantum communication. Hence, most schemes are developed and studied with unique methodologies, each with its inherent challenges. Our research focuses on interconnecting these schemes appearing to be unrelated to each other, based on the idea that the unique advantages of one scheme can compensate for the limitations of another. In this paper, we introduce an asymptotic teleportation scheme requiring the receiver to perform a classical selection task followed by a quantum correction. This scheme bridges standard teleportation with port-based teleportation through the transformation of joint measurements. Specifically, we categorize and analytically investigate protocols within this scheme for qubit systems. Given that linear optics teleportation protocol without ancilla qubits is contained in the two non-trivial groups, we provide a novel perspective on its expansion. Furthermore, we discuss the potential application of a protocol from one of these groups as a universal programmable processor and extend these protocols to higher-dimensional systems while maintaining the same properties and potential, providing the analytic form of the joint measurement and its performance. These results thereby propose new avenues for developing a quantum network in higher-dimensional systems.

quant-ph↗

arXiv2024

Estimating Quantum Mutual Information Through a Quantum Neural Network

We propose a method of quantum machine learning called quantum mutual information neural estimation (QMINE) for estimating von Neumann entropy and quantum mutual information, which are fundamental properties in quantum information theory. The QMINE proposed here basically utilizes a technique of quantum neural networks (QNNs), to minimize a loss function that determines the von Neumann entropy, and thus quantum mutual information, which is believed more powerful to process quantum datasets than conventional neural networks due to quantum superposition and entanglement. To create a precise loss function, we propose a quantum Donsker-Varadhan representation (QDVR), which is a quantum analog of the classical Donsker-Varadhan representation. By exploiting a parameter shift rule on parameterized quantum circuits, we can efficiently implement and optimize the QNN and estimate the quantum entropies using the QMINE technique. Furthermore, numerical observations support our predictions of QDVR and demonstrate the good performance of QMINE.

quant-ph↗

arXiv2024

Port-based entanglement teleportation via noisy resource states

Port-based teleportation (PBT) represents a variation of the standard quantum teleportation and is currently being employed and explored within the field of quantum information processing owing to its various applications. In this study, we focus on PBT protocol when the resource state is disrupted by local Pauli noises. Here, we fully characterise the channel of the noisy PBT protocol using Krauss representation. Especially, by exploiting the application of PBT for entanglement distribution necessary in realizing quantum networks, we investigate entanglement transmission through this protocol for each qubit considering noisy resource states, denoted as port-based entanglement teleportation (PBET). Finally, we derive upper and lower bounds for the teleported entanglement as a function of the initial entanglement and the noises. Our study demonstrates that quantum entanglement can be efficiently distributed by protocols utilizing large-sized resource states in the presence of noise and is expected to serve as a reliable guide for developing optimized PBET protocols. To obtain these results, we address that the order of entanglement of two qubit states is preserved through the local Pauli channel, and identify the boundaries of entanglement loss through this teleportation channel.

quant-ph↗

arXiv2023

Weighted $p$-Rényi Entropy Power Inequality: Information Theory to Quantum Shannon Theory

We study the $p$-Rényi entropy power inequality with a weight factor $t$ on two independent continuous random variables $X$ and $Y$. The extension essentially relies on a modulation on the sharp Young's inequality due to Bobkov and Marsiglietti. Our research provides a key result that can be used as a fundamental research finding in quantum Shannon theory, as it offers a Rényi version of the entropy power inequality for quantum systems.

quant-ph↗

arXiv2023

Quantum Rényi Entropy Functionals for Bosonic Gaussian Systems

In this study, the quantum Rényi entropy power inequality of order $p>1$ and power $κ$ is introduced as a quantum analog of the classical Rényi-$p$ entropy power inequality. To derive this inequality, we first exploit the Wehrl-$p$ entropy power inequality on bosonic Gaussian systems via the mixing operation of quantum convolution, which is a generalized beam-splitter operation. This observation directly provides a quantum Rényi-$p$ entropy power inequality over a quasi-probability distribution for $D$-mode bosonic Gaussian regimes. The proposed inequality is expected to be useful for the nontrivial computing of quantum channel capacities, particularly universal upper bounds on bosonic Gaussian quantum channels, and a Gaussian entanglement witness in the case of Gaussian amplifier via squeezing operations.

