Quantum computing (QC) has played an important role as a modern research topic because the quantum mechanics phenomena (entanglement, superposition, projective measurement) can be used for different purposes such as data storage, communications and data processing, increasing security, and processing power.
The design of quantum logic gates (or quantum gates) is the basis for QC circuit model. There have been proposals and implementations of the qubit and quantum gates for several physical systems [1
], where the qubit is represented as charge states using trapped ions, nuclear magnetic resonance (NMR) using the magnetic spin of ions, with light polarization as qubit or spin in solid-state nanostructures. Spin qubits in graphene nanoribbons have been also proposed. Some obstacles are present, in every implementation, related to the properties of the physical system like short coherence time in spin qubits and charge qubits or null interaction between photons, which is necessary to design two-qubit quantum logic gates. Most of the quantum algorithms have been implemented in NMR as Shor's algorithm [2
] for the factorization of numbers. Any quantum algorithm can be done by the combination of one-qubit universal quantum logic gates like arbitrary rotations over Bloch sphere axes (X
), and Z
)) or the Pauli gates (
) and two-qubit quantum gates like controlled NOT which is a genuine two-qubit quantum gate.
The implementation of gates using graphene to make quantum dots seems appropriate because this material is naturally low dimensional, and the isotope 12
C (most common in nature) has no nuclear spin because the sum of spin particles in the nucleus is neutralized. This property can be helpful to increase time coherence as seen by the proposal of graphene nanoribbons (GPNs) [3
] and Z-shape GPN for spin qubit [4
In this work, we propose the implementation of three one-qubit quantum gates using the states of a circular graphene quantum dot (QD) to define the qubit. The control is made with pulse width modulation and coherent light which induce an oscillating electric field. The time-dependent Schrodinger equation is solved to describe the amplitude of being in a QD state Cj
). Two bound states are chosen to be the computational basis |0
1/2 and j
−1/2, respectively, which form the qubit subspace. In this work, we studied the general n-state problem with all dipolar and onsite interactions included so that the objective is to optimize the control parameters of the time-dependent physical interaction in order to minimize the probability of leaking out of the qubit subspace and achieve the desired one-qubit gates successfully. The control parameters are obtained using a genetic algorithm which finds efficiently the optimal values for the gate implementation where the genes are: the magnitude (ϵ0
) and direction (ρ
) of electric field, magnitude of gate voltage (Vg0
), and pulse width (τv
). The fitness is defined as the gate fidelity at the measured time to obtain the best fitness, which means the best control parameters were found to produce the desired quantum gate. We present our findings and the evolution of the charge density and pseudospin current in the quantum dot under the gate effect.