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Time Table
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[August 12 (Monday)]
Invited talk 1. Hur Tak (Yonsei University): Understanding Generalization in Quantum Machine Learning with Margins
Quantum machine learning (QML) stands out as an innovative application of quantum computation. The success of QML algorithm does not solely depend on how well the model fits the training data but, more importantly, on their ability to accurately predict the outcomes of previously unseen data. This crucial capability, known as generalization, has been extensively explored and analyzed through the lens of statistical learning theory. However, recent studies have highlighted the limitations of current understandings of generalization based on uniform bounds in both classical and quantum machine learning frameworks. In this work, we propose a complexity measure based on margin distribution, which can accurately capture the generalization performance of QML models.
Invited talk 2. Wonjun Lee (POSTECH): Pseudo-Chaotic Quantum Many-Body Dynamics
With limited access to the measurement outcomes of quantum computations, states possessing maximal quantum resources, such as entanglement and magic, become indistinguishable from those with exponentially smaller quantities of these resources. This unexpected indistinguishability between states with exponentially separated quantum resources has recently been discussed and termed ‘pseudo-quantumness’ [1,2]. Building on this progress, we introduce a new concept called ‘pseudo-chaotic dynamics’ and explore its consequences [3]. Pseudo-chaotic dynamics is not ergodic, yet it is indistinguishable from maximally quantum chaotic dynamics according to various defining metrics of quantum chaos, including the scaling of out-of-time ordered correlators (OTOCs), level statistics, and Krylov complexity. We explicitly construct an ensemble of such pseudo-chaotic unitary evolutions and confirm their pseudo-chaotic nature through extensive numerical simulations and analytic proofs. Additionally, we demonstrate that these unitary evolutions can generate prototypical pseudo-quantum states, specifically random subset-phase states [1], from initial computational states. Finally, we construct an explicit circuit architecture for these pseudo-chaotic dynamics and show that its depth can be tightly bound by polylog(n) with the system size n.
- Reference
[1] Aaronson et al., arxiv:2211.00747 (2022)
[2] Gu et al., Phys. Rev. Lett. 132, 210602 (2024)
[3] Wonjun Lee et al., arxiv:2408.xxxxx (2024)
Lecture 1. Jong Yeon Lee (UIUC): Quantum Codes and Many-body Physics of Information
- Part 1: Overview on quantum error correction and introduce various quantum codes, encoding, and decoding
- Part 2: Understanding fundamental error threshold in quantum codes and its connection to many-body physics
* Keywords: Quantum error correction, Encoding, Decoding, Decoherence, Single-shot decodability, CSS codes, Subsystem codes, Coherent information, Topological orders, Symmetry protected topological phases, SYK models
[August 13 (Tuesday)]
Lecture 2. Joon Hee Choi (Stanford Univ.): Quantum metrology and sensing
- Part 1: Introduction to Quantum Sensing
Quantum sensing involves using a quantum system, quantum properties, or quantum phenomena to measure physical quantities. This lecture will introduce the fundamental principles, methods, and concepts of quantum sensing, aiming to foster collaboration between experimentalists and theorists.
- Part 2: Introduction to Quantum Metrology
Quantum metrology is the study and application of quantum phenomena to perform measurements with greater precision than is possible using classical techniques. This lecture will introduce important recent advances in quantum metrology, focusing on experiments with programmable quantum hardware.
* Keywords: Quantum Fisher Information, Cramer-Rao bound, KL-divergence, distinguishability, trace distance (L1/L2 norms), MLE, Heisenberg Limit, Standard Quantum Limit, Quantum Projection Noise, Shot Noise, Shannon Entropy, Quantum Sensing Pulse Sequences.
[September 26 (Thursday)]
Invited talk 4. Byeongseon Go (Seoul National University): The noise-robust approach to the quantum computational advantage of boson sampling
Boson sampling stands out as a promising approach toward experimental demonstration of quantum computational advantage. However, the presence of physical noises in near-term experiments hinders the realization of the quantum computational advantage with boson sampling. In this talk, we introduce our two main approaches to address this issue. First, to reduce the noise effect, we explore the classical hardness of boson sampling confined in shallow-depth linear optical circuits. Second, since physical noise in near-term boson sampling devices is inevitable, we investigate the classical hardness of boson sampling in noisy environments.
