Optimal Circuit Decomposition of Reversible Quantum Gates on IBM Quantum Computers

Abstract

A critical task in utilizing quantum physics in many application fields is circuit design using reversible quantum gates. Using decomposition techniques enables transformation of unitary matrices into fundamental quantum gates. Any 3x3 reversible quantum gate can be decomposed into single-qubit rotation gates and two qubit CNOT gates. In this chapter, quantum implementations of FRSG1, URG, JTF1 and R gates into CNOT gates and single qubit U3 gates with different optimization levels on a platform provided by IBM have been discussed. FRSG1 and JTF1 gates are important in applications like Stochastic computing, fingerprint authentication system, and parity generation circuits. URG gate is better in terms of number of complex functions and can be utilized to design quantum comparator circuits. R gate plays an important role in inverting and duplicating a signal. In FRSG1, URG, JTF1 and R gates, the implementation count of single qubit gates decreases by 56%, 11%, 71%, and 62%, respectively and the count of two qubit gates reduces by 15%, 26%, 41%, and 5% respectively after optimization.