Abstract
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
†
which is not possible for CNOT and
iSWAP
gates; further, we conjecture that three applications of
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
B
gates that can generate all two-qubit gates. In the end, we mention about the schemes to implement
B
gate in ion-trap quantum computers.