Invited talk 5. Gwonhak Lee (Sungkyunkwan University): Mitigating Errors in Quantum Krylov Subspace Diagonalization
Quantum Krylov subspace diagonalization (QKSD) is an emerging method used in place of quantum phase estimation in the early fault-tolerant era, where the limited depth of error-corrected quantum circuit is available. In contrast to the classical Krylov subspace diagonalization (KSD) or the Lanczos method, QKSD exploits the quantum computer to efficiently estimate the eigenvalues of large-size Hamiltonians through a faster Krylov projection. However, unlike classical KSD, which is solely concerned with machine precision, QKSD is inherently accompanied by errors originating from a finite number of samples, which are suppressed much slowly. Moreover, due to the difficulty establishing an artificial orthogonal basis, ill-conditioning problems are often encountered, rendering the solution vulnerable to noise. In this work, we analyze the relationship between the sampling noise and its effects on eigenvalues. We also propose techniques to reduce the sampling error and to cope with large condition numbers by eliminating the ill-conditioned bases.
Lecture 3. Kyunjoo Noh (AWS): Bosonic Quantum Error Correction
A popular approach for realizing fault-tolerant quantum computers is to construct logical qubits encoded in a surface code (or its variants), where each physical qubit uses a simple encoding into two levels of a physical element. Recently, various types of bosonic qubits (such as GKP qubits and cat qubits) have been proposed as an alternative to these simple two-level qubits. Bosonic qubits offer unique advantages since they are themselves protected at the single bosonic mode level using the redundancies provided by the infinite-dimensionality of a bosonic mode. Such favorable noise properties can then be utilized to reduce the overall resource overhead associated with implementing quantum error correction (QEC).
In this lecture, I'll first motivate quantum error correction by discussing the adverse effects of noise in one-dimensional random quantum circuit sampling. Then, I will give an overview of the field of bosonic QEC, including an introduction to general QEC as well. Finally, I will present an experimental demonstration of QEC using a distance-5 repetition cat code. Notably, the noise channel of each bosonic cat qubit is biased towards phase-flip errors since the bit-flip errors are physically suppressed at the single bosonic mode level. This noise bias allows us to use a simple one-dimensional repetition code as opposed to a two-dimensional surface code. Our experiment thus serves as a promising first step in taking advantage of bosonic qubits, and additionally noise bias, to improve the hardware efficiency of quantum error correction.
[September 27 (Friday)]
Invited talk 6. Ju-Yeon Gyhm (Seoul National University): The optimal squeezing process for quantum metrology by increasing the winding number
Quantum metrology has an advantage over its classical counterpart described by the Heisenberg limit. One of the conditions for realizing this advantage is preparing quantum states with superextensive sensitivity, quantified by the Quantum Fisher Information (QFI). In 2017, a concept called quantum critical metrology was proposed, which enhances QFI by exploiting the divergence of physical quantities at the quantum critical point. While it is clear that the QFI becomes superextensive at the critical point, the challenge remains in how to reach this quantum critical point. We determine the optimal process for reaching the critical point in the Dicke model. The Dicke model exhibits a critical point where the state is highly squeezed and the QFI diverges. However, previous methods relied on adiabatic processes, which require an extensive total time. We point out that the winding number, topological order, of the trajectories, determined by the dynamics in phase space, is crucial in reducing the total time needed to achieve a high QFI. We developed an optimal process that increases the QFI by optimizing the winding number relative to the total time. The process allows the exponential scaling of the squeezing parameter and the QFI by time. Considering that the QFI scales with the fourth power of the total time at previous research, our process is more advantageous than previous methods. Moreover, we prove that a fourth of the total time behavior comes from zero winding number of adiabatic processes. In addition to optimizing the winding number, we also consider the process's robustness under inaccuracies from environment and control. The optimal process consists of having an exponential property under dissipative dynamics and inaccurate control. Our approach for a closed system is still optimal for the time independent Lindblad dynamics for any dissipative parameter. It implies that our process is not only theoretically optimal but realizable to prepare the quantum state for quantum metrology.
Lecture 4. Kimin Park (Palacky University): Qubit-bosonic systems for continuous-variable quantum resource
In this talk, I will explore recent advancements in continuous-variable quantum information, emphasizing quantum sensing and computation using qubit-bosonic systems. It highlights the integration of discrete- and continuous-variable systems for enhanced quantum resources, leveraging qubit-oscillator interactions for robust non-Gaussian states and gates crucial for continuous-variable quantum technologies.