Simulation of the elementary evolution operator with the motional states of an ion in an anharmonic trap

Abstract

Following a recent proposal of L. Wang and D. Babikov, J. Chem. Phys. 137, 064301 (2012), we theoretically illustrate the possibility of using the motional states of a $C{d}^{+}$ ion trapped in a slightly anharmonic potential to simulate the single-particle time-dependent Schrödinger equation. The simulated wave packet is discretized on a spatial grid and the grid points are mapped on the ion motional states which define the qubit network. The localization probability at each grid point is obtained from the population in the corresponding motional state. The quantum gate is the elementary evolution operator corresponding to the time-dependent Schrödinger equation of the simulated system. The corresponding matrix can be estimated by any numerical algorithm. The radio-frequency field able to drive this unitary transformation among the qubit states of the ion is obtained by multi-target optimal control theory. The ion is assumed to be cooled in the ground motional state and the preliminary step consists in initializing the qubits with the amplitudes of the initial simulated wave packet. The time evolution of the localization probability at the grids points is then obtained by successive applications of the gate and reading out the motional state population. The gate field is always identical for a given simulated potential, only the field preparing the initial wave packet has to be optimized for different simulations. We check the stability of the simulation against decoherence due to fluctuating electric fields in the trap electrodes by applying dissipative Lindblad dynamics.

31 pages, 8 figures. Revised version. New title, new figure and new references

References in corpus (17)

• Quantum Computing
• Simulated Quantum Computation of Molecular Energies
• Scalable multi-particle entanglement of trapped ions
• Quantum computing with trapped ions
• High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit
• Polynomial-time quantum algorithm for the simulation of chemical dynamics
• Simulating chemistry using quantum computers
• Digital quantum simulation of fermionic models with a superconducting circuit
• Schemes for robust quantum computation with polar molecules
• Scaling and Suppression of Anomalous Quantum Decoherence in Ion Traps
• Employing trapped cold ions to verify the quantum Jarzynski equality
• Large Scale Quantum Computation in an Anharmonic Linear Ion Trap
• Quantum simulation of the single-particle Schrodinger equation
• Implementation of Quantum Logic Gates Using Polar Molecules in Pendular States
• Laser control in a bifurcating region
• Cooperating or Fighting with Decoherence in the Optimal Control of Quantum Dynamics
• Not gate in a cis-trans photoisomerization model