Optimal Hamiltonian simulation for time-periodic systems

The implementation of time-evolution operators $U(t)$, called Hamiltonian simulation, is one of the most promising usage of quantum computers. For time-independent Hamiltonians, qubitization has recently established efficient realization of time-evolution $U(t)=e^{-iHt}$, with achieving the optimal computational resource both in time $t$ and an allowable error $\varepsilon$. In contrast, those for time-dependent systems require larger cost due to the difficulty of handling time-dependency. In this paper, we establish optimal/nearly-optimal Hamiltonian simulation for generic time-dependent systems with time-periodicity, known as Floquet systems. By using a so-called Floquet-Hilbert space equipped with auxiliary states labeling Fourier indices, we develop a way to certainly obtain the target time-evolved state without relying on either time-ordered product or Dyson-series expansion. Consequently, the query complexity, which measures the cost for implementing the time-evolution, has optimal and nearly-optimal dependency respectively in time $t$ and inverse error $\varepsilon$, and becomes sufficiently close to that of qubitization. Thus, our protocol tells us that, among generic time-dependent systems, time-periodic systems provides a class accessible as efficiently as time-independent systems despite the existence of time-dependency. As we also provide applications to simulation of nonequilibrium phenomena and adiabatic state preparation, our results will shed light on nonequilibrium phenomena in condensed matter physics and quantum chemistry, and quantum tasks yielding time-dependency in quantum computation.Comment: 55 pages, 2 figures, 1 tabl

Recursive Quantum Eigenvalue/Singular-Value Transformation: Analytic Construction of Matrix Sign Function by Newton Iteration

Quantum eigenvalue transformation (QET) and its generalization, quantum singular value transformation (QSVT), are versatile quantum algorithms that allow us to apply broad matrix functions to quantum states, which cover many of significant quantum algorithms such as Hamiltonian simulation. However, finding a parameter set which realizes preferable matrix functions in these techniques is difficult for large-scale quantum systems: there is no analytical result other than trivial cases as far as we know and we often suffer also from numerical instability. We propose recursive QET or QSVT (r-QET or r-QSVT), in which we can execute complicated matrix functions by recursively organizing block-encoding by low-degree QET or QSVT. Owing to the simplicity of recursive relations, it works only with a few parameters with exactly determining the parameters, while its iteration results in complicated matrix functions. In particular, by exploiting the recursive relation of Newton iteration, we construct the matrix sign function, which can be applied for eigenstate filtering for example, in a tractable way. We show that an analytically-obtained parameter set composed of only $8$ different values is sufficient for executing QET of the matrix sign function with an arbitrarily small error $\varepsilon$. Our protocol will serve as an alternative protocol for constructing QET or QSVT for some useful matrix functions without numerical instability.Comment: 10 pages, 1figur

Deep variational quantum eigensolver for excited states and its application to quantum chemistry calculation of periodic materials

A programmable quantum device that has a large number of qubits without fault-tolerance has emerged recently. Variational quantum eigensolver (VQE) is one of the most promising ways to utilize the computational power of such devices to solve problems in condensed matter physics and quantum chemistry. As the size of the current quantum devices is still not large for rivaling classical computers at solving practical problems, Fujii et al. proposed a method called “Deep VQE”, which can provide the ground state of a given quantum system with the smaller number of qubits by combining the VQE and the technique of coarse graining [K. Fujii, K. Mitarai, W. Mizukami, and Y. O. Nakagawa, arXiv:2007.10917]. In this paper, we extend the original proposal of Deep VQE to obtain the excited states and apply it to quantum chemistry calculation of a periodic material, which is one of the most impactful applications of the VQE. We first propose a modified scheme to construct quantum states for coarse graining in Deep VQE to obtain the excited states. We also present a method to avoid a problem of meaningless eigenvalues in the original Deep VQE without restricting variational quantum states. Finally, we classically simulate our modified Deep VQE for quantum chemistry calculation of a periodic hydrogen chain as a typical periodic material. Our method reproduces the ground-state energy and the first-excited-state energy with the errors up to O(1)% despite the decrease in the number of qubits required for the calculation by two or four compared with the naive VQE. Our result will serve as a beacon for tackling quantum chemistry problems with classically-intractable sizes by smaller quantum devices in the near future

Spred2-deficiency enhances the proliferation of lung epithelial cells and alleviates pulmonary fibrosis induced by bleomycin

The mitogen-activated protein kinase (MAPK) pathways are involved in many cellular processes, including the development of fibrosis. Here, we examined the role of Sprouty-related EVH-1-domain-containing protein (Spred) 2, a negative regulator of the MAPK-ERK pathway, in the development of bleomycin (BLM)-induced pulmonary fibrosis (PF). Compared to WT mice, Spred2−/− mice developed milder PF with increased proliferation of bronchial epithelial cells. Spred2−/− lung epithelial cells or MLE-12 cells treated with spred2 siRNA proliferated faster than control cells in vitro. Spred2−/− and WT macrophages produced similar levels of TNFα and MCP-1 in response to BLM or lipopolysaccharide and myeloid cell-specific deletion of Spred2 in mice had no effect. Spred2−/− fibroblasts proliferated faster and produced similar levels of MCP-1 compared to WT fibroblasts. Spred2 mRNA was almost exclusively detected in bronchial epithelial cells of naïve WT mice and it accumulated in approximately 50% of cells with a characteristic of Clara cells, 14 days after BLM treatment. These results suggest that Spred2 is involved in the regulation of tissue repair after BLM-induced lung injury and increased proliferation of lung bronchial cells in Spred2−/− mice may contribute to faster tissue repair. Thus, Spred2 may present a new therapeutic target for the treatment of PF

A comprehensive survey on quantum computer usage: How many qubits are employed for what purposes?

Quantum computers (QCs), which work based on the law of quantum mechanics, are expected to be faster than classical computers in several computational tasks such as prime factoring and simulation of quantum many-body systems. In the last decade, research and development of QCs have rapidly advanced. Now hundreds of physical qubits are at our disposal, and one can find several remarkable experiments actually outperforming the classical computer in a specific computational task. On the other hand, it is unclear what the typical usages of the QCs are. Here we conduct an extensive survey on the papers that are posted in the quant-ph section in arXiv and claim to have used QCs in their abstracts. To understand the current situation of the research and development of the QCs, we evaluated the descriptive statistics about the papers, including the number of qubits employed, QPU vendors, application domains and so on. Our survey shows that the annual number of publications is increasing, and the typical number of qubits employed is about six to ten, growing along with the increase in the quantum volume (QV). Most of the preprints are devoted to applications such as quantum machine learning, condensed matter physics, and quantum chemistry, while quantum error correction and quantum noise mitigation use more qubits than the other topics. These imply that the increase in QV is fundamentally relevant, and more experiments for quantum error correction, and noise mitigation using shallow circuits with more qubits will take place.Comment: 14 pages, 5 figures, figures regenerate

Floquet系における非平衡量子多体現象

付記する学位プログラム名: 京都大学卓越大学院プログラム「先端光・電子デバイス創成学」京都大学新制・課程博士博士(理学)甲第23694号理博第4784号新制||理||1685(附属図書館)京都大学大学院理学研究科物理学・宇宙物理学専攻(主査)教授 川上 則雄, 教授 柳瀬 陽一, 教授 高橋 義朗学位規則第4条第1項該当Doctor of ScienceKyoto UniversityDFA