Simulation of the elementary evolution operator with the motional states of an ion in an anharmonic trap
arXiv:1501.02346 · doi:10.1063/1.4916355
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 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.
arXiv comment31 pages, 8 figures. Revised version. New title, new figure and new references
References in corpus (39)
- A variational eigenvalue solver on a quantum processor
- Quantum information with continuous variables
- Quantum Computing
- Spins in few-electron quantum dots
- Simulated Quantum Computation of Molecular Energies
- Quantum computation with trapped polar molecules
- Cold and Ultracold Molecules: Science, Technology, and Applications
- Scalable multi-particle entanglement of trapped ions
- Quantum computing with trapped ions
- Quantum simulation of the Dirac equation
- Large Scale Modular Quantum Computer Architecture with Atomic Memory and Photonic Interconnects
- High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit
- Heating of trapped ions from the quantum ground state
- 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
- Molecular Quantum Computing by an Optimal Control Algorithm for Unitary Transformations
- Optimal control theory for unitary transformations
- Quantum Computation with Vibrationally Excited Molecules
- Schemes for robust quantum computation with polar molecules
- Scaling and Suppression of Anomalous Quantum Decoherence in Ion Traps
- From transistor to trapped-ion computers for quantum chemistry
- Employing trapped cold ions to verify the quantum Jarzynski equality
- Large Scale Quantum Computation in an Anharmonic Linear Ion Trap
- Efficient Quantum Circuits for Diagonal Unitaries Without Ancillas
- Quantum simulation of the single-particle Schrodinger equation
- A microscopic model of electronic field noise heating in ion traps
- Experimental Implementation of the Deutsch-Jozsa Algorithm for Three-Qubit Functions using Pure Coherent Molecular Superpositions
- Quantum Algorithm for Molecular Properties and Geometry Optimization
- Implementation of Quantum Logic Gates Using Polar Molecules in Pendular States
- Decoherence and fidelity in ion traps with fluctuating trap parameters
- Entanglement of polar symmetric top molecules as candidate qubits
- Laser control in a bifurcating region
- Manipulating motional states by selective vibronic interaction in two trapped ions
- Influence of monolayer contamination on electric-field-noise heating in ion traps
- Toward scalable information processing with ultracold polar molecules in an electric field: a numerical investigation
- Generation of two-mode nonclassical motional states and a Fredkin gate operation in a two-dimensional ion trap
- Cooperating or Fighting with Decoherence in the Optimal Control of Quantum Dynamics
- Not gate in a cis-trans photoisomerization model