Publications

2024

1. QAlgo

   

   Rank Is All You Need: Estimating the Trace of Powers of Density Matrices

   Myeongjin Shin, Junseo Lee, Seungwoo Lee, and 1 more author

   arXiv preprint arXiv:2408.00314, 2024

   Abs LINK

   Estimating the trace of powers of identical k density matrices (i.e., \textTr(ρ^k)) is a crucial subroutine for many applications such as calculating nonlinear functions of quantum states, preparing quantum Gibbs states, and mitigating quantum errors. Reducing the requisite number of qubits and gates is essential to fit a quantum algorithm onto near-term quantum devices. Inspired by the Newton-Girard method, we developed an algorithm that uses only \mathcalO(r) qubits and \mathcalO(r) multi-qubit gates, where r is the rank of ρ. We prove that the estimation of {\textTr(ρ^i)}_i=1^r is sufficient for estimating the trace of powers with large k > r. With these advantages, our algorithm brings the estimation of the trace of powers closer to the capabilities of near-term quantum processors. We show that our results can be generalized for estimating \textTr(Mρ^k), where M is an arbitrary observable, and demonstrate the advantages of our algorithm in several applications.

2. QML

   

   Estimating quantum mutual information through a quantum neural network

   Myeongjin Shin, Junseo Lee, and Kabgyun Jeong

   Quantum Information Processing, 2024

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   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.

3. QML

   

   Disentanglement Provides a Unified Estimation for Quantum Entropies and Distance Measures

   Myeongjin Shin, Seungwoo Lee, Junseo Lee, and 4 more authors

   arXiv preprint 2401.07716, 2024

   Abs LINK

   The estimation of fundamental properties in quantum information theory, including von Neumann entropy, Rényi entropy, Tsallis entropy, quantum relative entropy, trace distance, and fidelity, has received significant attention. While various algorithms exist for individual property estimation, a unified approach is lacking. This paper proposes a unified methodology using Layerwise Quantum Convolutional Neural Networks (LQCNN). Recent studies exploring parameterized quantum circuits for property estimation face challenges such as barren plateaus and complexity issues in large qubit states. In contrast, our work overcomes these challenges, avoiding barren plateaus and providing a practical solution for large qubit states. Our first contribution offers a mathematical proof that the LQCNN structure preserves fundamental properties. Furthermore, our second contribution analyzes the algorithm’s complexity, demonstrating its avoidance of barren plateaus through a structured local cost function.

4. QAlgo

   

   Assessing Quantum Integer Factorization Performance with Shor’s Algorithm

   Junseo Lee

   In Quantum Computing: A Journey into the Next Frontier of Information and Communication Security . M. Hammoudeh, A. T. Essa, A. M. Sherbeeni, C. M. Firth, and A. S. Essa, Eds., CRC Press , 2024

   Abs LINK

   With the advancement of quantum technologies, there is a potential threat to traditional encryption systems based on integer factorization. Therefore, developing techniques for accurately measuring the performance of associated quantum algorithms is crucial, as it can provide insights into the practical feasibility from the current perspective. In this chapter, we aim to analyze the time required for integer factorization tasks using Shor’s algorithm within a gate-based quantum circuit simulator of the matrix product state type. Additionally, we observe the impact of parameter pre-selection in Shor’s algorithm. Specifically, this pre-selection is expected to increase the success rate of integer factorization by reducing the number of iterations and facilitating performance measurement under fixed conditions, thus enabling scalable performance evaluation even on real quantum hardware.

2023

1. QST

   

   Quantum Rényi entropy functionals for bosonic gaussian systems

   Junseo Lee, and Kabgyun Jeong

   Physics Letters A. (Special Issue) Foundations and Applications of Quantum Optics , 2023

   Abs LINK

   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.

2. QST

   

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

   Junseo Lee, Hyeonjun Yeo, and Kabgyun Jeong

   International Journal of Theoretical Physics, 2023

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   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.

3. QML

   

   Mutual Information Maximizing Quantum Generative Adversarial Network and Its Applications in Finance

   Mingyu Lee, Myeongjin Shin, Junseo Lee, and 1 more author

   arXiv preprint 2309.01363, 2023

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   One of the most promising applications in the era of NISQ (Noisy Intermediate-Scale Quantum) computing is quantum machine learning. Quantum machine learning offers significant quantum advantages over classical machine learning across various domains. Specifically, generative adversarial networks have been recognized for their potential utility in diverse fields such as image generation, finance, and probability distribution modeling. However, these networks necessitate solutions for inherent challenges like mode collapse. In this study, we capitalize on the concept that the estimation of mutual information between high-dimensional continuous random variables can be achieved through gradient descent using neural networks. We introduce a novel approach named InfoQGAN, which employs the Mutual Information Neural Estimator (MINE) within the framework of quantum generative adversarial networks to tackle the mode collapse issue. Furthermore, we elaborate on how this approach can be applied to a financial scenario, specifically addressing the problem of generating portfolio return distributions through dynamic asset allocation. This illustrates the potential practical applicability of InfoQGAN in real-world contexts.

2021

1. QST

   

   High-dimensional Private Quantum Channels and Regular Polytopes

   Junseo Lee, and Kabgyun Jeong

   Communications in Physics, 2021

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   As the quantum analog of the classical one-time pad, the private quantum channel (PQC) plays a fundamental role in the construction of the maximally mixed state (from any input quantum state), which is very useful for studying secure quantum communications and quantum channel capacity problems. However, the undoubted existence of a relation between the geometric shape of regular polytopes and private quantum channels in the higher dimension has not yet been reported. Recently, it was shown that a one-to-one correspondence exists between single-qubit PQCs and three-dimensional regular polytopes (i.e., regular polyhedra). In this paper, we highlight these connections by exploiting two strategies known as a generalized Gell-Mann matrix and modified quantum Fourier transform. More precisely, we explore the explicit relationship between PQCs over a qutrit system (i.e., a three-level quantum state) and regular 4-polytope. Finally, we attempt to devise a formula for connections on higher dimensional cases.

2018

1. QST

   

   Single Qubit Private Quantum Channels and 3-Dimensional Regular Polyhedra

   Kabgyun Jeong, Junseo Lee, Jin Tae Choi, and 5 more authors

   New Phys.: Sae Mulli, 2018

   Abs LINK

   A private quantum channel (PQC) in quantum cryptography is one of the most well-known quantum cryptographic protocols using a secret key obtained from the quantum key distribution (QKD) protocol, and it is called a quantum one-time pad or random unitary channel and so on. The reason a PQC is important is that the output state of the channel always gives rise to a maximally mixed state, so the quantum communication can be secured without any external eavesdropping; thus, it preserves information-theoretic security. We explicitly construct five kinds of single-qubit PQCs and try to connect each to a 3-dimensional polyhedron. We expand a corresponding method between four unitary matrices given by Pauli matrices and the regular tetrahedron, and find specific unitary matrices corresponding to another four regular polyhedra. Each unitary matrix is naturally connected to a pre-shared key obtained by using the QKD protocol, which completes a model of five kinds of PQCs for the single-qubit state. Finally, we analyze a trade-off relation between security and efficiency for the PQC.