Anisotropic Spin Cluster as a Qubit

We study an anisotropic spin cluster of 3 spin S=1/2 particles with antiferromagnetic exchange interactionwith non-uniform coupling constants.A time-dependent magnetic field is applied to control the time evolution of thecluster.It is well known that for an odd number of sites a spin cluster qubit can be defined in terms of the ground statedoublet.The universal one-qubit logic gate can be constructed from the time evolution operator of the non-autonomousmany-body system,and the six basic one-qubit gates can be realized by adjusting the applied time-dependent magneticfield.

Function synthesis algorithm based on RTD-based three-variable universal logic gates

Compared with complementary metal–oxide semiconductor(CMOS), the resonant tunneling device(RTD) has better performances; it is the most promising candidate for next-generation integrated circuit devices. The universal logic gate is an important unit circuit because of its powerful logic function, but there are few function synthesis algorithms that can implement an n-variable logical function by RTD-based universal logic gates. In this paper, we propose a new concept, i.e., the truth value matrix. With it a novel disjunctive decomposition algorithm can be used to decompose an arbitrary n-variable logical function into three-variable subset functions. On this basis, a novel function synthesis algorithm is proposed, which can implement arbitrary n-variable logical functions by RTD-based universal threshold logic gates(UTLGs), RTD-based three-variable XOR gates(XOR3s), and RTD-based three-variable universal logic gate(ULG3s). When this proposed function synthesis algorithm is used to implement an n-variable logical function, if the function is a directly disjunctive decomposition one, the circuit structure will be very simple, and if the function is a non-directly disjunctive decomposition one, the circuit structure will be simpler than when using only UTLGs or ULG3s. The proposed function synthesis algorithm is straightforward to program, and with this algorithm it is convenient to implement an arbitrary n-variable logical function by RTD-based universal logic gates.

Axiomatization for 1-level universal AND operator

The aim of this article is the partial axiomatization for 1-level universal logic. A propositional calculus formal deductive system ULh∈（0,1） based on l-level universal AND operator of universal logic is algebra LПIG is introduced. The of system ULh∈（0,1） are proved. built up. The corresponding soundness and the completeness