美国马里兰大学宿愿博士量子计算报告(研讨)

来源:信息科学与技术学院  作者:罗明星  日期:2019-12-09  点击数:684

报告题目(Title):  Algorithms for quantum computers (量子计算机算法简介)

报告专家(Speaker):  Yuan Su, PhD student in Computer Science,University of Maryland, USA

报告地点(Venue):  西南交通大学犀浦校区4号楼(X4158)

报告时间(Time):  2019-12-25 周三 9:30-10:30

主持人(Chair):  罗明星


内容提要(Outline of the talk):

Quantum computers hold the promise of solving certain problems more efficiently than classical computation devices. In this talk, I will give a tutorial introduction to quantum algorithms for quantum computers. I will start by explaining the basics of quantum computation, such as quantum states, quantum operations, quantum measurements, and multi-qubit systems. I will then discuss a selection of quantum algorithms, including algorithms for the Deutsch’s Problem, unstructured search, factoring integers, simulating quantum physics, and solving linear systems. I will conclude by mentioning latest advances in the field. No background beyond basic linear algebra is assumed.


报告人简介(Short Biography of the speaker)

Yuan Su is a fifth-year PhD student in Computer Science at the University of Maryland, researching quantum computing under the supervision of Dr. Andrew Childs. He received his bachelor’s degree in Computer Science from the Beijing University of Posts and Telecommunications, and his master’s degree in Applied Mathematics from Peking University. His research focuses mainly on the theoretical side of quantum simulation, with the purpose of understanding and optimizing the performance of quantum algorithms for simulating quantum physics. His work has been published in journals and conference proceedings including PNAS, PRX, PRL, and STOC. He is a recipient of the 2019 Google PhD Fellowship in quantum computing.



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附:量子计算模拟研讨日程(周三至周五):


报告题目(Title):  Toward the first quantum simulation with quantum speedup

报告专家(Speaker):  Yuan Su, PhD student in Computer Science,University of Maryland, USA

报告地点(Venue):  西南交通大学犀浦校区9号楼(X9428)

报告时间(Time):  2019-12-25 周三 14:00-17:00

主持人(Chair):  罗明星


内容提要(Outline of the talk):

We aim to identify a practical problem that is beyond the reach of current classical computers, but that requires the fewest resources for a quantum computer. We consider quantum simulation of spin systems, which could be applied to understand condensed matter phenomena. We synthesize explicit circuits for three leading quantum simulation algorithms, using diverse techniques to tighten error bounds and optimize circuit implementations. Quantum signal processing appears to be preferred among algorithms with rigorous performance guarantees, whereas higher-order product formulas prevail if empirical error estimates suffice. Our circuits are orders of magnitude smaller than those for the simplest classically infeasible instances of factoring and quantum chemistry, bringing practical quantum computation closer to reality.




报告题目(Title):  Nearly optimal lattice simulation by product formulas

报告专家(Speaker):  Yuan Su, PhD student in Computer Science,University of Maryland, USA

报告地点(Venue):  西南交通大学犀浦校区9号楼(X9428)

报告时间(Time):  2019-12-26 周四 9:30-11:30,周四 14:30-16:30

主持人(Chair):  罗明星


内容提要(Outline of the talk):

Product formulas provide a straightforward yet surprisingly efficient approach to quantum simulation. We show that this algorithm can simulate an n-qubit Hamiltonian with nearest neighbor interactions evolving for time t using only (nt)1+o(1) gates. While it is reasonable to expect this complexity—in particular, this was claimed without rigorous justification by Jordan, Lee, and Preskill—we are not aware of a straightforward proof. Our approach is based on an analysis of the local error structure of product formulas, as introduced by Descombes and Thalhammer and significantly simplified here. We prove error bounds for canonical product formulas, which include well-known constructions such as the Lie-Trotter-Suzuki formulas. We also develop a local error representation for time-dependent Hamiltonian simulation, and we discuss generalizations to periodic boundary conditions, constant-range interactions, and higher dimensions. Combined with a previous lower bound, our result implies that product formulas can simulate lattice Hamiltonians with nearly optimal gate complexity.





报告题目(Title):  Quantum singular value transformation and beyond

报告专家(Speaker):  Yuan Su, PhD student in Computer Science,University of Maryland, USA

报告地点(Venue):  西南交通大学犀浦校区9号楼(X9428)

报告时间(Time):  2019-12-27周五 9:30-11:30,周五 14:30-16:30

主持人(Chair):  罗明星


内容提要(Outline of the talk):

We develop a new “Singular value transformation” algorithm capable of harnessing the exponential advantage, that can apply polynomial transformations to the singular values of a block of a unitary, generalizing the optimal Hamiltonian simulation results of Low and Chuang [LC17a]. The proposed quantum circuits have a very simple structure, often give rise to optimal algorithms and have appealing constant factors, while typically only use a constant number of ancilla qubits. We show that singular value transformation leads to novel algorithms. We give an efficient solution to a “non-commutative” measurement problem used for efficient ground-state-preparation of certain local Hamiltonians, and propose a new method for singular value estimation. We also show how to exponentially improve the complexity of implementing fractional queries to unitaries with a gapped spectrum. Finally, as a quantum machine learning application we show how to efficiently implement principal component regression.


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