High fidelity readout scheme for rare-earth solid state quantum computing

We propose and analyze a high fidelity readout scheme for a single instance approach to quantum computing in rare-earth-ion-doped crystals. The scheme is based on using different species of qubit and readout ions, and it is shown that by allowing the closest qubit ion to act as a readout buffer, the readout error can be reduced by more than an order of magnitude. The scheme is shown to be robust against certain experimental variations, such as varying detection efficiencies, and we use the scheme to predict the expected quantum fidelity of a CNOT gate in these solid state systems. In addition, we discuss the potential scalability of the protocol to larger qubit systems. The results are based on parameters which we believed are experimentally feasible with current technology, and which can be simultaneously realized.

Experimental creation and analysis of displaced number states

We create displaced number states, which are nonclassical generalizations of coherent states, of a vibrational mode of a single trapped ion.

Interaction of a Laser with a Qubit in Thermal Motion and its Application to Robust and Efficient Readout

We present a detailed theoretical and experimental study on the optical control of a trapped-ion qubit subject to thermally induced fluctuations of the Rabi frequency. The coupling fluctuations are caused by thermal excitation on three harmonic oscillator modes. We develop an effective Maxwell-Boltzmann theory which leads to a replacement of several quantized oscillator modes by an effective continuous probability distribution function for the Rabi frequency. The model is experimentally verified for driving the quadrupole transition with resonant square pulses. This allows for the determination of the ion temperature with an accuracy of better than 2% of the temperature pertaining to the Doppler cooling limit TD over a range from 0.5TD to 5TD. The theory is then applied successfully to model experimental data for rapid adiabatic passage (RAP) pulses. We apply the model and the obtained experimental parameters to elu- cidate the robustness and efficiency of the RAP process by means of numerical simulations.

Precision measurements in ion traps using slowly moving standing waves

The present paper describes the experimental implementation of a measuring technique employing a slowly moving, near resonant, optical standing wave in the context of trapped ions. It is used to measure several figures of merit that are important for quantum computation in ion traps and which are otherwise not easily obtainable. Our technique is shown to offer high precision, and also in many cases using a much simpler setup than what is normally used. We demonstrate here measurements of i) the distance between two crystalline ions, ii) the Lamb-Dicke parameter, iii) temperature of the ion crystal, and iv) the interferometric stability of a Raman setup. The exact distance between two ions, in units of standing wave periods, is very important for motional entangling gates, and our method offers a practical way of calibrating this distance in the typical lab situation.

Extracting high fidelity quantum computer hardware from random systems

An overview of current status and prospects of the development of quantum computer hardware based on inorganic crystals doped with rare-earth ions is presented. Major parts of the experimental work in this area has been done in two places, Canberra, Australia and Lund, Sweden, and the present description follows more closely the Lund work. Techniques will be described that include optimal filtering of the initially inhomogeneously broadened profile down to well separated and narrow ensembles, as well as the use of advanced pulse-shaping in order to achieve robust arbitrary single-qubit operations with fidelities above 90%, as characterized by quantum state tomography. It is expected that full scalability of these systems will require the ability to determine the state of single rare-earth ions. It has been proposed that this can be done using special readout ions doped into the crystal and an update is given on the work to find and characterize such ions. Finally, a few aspects on the possibilities for remote entanglement of ions in separate rare-earth-ion-doped crystals are considered.

Experimental quantum state tomography of a solid state qubit

Full quantum state tomography is used to characterize the state of an ensemble based qubit implemented through two hyperfine levels in Pr3+ ions, doped into a Y2SiO5 crystal. We experimentally verify that single-qubit rotation errors due to inhomogeneities of the ensemble can be suppressed using the Roos-Moelmer dark state scheme. Fidelities above >90%, presumably limited by excited state decoherence, were achieved. Although not explicitly taken care of in the Roos-Moelmer scheme, it appears that also decoherence due to inhomogeneous broadening on the hyperfine transition is largely suppressed.