Optimal Transport with Cyclic Symmetry

We propose novel fast algorithms for optimal transport (OT) utilizing a cyclic symmetry structure of input data. Such OT with cyclic symmetry appears universally in various real-world examples: image processing, urban planning, and graph processing. Our main idea is to reduce OT to a small optimization problem that has significantly fewer variables by utilizing cyclic symmetry and various optimization techniques. On the basis of this reduction, our algorithms solve the small optimization problem instead of the original OT. As a result, our algorithms obtain the optimal solution and the objective function value of the original OT faster than solving the original OT directly. In this paper, our focus is on two crucial OT formulations: the linear programming OT (LOT) and the strongly convex-regularized OT, which includes the well-known entropy-regularized OT (EROT). Experiments show the effectiveness of our algorithms for LOT and EROT in synthetic/real-world data that has a strict/approximate cyclic symmetry structure. Through theoretical and experimental results, this paper successfully introduces the concept of symmetry into the OT research field for the first time

Si/SiGe2重量子ドットにおけるスピン量子ビットの実験的研究

学位の種別: 課程博士審査委員会委員 : (主査)東京大学教授 樽茶 清悟, 大阪大学教授 大岩 顕, 東京大学教授 中村 泰信, 筑波大学教授 都倉 康弘, 東京大学准教授 長田 俊人University of Tokyo(東京大学

Feedback-based active reset of a spin qubit in silicon

Feedback control of qubits is a highly demanded technique for advanced quantum information protocols such as quantum error correction. Here we demonstrate active reset of a silicon spin qubit using feedback control. The active reset is based on quantum non-demolition readout of the qubit and feedback according to the readout results, which is enabled by hardware data processing and sequencing. We incorporate a cumulative readout technique to the active reset protocol, enhancing initialization fidelity above a limitation imposed by accuracy of the single QND measurement fidelity. Based on an analysis of the reset protocol, we suggest a way to achieve the initialization fidelity sufficient for the fault-tolerant quantum computation

A shuttling-based two-qubit logic gate for linking distant silicon quantum processors

Control of entanglement between qubits at distant quantum processors using a two-qubit gate is an essential function of a scalable, modular implementation of quantum computation. Among the many qubit platforms, spin qubits in silicon quantum dots are promising for large-scale integration along with their nanofabrication capability. However, linking distant silicon quantum processors is challenging as two-qubit gates in spin qubits typically utilize short-range exchange coupling, which is only effective between nearest-neighbor quantum dots. Here we demonstrate a two-qubit gate between spin qubits via coherent spin shuttling, a key technology for linking distant silicon quantum processors. Coherent shuttling of a spin qubit enables efficient switching of the exchange coupling with an on/off ratio exceeding 1,000 , while preserving the spin coherence by 99.6% for the single shuttling between neighboring dots. With this shuttling-mode exchange control, we demonstrate a two-qubit controlled-phase gate with a fidelity of 93%, assessed via randomized benchmarking. Combination of our technique and a phase coherent shuttling of a qubit across a large quantum dot array will provide feasible path toward a quantum link between distant silicon quantum processors, a key requirement for large-scale quantum computation