Construction of two-qubit gates using B Gate

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 <?CDATA √iSWAP?> 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 <?CDATA √B?> B gate, an unexplored non-perfect entangler of the form, <?CDATA exp (iπ (σ ̂ₓ⊗ σ ̂ₓ)8+iπ (σ ̂y⊗ σ ̂y)16)?> 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 <?CDATA √B?> B gate. Using this condition, we show that the gates that can be generated by two and three applications of <?CDATA √B?> 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 <?CDATA √B?> B gate can generate both <?CDATA √SWAP?> SWAP and <?CDATA √SWAP?> SWAP † which is not possible for CNOT and <?CDATA √iSWAP?> iSWAP gates; further, we conjecture that three applications of <?CDATA √B?> B gate can generate all perfect entanglers. Finally, we discuss about the construction of a three independent parameter universal two-qubit quantum circuit using four <?CDATA √B?> B gates that can generate all two-qubit gates. In the end, we mention about the schemes to implement <?CDATA √B?> B gate in ion-trap quantum computers.