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Quantum Computing with Trapped Ion Hyperfine Qubits

Quantum Computing with Trapped Ion Hyperfine Qubits. General requirements. A scalable system of well-defined qubits A method to reliably initialize the quantum system Long coherence times Existence of universal gates An efficient measurement scheme. Type of qubits for trapped ion.

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Quantum Computing with Trapped Ion Hyperfine Qubits

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  1. Quantum Computing with Trapped Ion Hyperfine Qubits

  2. General requirements • A scalable system of well-defined qubits • A method to reliably initialize the quantum system • Long coherence times • Existence of universal gates • An efficient measurement scheme

  3. Type of qubits for trapped ion • Optical qubits - derived from ground state and an excited metastable state separated by an optical frequency • Hyperfine qubits - derived from electronic ground-state hyperfine levels separated by a microwave frequency

  4. Ion traps • Quadrupole ion trap: using DC and radio frequency (RF) ~1 MHz oscillating AC electric fields • Penning trap: using a constant magnetic field and a constant electric field

  5. Ponderomotive pseudopotential Oscillation frequency of ion

  6. Trapped ion hyperfine qubits • Electric field perturbations are small • Magnetic field perturbations can be reduced by coherence between two internal levels • Extremely long radioactive lifetime

  7. γe |e>

  8. Initialization and detection of qubits • Standard optical pumping to initialize HF qubits to either or • Polarized laser beam resonant with spacing level scatter either or

  9. HF Qubit Rotations: Single Qubit Gates • Microwave with frequency ωHF Big wavelength ~cm - good for joint rotations of all qubits - difficult for individual qubits rotation. • Stimulated Raman Transitions (STR) - two laser fields with detuning Δ from excited state and differing in frequency by ωHF, Δ>>γe - SRT Rabi frequency: ΩSRT=g1g2*/ Δ - individual qubits rotation can be achieved

  10. Interactions between HF qubits: entangling qubit gates • Interaction Hamiltonian • Motion-sensitive stimulated Raman transitions • Spin-dependent optical forces

  11. Motion-sensitive stimulated Raman transitions Rotating wave approximation :

  12. k=-1 J-C Hamiltonian

  13. Spin-dependent optical forces • Laser beams’ dipole force depends upon the state of the qubit |S> and certain excited state (atomic selection rules). • Appropriate polarization of the light. • Use intensity gradient of a laser beam or standing wave to control the motion of ion.

  14. With an intensity gradient (focusing or standing wave)

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