quant-ph↗

arXiv2023

Sample-size-reduction of quantum states for the noisy linear problem

Quantum supremacy poses that a realistic quantum computer can perform a calculation that classical computers cannot in any reasonable amount of time. It has become a topic of significant research interest since the birth of the field, and it is intrinsically based on the efficient construction of quantum algorithms. It has been shown that there exists an expeditious way to solve the noisy linear (or learning with errors) problems in quantum machine learning theory via a well-posed quantum sampling over pure quantum states. In this paper, we propose an advanced method to reduce the sample size in the noisy linear structure, through a technique of randomizing quantum states, namely, $\varepsilon$-random technique. Particularly, we show that it is possible to reduce a quantum sample size in a quantum random access memory (QRAM) to the linearithmic order, in terms of the dimensions of the input-data. Thus, we achieve a shorter run-time for the noisy linear problem.

quant-ph↗

arXiv2022

Decomposed entropy and estimation of output power in deformed microcavity lasers

Park et al. [Phys. Rev. A 106, L031504 (2022)] showed that the Shannon entropy of the probability distribution of a single random variable for far-field profiles (FFPs) in deformed microcavity lasers can efficiently measure the directionality of deformed microcavity lasers. In this study, we instead consider two random variables of FFPs with joint probability distributions and introduce the decomposed (Shannon) entropy for the peak intensity of directional emissions. This provides a new foundation such that the decomposed entropy can estimate the degree of the output power at given FFPs without any further information.

physics.optics↗

arXiv2022

Entropic comparison of Landau-Zener and Demkov interactions in the phase space of a quadrupole billiard

We investigate two types of avoided crossings in a chaotic billiard within the framework of information theory. The Shannon entropy in the phase space for the Landau--Zener interaction increases as the center of the avoided crossing is approached. Meanwhile, that for the Demkov interaction decreases as the center of avoided crossing is passed by with an increase in the deformation parameter. This feature can provide a new indicator for scar formation. In addition, it is found that the Fisher information of the Landau--Zener interaction is significantly larger than that of the Demkov interaction.

nlin.CD↗

arXiv2022

Entropic measure of directional emissions in microcavity lasers

We propose a noble notion of the directional emission in microcavity lasers. First, Shannon entropy of the far-field profiles in the polar coordinate can quantify the degree of unidirectionality of the emission, while previous notions about the unidirectionality can not efficiently measure in the robust range against a variation of the deformation parameter. Second, a divergence angle of the directional emission is defined phenomenologically in terms of full width at half maximum, and it is barely applicable to a complicated peak structure. However, Shannon entropy of semi-marginal probability of the far-field profiles in the cartesian coordinate can present equivalent results, and moreover it is applicable to even the cases with a complicated peak structure of the emission.

physics.optics↗

arXiv2022

Double exceptional points generated by the strong imaginary coupling of a non-Hermitian Hamiltonian in an optical microcavity

Exceptional points (EPs) have recently attracted considerable attention in the study of non-Hermitian systems and in applications such as sensors and mode switching. In particular, nontrivial topological structures of EPs have been studied intensively in relation to encircling EPs. Thus, EP generation is currently an important issue in several fields. To generate multiple EPs, multiple levels or composite physical systems have been employed with Hermitian couplings. In this study, we generate multiple EPs on two-level systems in a single microcavity by adopting the non-Hermitian coupling of a non-Hermitian Hamiltonian under the imaginary (dominant) coupling. The topological structures of Riemann surfaces generated by non-Hermitian coupling exhibit features that are different from those of Riemann surfaces generated by Hermitian coupling. The features of these topological structures of Riemann surfaces were verified by encircling multiple EPs and using a Riemann sphere.

quant-ph↗

arXiv2022

Polynomial T-depth Quantum Solvability of Noisy Binary Linear Problem: From Quantum-Sample Preparation to Main Computation

The noisy binary linear problem (NBLP) is known as a computationally hard problem, and therefore, it offers primitives for post-quantum cryptography. An efficient quantum NBLP algorithm that exhibits a polynomial quantum sample and time complexities has recently been proposed. However, the algorithm requires a large number of samples to be loaded in a highly entangled state and it is unclear whether such a precondition on the quantum speedup can be obtained efficiently. Here, we present a complete analysis of the quantum solvability of the NBLP by considering the entire algorithm process, namely from the preparation of the quantum sample to the main computation. By assuming that the algorithm runs on "fault-tolerant" quantum circuitry, we introduce a reasonable measure of the computational time cost. The measure is defined in terms of the overall number of T gate layers, referred to as T-depth complexity. We show that the cost of solving the NBLP can be polynomial in the problem size, at the expense of an exponentially increasing logical qubits.

quant-ph↗