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Because ternary computer has more superiority than other d-ary number systems, we focus on the investigation of ternary elementary quantum gates and the synthesis algorithm of ternary quantum logic circuits. Above all, Pauli operators and their matrices on qutrit are introduced. Then eight qutrit operators are selected as elementary operators and eight qutrit quantum logic gates are defined. Permutation groups are introduced to characterize the quantum gates and quantum logic circuits. Some important qutrit quantum logic gates are defined also, such as QNOT, QKCXi, EQKCXi, QSwap, QCNOT and EQCNOT. Based on these elementary gates, we prove two very important theorems: (1) all qutrit quantum reversible logic circuit can be generated by Xi gate and QKCXi gate; (2) all qutrit quantum reversible logic circuits can be generated by Xi gate and QCNOT gate. The two theorems indicate that any complicated qutrit quantum reversible circuit can be constructed by the simplest ternary quantum gate. This will greatly simplify the implementation difficulty of quantum circuit. Subsequently, we propose a synthesis algorithm for qutrit quantum reversible logic circuit, which is verified through simulation experiment by the computer program we have designed. [ABSTRACT FROM AUTHOR]

With the increase of the complexity of circuits, fast estimation can provide some vital information for optimal layout decisions. Fast congestion prediction plays an important role in the physical layout of VLSI design. In this paper, we present a probabilistic estimation approach with via minimization constraints. Our model is more realistic than previous models. It has more flexibility for wires to have more usage area to bypass congested regions and blockages. The experiment on routing benchmarks demonstrates the effectiveness of our approach. [ABSTRACT FROM AUTHOR]