R. Blatt

Implementation of the Deutsch–Jozsa algorithm on an ion-trap quantum computer

Determining classically whether a coin is fair (head on one side, tail on the other) or fake (heads or tails on both sides) requires an examination of each side. However, the analogous quantum procedure (the Deutsch–Jozsa algorithm) requires just one examination step. The Deutsch–Jozsa algorithm has been realized experimentally using bulk nuclear magnetic resonance techniques, employing nuclear spins as quantum bits (qubits). In contrast, the ion trap processor utilises motional and electronic quantum states of individual atoms as qubits, and in principle is easier to scale to many qubits. Experimental advances in the latter area include the realization of a two-qubit quantum gate, the entanglement of four ions, quantum state engineering and entanglement-enhanced phase estimation. Here we exploit techniques developed for nuclear magnetic resonance to implement the Deutsch–Jozsa algorithm on an ion-trap quantum processor, using as qubits the electronic and motional states of a single calcium ion. Our ion-based implementation of a full quantum algorithm serves to demonstrate experimental procedures with the quality and precision required for complex computations, confirming the potential of trapped ions for quantum computation.

Absolute frequency measurement of the 40Ca+ 4s(2)S_(1/2)-3d(2)D_(5/2) clock transition.

We report on the first absolute transition frequency measurement at the 10 -15 level with a single, laser-cooled 40 Ca + ion in a linear Paul trap. For this measurement, a frequency comb is referenced to the transportable Cs atomic fountain clock of LNE-SYRTE and is used to measure the 40 Ca + 4s 2 S 1/2 -3d 2 D 5/2 electric-quadrupole transition frequency. After the correction of systematic shifts, the clock transition frequency v Ca + = 411 042 129 776 393.2 (1.0) Hz is obtained, which corresponds to a fractional uncertainty within a factor of 3 of the Cs standard. In addition, we determine the Lande g factor of the 3d 2 D 5/2 level to be g 5/2 = 1.2003340(3).

Experimental quantum-information processing withC43a+ions

For quantum information processing (QIP) with trapped ions, the isotope 43Ca+ offers the combined advantages of a quantum memory with long coherence time, a high fidelity read out and the possibility of performing two qubit gates on a quadrupole transition with a narrow-band laser. Compared to other ions used for quantum computing, 43Ca+ has a relatively complicated level structure. In this paper we discuss how to meet the basic requirements for QIP and demonstrate ground state cooling, robust state initialization and efficient read out for the hyperfine qubit with a single 43Ca+ ion. A microwave field and a Raman light field are used to drive qubit transitions, and the coherence times for both fields are compared. Phase errors due to interferometric instabilities in the Raman field generation do not limit the experiments on a time scale of 100 ms. We find a quantum information storage time of many seconds for the hyperfine qubit.

Absolute Frequency Measurement of the 40Ca+ 4s 2S1/2 -3d2D5/2 Clock Transition

We report on the first absolute transition frequency measurement at the 10 -15 level with a single, laser-cooled 40 Ca + ion in a linear Paul trap. For this measurement, a frequency comb is referenced to the transportable Cs atomic fountain clock of LNE-SYRTE and is used to measure the 40 Ca + 4s 2 S 1/2 -3d 2 D 5/2 electric-quadrupole transition frequency. After the correction of systematic shifts, the clock transition frequency v Ca + = 411 042 129 776 393.2 (1.0) Hz is obtained, which corresponds to a fractional uncertainty within a factor of 3 of the Cs standard. In addition, we determine the Lande g factor of the 3d 2 D 5/2 level to be g 5/2 = 1.2003340(3).

Addressing and Cooling of Single Ions in Paul Traps

The use of cold trapped ions for quantum information processing requires the preparation of linear strings of ions at low temperatures and the coherent manipulation by laser light of the quantum state of individual ions in the string. In our experiment, 40Ca+ ions are trapped in a linear Paul trap, forming crystallized linear strings when laser cooled. These strings are observed by fluorescence detection on the S1/2-P1/2 dipole transition at 397 nm using a photomultiplier and a CCD camera. The narrow S1/2-D5/2 quadrupole transition at 729 nm is used to investigate and manipulate the vibrational motion of the ion in the trap. The spectral resolution obtained up to now on this transition is 2 · 10—12, proving long coherence time of the two-level system. Addressing of individual ions in the string is achieved, using a tightly focused laser beam at 729 nm, and detected by the observation of quantum jumps from the S1/2 to the D5/2 level. These experimental techniques make ions in a superposition of their S1/2 and D5/2 states suitable as qubits for quantum information processing. The realization of a two-ion quantum gate furthermore requires ground-state cooling of the string. The status of current experiments is reviewed and techniques to achieve ground-state cooling of ion strings are discussed.

ABSOLUTE FREQUENCY MEASUREMENT OF THE 40Ca+ 4s 2S1/2 - 3d 2D5/2 CLOCK TRANSITION

We report on the first absolute transition frequency measurement at the 10;{-15} level with a single, laser-cooled 40Ca+ ion in a linear Paul trap. For this measurement, a frequency comb is referenced to the transportable Cs atomic fountain clock of LNE-SYRTE and is used to measure the 40Ca+ 4s ;{2}S_{1/2}-3d ;{2}D_{5/2} electric-quadrupole transition frequency. After the correction of systematic shifts, the clock transition frequency nu_{Ca;{+}}=411 042 129 776 393.2(1.0) Hz is obtained, which corresponds to a fractional uncertainty within a factor of 3 of the Cs standard. In addition, we determine the Landé g factor of the 3d;{2}D_{5/2} level to be g_{5/2}=1.200 334 0(3).

High-fidelity entanglement of Ca + 43 hyperfine clock states

In an experiment using the odd calcium isotope

Absolute frequency measurement of 40 Ca + in a Paul trap

^{43}mathrm{Ca}^{+}

Laser Spectroscopy: Proceedings of the XIV International Conference

, we combine the merits of a high-fidelity entangling operation on an optical transition (optical qubit) with the long coherence times of two ``clock states in the hyperfine ground state (hyperfine qubit) by mapping between these two qubits. For state initialization, state detection, global qubit rotations, and mapping operations, errors smaller than 1% are achieved, whereas the entangling gate adds errors of 2.3%. Based on these operations, we create Bell states with a fidelity of 96.9(3)% in the optical qubit and a fidelity of 96.7(3)% when mapped to the hyperfine states. In the latter case, the entanglement is preserved for

Absolute Frequency Measurement of theCa+404sS1/22−3dD5/22Clock Transition

96(3)phantom{rule{0.3em}{0ex}}mathrm{ms}