Optical lattice is a versatile platform to study fundamental physics in a controllable way. Recent developments include quantum simulation of condensed matter physics in view of phase transitions. As quantum entanglement plays a crucial role in the emergent phase transitions, it is of crucial importance to characterize quantum correlations in optical lattice. Unlike the popular approach based on the entanglement entropy, we here introduce an experimentally observable form of entanglement criterion that captures the features of quantum phase transitions critically.

We establish a trade-off between distinguishability and state disturbance in local state discrimination. Also, we compute entanglement cost for perfect non-destructive local state discrimination, and discuss entanglement certification as an application.

Recursive QAOA (RQAOA) is the variant of QAOA to overcome obstacles of low-level QAOA. RQAOA iteratively applies QAOA while progressively reducing the problem size through a recursive process. There are several instances in which RQAOA can get a better solution than QAOA or even get the optimal solution. In this work, we first analytically prove the limitation of the level-1 QAOA for solving MAX-CUT problem on bipartite graphs. Moreover, we observe that RQAOA outperforms QAOA, but it cannot guarantee the optimal solution when the number of nodes increases by numerical simulation. To improve the performance of RQAOA, we propose a modified RQAOA which reduces the region of optimization in QAOA subroutine, and we prove that our modified RQAOA can perfectly solve MAX-CUT on bipartite graphs.

Quantum networks aim to communicate distant quantum devices, such as quantum computers. In this context, a critical requirement is the secure and reliable transmission of arbitrary quantum states. Quantum teleportation is widely used to transmit arbitrary quantum states. However, it requires entanglement swapping and purification to distribute entanglements over long distances, introducing significant overhead and complexity. These challenges limit its practicality for real-world quantum communication networks. To address this limitation, we propose a novel scheme for directly transmitting quantum states encoded using error-correction codes.

The proposed scheme leverages the robustness of quantum error correction codes to ensure secure and reliable quantum communication. By encoding quantum states with error-correction codes and strategically injecting uncorrectable errors, we enhance the security and reliability of the transmission process. Our approach reduces the overhead associated with entanglement distribution and provides a high tolerance for transmission errors. This study presents an advancement in practical and scalable quantum communication networks.

In this presentation, we explore the question "QMA ≠ NP?" and delve into the remaining challenges in the field of quantum complexity theory. We will discuss the No Low-Energy Trivial States (NLTS) Theorem and the Quantum Probabilistically Checkable Proofs (PCP) Conjecture, examining their implications and the current progress in understanding these critical problems.

In quantum computers based on quantum error correction codes, magic states are essential for implementing universal quantum operations. However, magic states are generally not error-resistant, necessitating a distillation process. Despite differences between magic state distillation and quantum error correction frameworks, protocols utilizing stabilizer codes have demonstrated high performance and have been further developed and applied. Nevertheless, there remains no rigorous and clear answer to whether using stabilizer codes represents the optimal method for magic state distillation. We aim to address this question using resource theory and propose directions for the advancement of magic state distillation protocols.

  형사재판에서 증거가 실질적인 가치를 갖기 위해서는 증거능력과 증명력이 필요하다. 본 발표에서는 증거능력을 중심으로 디지털 증거의 특수성으로 인한 압수수색 절차와 기술적 한계점을 근거 법령과 함께 살펴보고, 향후 양자컴퓨터에 대한 압수수색의 가능성에 대해 고찰한다. 나아가 양자컴퓨터에 대한 압수수색 과정에서 발생할 수 있는 기술적 한계와 법적 한계를 바탕으로 수사기관이 대비해야 할 점들을 살펴보고자 한다.

  Research on human consciousness has progressed through experimental studies of human behavior in the fields of psychology and cognitive science. With the development of brain imaging technologies, neuroscience has also produced various findings by combining brain imaging with experimental studies. However, current research has not provided a definitive answer to the nature of human consciousness. In the 1990s, Penrose proposed the theory of "Orchestrated Objective Reduction" (Orch-OR), suggesting that human consciousness might follow quantum mechanisms. Penrose suggested that objective reduction represents neither randomness nor algorithmic processing but instead a non-computable influence in spacetime geometry from which mathematical understanding and, by later extension, consciousness are derived. This presentation aims to summarize the research trends on the quantum approach to human consciousness to date and provide a brief explanation of the relevant theoretical background.

 발표자가 Team QST에 들어온지도 어언 6개월, 반년이 지났다. 매주 전체 미팅과 개별 미팅에 참석하여 일주일 동안 있었던 일을 이야기하고, 해커톤도 형들과 나가는 등 팀 멤버들과 최대한 접점을 만들고자 노력하였으나, 6개월이라는 시간 동안 발표자 본인을 깊이 있게 드러낼 수 있는 기회가 적었던 것 또한 사실이다. 따라서 본 발표는 발표자의 고등학교 생활과 6개월 남짓한 대학교 1학년 1학기 생활을 돌이켜보며, ‘정재훈은 어떤 사람인지’를 명확히 전달하는 데 중점을 둔다. 특히나 고등학교 시절 겪어온, 내신 수학 시험과 관련한 트라우마적 경험을 이야기하며 이를 해결하기 위해 기울였던 노력을 소개하고, 수학이 발표자에게 지니는 함의를 설득력 있게 전달하는 데에도 또 다른 목표가 있다. 발표의 마지막에서는, 자유전공학부 1학년 재학생으로서 발표자가 그리는 본인의 미래에 관해서도 간략히 소개할 예정이다. 즉, 이 발표를 통해서는 발표자의 과거, 현재, 미래를 모두 총체적으로 조망하여 ‘정재훈’이라는 인간을 명확히 청중에게 전달하고자 한다.

