Quantum logic gates and circuits construction

Sumathi Pawar, Suchetha N V, Ramasubramanian Murugesan +2 more

Fuyou Fan, Guowu Yang, Gang Yang +1 more

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.

Saleem Mohammed Ridha Taha

Xiao Fang-ying

Owing to the exponential nature of the memory or run-time complexity,many existing methods can only synthesize 3-qubit logic circuits using quantum logic gate library,however,a few can optimally synthesize 3-qubit logic circuits for quantum NOT,CNOT,Controlled-V and Controlled-V+(NCV)gates,the key approach reduces the NCV quantum circuit synthesis problem to four-valued logic synthesis.This paper proposes using NCV gates to create a new quantum logic gate library,which is exactly the same as NCV gate library in the synthesis of all optimal 3-qubit circuits,thus it also reduces the four-valued logic synthesis to easily solved two-valued logic synthesis.We present a 3-qubit efficient synthesis algorithms based on perfect hash function,which can quickly construct all optimal 3-qubit circuits——the average speed that synthesizes circuits with minimum cost is nearly 127 times faster than that of the best result of Maslov 2007.

Xinlan Zhou

H. R. Bhagyalakshmi, Venkatesha M.K

Reversible logic is very essential for the construction of low power, low loss computational structures which are very essential for the construction of arithmetic circuits used in quantum computation, nano technology and other low power digital circuits. In this paper two designs of an optimized parallel multiplier circuit using reversible logic gates is presented. Multipliers are very essential for the construction of various computational units of a quantum computer. Duplication of operand bits are achieved using two gates namely BVF gate and CFO gate. The multiplier circuit uses DPG gates and a new 4 X 4 reversible logic gate called PPG gate. The proposed work is best compared to the other existing circuits. Keywords: Reversible logic circuits, Partial products, multiplier, quantum computing, Nanotechnology.