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Register a new userHigh-fidelity state detection and tomography of a single ion Zeeman qubit
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We demonstrate high-fidelity Zeeman qubit state detection in a single trapped 88 Sr+ ion. Qubit readout is performed by shelving one of the qubit states to a metastable level using a narrow linewidth diode laser at 674 nm followed by state-selective fluorescence detection. The average fidelity reached for the readout of the qubit state is 0.9989(1). We then measure the fidelity of state tomography, averaged over all possible single-qubit states, which is 0.9979(2). We also fully characterize the detection process using quantum process tomography. This readout fidelity is compatible with recent estimates of the detection error-threshold required for fault-tolerant computation, whereas high-fidelity state tomography opens the way for high-precision quantum process tomography.
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Qubit state detection is an important part of a quantum computation. As number of qubits in a quantum register increases, it is necessary to maintain high fidelity detection to accurately measure the multi-qubit state. Here we present experimental demonstration of high-fidelity detection of a multi-qubit trapped ion register with average single qubit detection error of 4.2(1.5) ppm and a 4-qubit state detection error of 17(2) ppm, limited by the decay lifetime of the qubit, using a novel single-photon-sensitive camera with fast data collection, excellent temporal and spatial resolution, and low instrumental crosstalk.
We present an example of quantum process tomography performed on a single solid state qubit. The qubit used is two energy levels of the triplet state in the Nitrogen-Vacancy defect in Diamond. Quantum process tomography is applied to a qubit which has been allowed to decohere for three different time periods. In each case the process is found in terms of the $chi$ matrix representation and the affine map representation. The discrepancy between experimentally estimated process and the closest physically valid process is noted.
The tomographic reconstruction of the state of a quantum-mechanical system is an essential component in the development of quantum technologies. We present an overview of different tomographic methods for determining the quantum-mechanical density matrix of a single qubit: (scaled) direct inversion, maximum likelihood estimation (MLE), minimum Fisher information distance, and Bayesian mean estimation (BME). We discuss the different prior densities in the space of density matrices, on which both MLE and BME depend, as well as ways of including experimental errors and of estimating tomography errors. As a measure of the accuracy of these methods we average the trace distance between a given density matrix and the tomographic density matrices it can give rise to through experimental measurements. We find that the BME provides the most accurate estimate of the density matrix, and suggest using either the pure-state prior, if the system is known to be in a rather pure state, or the Bures prior if any state is possible. The MLE is found to be slightly less accurate. We comment on the extrapolation of these results to larger systems.
We demonstrate a coherence time of 2.1(1)~s for electron spin superposition states of a single trapped $^{40}$Ca$^+$ ion. The coherence time, measured with a spin-echo experiment, corresponds to residual rms magnetic field fluctuations $leq$~2.7$times$10$^{-12}$~T. The suppression of decoherence induced by fluctuating magnetic fields is achieved by combining a two-layer $mu$-metal shield, which reduces external magnetic noise by 20 to 30~dB for frequencies of 50~Hz to 100~kHz, with Sm$_2$Co$_{17}$ permanent magnets for generating a quantizing magnetic field of 0.37~mT. Our results extend the coherence time of the simple-to-operate spin qubit to ultralong coherence times which so far have been observed only for magnetic insensitive transitions in atomic qubits with hyperfine structure.
Highly state-selective, weakly dissipative population transfer is used to irreversibly move the population of one ground state qubit level of an atomic ion to an effectively stable excited manifold with high fidelity. Subsequent laser interrogation accurately distinguishes these electronic manifolds, and we demonstrate a total qubit state preparation and measurement (SPAM) inaccuracy $epsilon_mathrm{SPAM} < 1.7 times 10^{-4}$ ($-38 mbox{ dB}$), limited by imperfect population transfer between qubit eigenstates. We show experimentally that full transfer would yield an inaccuracy less than $8.0 times 10^{-5}$ ($-41 mbox{ dB}$). The high precision of this method revealed a rare ($approx 10^{-4}$) magnetic dipole decay induced error that we demonstrate can be corrected by driving an additional transition. Since this technique allows fluorescence collection for effectively unlimited periods, high fidelity qubit SPAM is achievable even with limited optical access and low quantum efficiency.
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