Construction of two-qubit gates using B Gate
M. Karthick Selvan, S. Balakrishnan · Physica Scripta · 2024
Abstract In the circuit model of quantum computation, an entangling two-qubit gate and a set of single-qubit gates are used as universal gate set or basis gates for doing quantum computation. CNOT and iSWAP gates, the perfect entanglers that can create maximally entangled two-qubit states in one application, are broadly used entangling two-qubit basis gates in quantum computers. In this paper, we analyze the potentiality of B gate, an unexplored non-perfect entangler of the form, exp i π ( σ ˆ x ⨂ σ ˆ x ) 8 + i π ( σ ˆ y ⨂ σ ˆ y ) 16 , as an entangling two-qubit basis gate in quantum computers by studying its ability to generate other two-qubit gates. We derive a necessary condition for a two-qubit gate to be generated by n applications of B gate. Using this condition, we show that the gates that can be generated by two and three applications of B gate are contained in the 50% and 92.97% of the volume of Weyl chamber of two-qubit gates, respectively. We prove that two applications of B gate can generate both SWAP and SWAP