We develop universal quantum computing models that form a family of quantum von Neumann architectures,with modular units of memory,control,CPU,and internet,besides input and output.This family contains three generatio...We develop universal quantum computing models that form a family of quantum von Neumann architectures,with modular units of memory,control,CPU,and internet,besides input and output.This family contains three generations characterized by dynamical quantum resource theory,and it also circumvents no-go theorems on quantum programming and control.Besides universality,such a family satisfies other desirable engineering requirements on system and algorithm design,such as modularity and programmability,hence serves as a unique approach to building universal quantum computers.展开更多
Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bound...Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L<sup>∞</sup>(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L<sup>2</sup>(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .展开更多
The reflection of a weak shock wave is considered using a shock polar. We present a sufficient condition under which the von Neumann paradox appears for the Euler equations.In an attempt to resolve the von Neumann par...The reflection of a weak shock wave is considered using a shock polar. We present a sufficient condition under which the von Neumann paradox appears for the Euler equations.In an attempt to resolve the von Neumann paradox for the Euler equations, two new types of reflection configuration, one called the von Neumann reflection(vNR) and the other called the Guderley reflection(GR), are observed in numerical calculations. Finally, we obtain that GR is a reasonable configuration and vNR is an unreasonable configuration to resolve the von Neumann paradox.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12047503 and 12105343)。
文摘We develop universal quantum computing models that form a family of quantum von Neumann architectures,with modular units of memory,control,CPU,and internet,besides input and output.This family contains three generations characterized by dynamical quantum resource theory,and it also circumvents no-go theorems on quantum programming and control.Besides universality,such a family satisfies other desirable engineering requirements on system and algorithm design,such as modularity and programmability,hence serves as a unique approach to building universal quantum computers.
文摘Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L<sup>∞</sup>(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L<sup>2</sup>(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .
基金Supported by Academic Discipline Project of Shanghai Dianji University (16JCXK02)Three campus Programs of Shanghai Dianji University (B1-0288-20-014-03-05)。
文摘The reflection of a weak shock wave is considered using a shock polar. We present a sufficient condition under which the von Neumann paradox appears for the Euler equations.In an attempt to resolve the von Neumann paradox for the Euler equations, two new types of reflection configuration, one called the von Neumann reflection(vNR) and the other called the Guderley reflection(GR), are observed in numerical calculations. Finally, we obtain that GR is a reasonable configuration and vNR is an unreasonable configuration to resolve the von Neumann paradox.