  얽힘이 긴 범위에 걸쳐 존재하는 GHZ 상태, Toric code 등은 얽힘이 전파되는데 시간이 걸리기 때문에 유니터리 회로만으로는 상수 시간 내에 준비할 수 없다. 그러나 측정과 피드포워드 연산은 비국소적인 작용이 가능하기 때문에 이를 활용해 양자 회로의 복잡도를 축소시킬 수 있다. 그 외의 주목할만한 상태로는 베테 가설 상태가 있다. 베테 가설 상태는 여러 1차원 해밀토니안의 고유벡터가 될 수 있는 상태로 양자 다체 물리에서 중요한 역할을 한다. 그러나 자유도가 지수적으로 커져서 이 상태를 양자 컴퓨터에 준비하는 것이 쉽지 않다. 본 발표에서는 측정과 피드포워드 연산을 활용해 베테 가설 상태 준비의 복잡도를 축소시키는 방법을 제시하고자 한다.

  The way multi-partite entanglement is distributed over a quantum system is key to understand its emerging properties and also to devise good classical approximation strategies. This time, I will talk about the idea using the example of a quantum state based on AME(5,2) over a dodecahedron. Moreover, we'll find out how to place the AME state in 4-dimensional space.

In classical information theory, the amount of information needed to know X given Y is expressed as partial information. Therefore, the uncommon information required to exchange two information can be expressed as the corresponding partial information. In quantum information theory, we can consider quantum partial information for systems A and B required to share the density matrix of system AB. However, when the two systems are entangled, this value can be negative. This implies that the quantum uncommon information required to exchange states cannot be expressed as partial information unlike in the classical case. In this presentation, we will examine how the upper and lower bounds of quantum uncommon information required for quantum state exchange are determined according to each protocol.

  We suggest an algorithm that estimates von Neumann entropy, Renyi entropy, Tsallis entropy, by only using few swap tests. We prove that by knowing the value of tr(rho), tr(rho^2), ... tr(rho^r), we can deduce a polynomial which the solution of the equation is the eigenvalues of rho, where r is the rank of rho. We can get the estimation of the values above by using swap test. Since the estimation has error, we prove that the error of quantum entropies are still small with error in the swap test. We pose a open question, to prove or disprove that this method can be applied to estimating trace distance or fidelity.

과학 혁명은 16세기와 17세기에 걸쳐 서양에서 일어난 지적 변화를 의미하며, 이 시기의 사회적, 문화적 배경은 혁명의 주된 촉진 요인이었다. 르네상스 인문주의, 기술적 지식의 지위 상승, 유럽의 팽창과 신대륙 발견과 같은 사회적 변화는 새로운 사고방식과 지식 탐구를 촉진했다. 과학자들은 전통적인 아리스토텔레스의 자연 철학에서 벗어나 관찰과 실험을 통한 경험적 방법을 중시하게 되었으며, 자연 세계에 대한 이해가 급격히 확대되었다. 이러한 지적 변화는 근대 과학의 기초를 형성하며, 오늘날 과학적 방법론의 근간을 이루게 되었다.

  Classical shadow proposed by Haung, Kueng, and Preskill is highly efficient for predicting quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables, and the energy variance of many-body local Hamiltonians [Haung et al., Nature Physics, 2020]. While traditional quantum tomography requires exponential resources, the approach based on classical shadows can predict M functions with high accuracy using only log(M) measurements. Follow-up research to the above paper published by Haung and the team also presents a model trained on a dataset consisting of certain quantum states and their classical shadows to predict measurements of observables of specific quantum states [Haung et al., Science, 2022]. In this presentation, we will introduce our team’s idea of exploring a reverse approach to the model in the second paper. We are investigating whether it is possible to predict the Matrix Product State (MPS) of an original quantum state from measurements of specific observables of the given quantum state. Since MPS is a powerful tool for clearly representing and analyzing many-body quantum systems, successfully predicting it could significantly contribute to understanding quantum entanglement, enhancing computational efficiency, and ensuring numerical stability. We will share our current research results, the challenges we have encountered, and our plans for future research.

  Traditionally, training QNN requires measuring the evolved state at each training iteration, leading to significant overhead and stability issues due to circuit noise. Reducing the number of measurements is crucial to address these challenges, especially in the current quantum computing hardware, which is not easily accessible.

We propose a new approach that requires just initial measurements, eliminating the need of measurements at every iteration in the training loop, by viewing the role of parameterized circuit as estimating the expectation values of parameterized observables for a constant quantum state. We apply a method known as classical shadows for the initial measurements, which efficiently estimates expectation values of a number of observables. We show that our approach theoretically reduces the required measurements logarithmically with respect to the number of training iteration and observables to estimate, and demonstrate our approach to solve quantum state discrimination problems.

본 발표에서는 대학원 생활에 관해 이야기해보고자 한다. 특히, 대학원생의 우울에 관하여 탐색하고, 일상생활에서 어떻게 대처할 수 있는지 살펴볼 예정이다. 이뿐만 아니라, 양자 컴퓨팅 기술이 사회과학, 특히 심리학 연구에 어떻게 쓰임이 될 수 있는지 간략히 소개하고자 한다. 

 The most fundamental goal in drug design is to predict whether a given molecule will bind to a target and if so how strongly. Quantum computing can simulate interactions between molecules more authentically, enabling us to predict the activity and safety of drug molecules more precisely during the drug design stage. Also quantum computers can perform complex quantum chemistry calculations, such as calculating molecular energies and electronic structures, which are essential for drug design and optimization. In this presentation, based on the recent analysis about the drug design on quantum computer [R. Santagati et al., Nat. Phys 20 (2024)] and other papers.