Implementation of three-qubit quantum computation with pendular states of polar molecules by optimal control

Abstract

Ultracold polar molecules have been considered as the possible candidates for quantum information processing due to their long coherence time and strong dipole-dipole interaction. In this paper, we consider three coupled polar molecules arranged in a linear chain and trapped in an electric field with gradient. By employing the pendular states of polar molecules as qubits, we successfully realize three-qubit quantum gates and quantum algorithms via the multi-target optimal control theory. Explicitly speaking, through the designs of the optimal laser pulses with multiple iterations, the triqubit Toffoli gate, the triqubit quantum adders, and the triqubit quantum Fourier transform can be achieved in only one operational step with high fidelities and large transition probabilities. Moreover, by combining the optimized Hadamard, oracle, and diffusion gate pulses, we simulate the Grover algorithm in the three-dipole system and show that the algorithm can perform well for search problems. In addition, the behaviors of the fidelity and the average transition probability with respect to iteration numbers are compared and analyzed for each gate pulse. Our findings could pave the way toward scalability for molecular quantum computing based on the pendular states and could be extended to implement multi-particle gate operation in the molecular system.

Realization of Heisenberg models of spin systems with polar molecules in pendular states

“…One potential application of polar molecules is in quantum computing, as originally proposed by DeMille two decades ago [11] . Since then, many aspects and variants have been extensively studied, including for both diatomic linear molecules and symmetric top molecules [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] . For linear molecules, the |00 and |10 pendular states are the most commonly used qubit states [12][13][14][15][16][17][18][19][20][21][22][23][24] .…”

“…Moreover, the internal structure of polar molecules is much richer than that of atoms or spins, allowing much richer physics. Given these unique properties, arrays of polar molecules are considered to be promising platforms for quantum computing and quantum information processing [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] , which is not unlike spins.…”

Realization of Heisenberg models of spin systems with polar molecules in pendular states

“…In between is the Luttinger liquid phase. 42 According to eqn (14), for polar molecules, J z /J only depends on me/B, so in Fig. 7(b) we show how J z /J changes when me/B increases from 0 to 12.…”

“…In order to obtain phase information about the polar molecule system, we still need to know the range of values of g/J. According to eqn (14), g/J depends on both me/B and O. So in Fig.…”

“…Moreover, the internal structure of polar molecules is much richer than that of atoms or spins, allowing much richer physics. Given these unique properties, arrays of polar molecules are considered to be promising platforms for quantum computing and quantum information processing, [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] which is not unlike spins.…”