Three-Qubit Quantum Entanglement for Si (S = 3/2, I = 1/2) Spin System

Abstract

In quantum information processing, spin-3/2 electron or nuclear spin states are known as twoqubit states. For SI (S ¼ 3=2; I ¼ 1=2) spin system, there are eight three-qubit states. In this study, first, three-qubit CNOT logic gates are obtained. Then three-qubit entangled states are obtained by using the matrix representation of Hadamard and three-qubit CNOT logic gates. By considering single 31 P@C 60 molecule as SI (S ¼ 3=2; I ¼ 1=2) spin system, three-qubit entangled states are also obtained using the magnetic resonance pulse sequences of Hadamard and CNOT logic gates.

Spin Quantum Computing with Endohedral Fullerenes

“…Up to three qubits (2 3 = 8) may thus be defined and entangled, 33 and even four qubits would be possible in the 𝑆𝑆 = 3 2 , 𝐼𝐼 = 3 2 spin system of the (not yet experimentally reported) As@C60 analogue. 34 The four levels of the high 𝑆𝑆 = 3 2 electron spin can in principle be used to encode either two qubits 33,35 or a ququart (a four-level generalization of the two-level qubit), which is useful in some quantum computing schemes and has been studied for analogous 𝐼𝐼 = 3 2 nuclear spins in the NMR domain. 36,37 In both cases, however, transition-selective addressing is mandatory, requiring a finite 'quadrupolar' splitting Hamiltonian of the form 𝑄𝑄𝐼𝐼 !…”