Although excluded from the standard account of the history of philosophy, Catharine Trotter Cockbum （1679-1749）avoided the 17th-century bias against female intellectual skills and was an active contributor to the ea...Although excluded from the standard account of the history of philosophy, Catharine Trotter Cockbum （1679-1749）avoided the 17th-century bias against female intellectual skills and was an active contributor to the early modemphilosophical discourse. In her Defence of Mr Locke＇s Essay （1702）, she defended Locke from several criticisms byThomas Burnet （1635-1715）. By analysing three of Bumet＇s main arguments, such as the theory of naturalconscience, his anti-voluntarism, and his belief in the immateriality of the soul, Trotter showed that he oftenmisinterpreted John Locke＇s principles, especially those concerning his moral epistemology.展开更多
In this paper,we discuss on the convergence and approximation of an α times integrated semigroups. The Trotter kato theorems for an α times integrated semigroups are obtained.
Given the Hamiltonian,the evaluation of unitary operators has been at the heart of many quantum algorithms.Motivated by existing deterministic and random methods,we present a hybrid approach,where Hamiltonians with la...Given the Hamiltonian,the evaluation of unitary operators has been at the heart of many quantum algorithms.Motivated by existing deterministic and random methods,we present a hybrid approach,where Hamiltonians with large amplitude are evaluated at each time step,while the remaining terms are evaluated at random.The bound for the mean square error is obtained,together with a concentration bound.The mean square error consists of a variance term and a bias term,arising,respectively,from the random sampling of the Hamiltonian terms and the operator-splitting error.Leveraging on the bias/variance trade-off,the error can be minimized by balancing the two.The concentration bound provides an estimate of the number of gates.The estimates are verified using numerical experiments on classical computers.展开更多
文摘Although excluded from the standard account of the history of philosophy, Catharine Trotter Cockbum （1679-1749）avoided the 17th-century bias against female intellectual skills and was an active contributor to the early modemphilosophical discourse. In her Defence of Mr Locke＇s Essay （1702）, she defended Locke from several criticisms byThomas Burnet （1635-1715）. By analysing three of Bumet＇s main arguments, such as the theory of naturalconscience, his anti-voluntarism, and his belief in the immateriality of the soul, Trotter showed that he oftenmisinterpreted John Locke＇s principles, especially those concerning his moral epistemology.
文摘In this paper,we discuss on the convergence and approximation of an α times integrated semigroups. The Trotter kato theorems for an α times integrated semigroups are obtained.
基金supported by the NSFC(Grant No.12031013)the Innovation Program of Shanghai Municipal Education Commission(Nos.2021-01-07-00-02-E00087)supported by the NSF(Grant Nos.DMS-1953120 and DMS-2111221)。
文摘Given the Hamiltonian,the evaluation of unitary operators has been at the heart of many quantum algorithms.Motivated by existing deterministic and random methods,we present a hybrid approach,where Hamiltonians with large amplitude are evaluated at each time step,while the remaining terms are evaluated at random.The bound for the mean square error is obtained,together with a concentration bound.The mean square error consists of a variance term and a bias term,arising,respectively,from the random sampling of the Hamiltonian terms and the operator-splitting error.Leveraging on the bias/variance trade-off,the error can be minimized by balancing the two.The concentration bound provides an estimate of the number of gates.The estimates are verified using numerical experiments on classical computers.
