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Journal of Experimental and Theoretical Physics Letters

Optimization of the Readout Fidelity of the Quantum State of an Optical Qubit in the 171Yb+ Ion

Nikita V. Semenin, A. S. Borisenko, Ilia V. Zalivako, Ilya A. Semerikov, Ksenia Yu. Khabarova, N. Kolachevsky

Published Oct 1, 2021• 18 citations
Publisher

Abstract

A scheme based on a laser cooling system has been proposed to detect the state of an optical qubit in the 171Yb+ ion. Analytical expressions have been derived for the readout fidelity including the dark photon counts and background. The parameters of the experiment have been numerically optimized to minimize the readout infidelity. The upper bound on the fidelity associated with a transient process at the beginning of the measurement procedure has been determined as 99.4%. The characteristic parameters of detection ensuring a sufficient proximity to the upper bound have been found.

DOI
10.1134/s0021364021200108

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A scheme based on a laser cooling system has been proposed to detect the state of an optical qubit in the 171Yb+ ion. Analytical expressions have been derived for the readout fidelity including the dark photon counts and background. The parameters of the experiment have been numerically optimized to minimize the readout infidelity. The upper bound on the fidelity associated with a transient process at the beginning of the measurement procedure has been determined as 99.4%. The characteristic parameters of detection ensuring a sufficient proximity to the upper bound have been found.
An increase in the readout fidelity of an optical qubit in a 171Yb+ ion by adding a microwave pumping stage before the measurement has been experimentally demonstrated. The introduction of a microwave π\pi π -pulse between the hyperfine components of the ion ground state before the readout makes it possible to avoid the optical pumping stage at the beginning of the measurement, which leads to a systematic error in the state determination. The conclusions of the theoretical model of the readout process have been experimentally confirmed and an increase in the readout accuracy from (98.98 ± 0.10)% to (99.48 ± 0.07)% has been demonstrated.
We determine the optimal parameters for a simple and efficient scheme of dispersive readout of a qubit. Depending on the qubit state (ground or excited), the resonance of a cavity is shifted either to the red or to the blue side. Qubit state is inferred by detecting the photon number transmitted through the cavity. It turns out that this kind of detection provides better measurement fidelity than the detection of the presence or absence of photons only. We show that radiating the cavity on either of the frequencies it shifts to results in a suboptimal measurement. The optimal frequency of the probe photons is determined, as well as the optimal ratio of the shift to the resonator leakage. It is shown that to maximize the fidelity of a long-lasting measurement, it is sufficient to use the parameters optimizing the signal-to-noise ratio in the photon count. One can reach 99% fidelity for a single-shot measurement in various physical realizations of the scheme.
We demonstrate single-shot qubit readout with a fidelity sufficient for fault-tolerant quantum computation. For an optical qubit stored in 40Ca+ we achieve 99.991(1)% average readout fidelity in 10(6) trials, using time-resolved photon counting. An adaptive measurement technique allows 99.99% fidelity to be reached in 145 micros average detection time. For 43Ca+, we propose and implement an optical pumping scheme to transfer a long-lived hyperfine qubit to the optical qubit, capable of a theoretical fidelity of 99.95% in 10 micros. We achieve 99.87(4)% transfer fidelity and 99.77(3)% net readout fidelity.
This thesis describes experimental demonstrations of high-fidelity readout of trapped ion quantum bits ("qubits") for quantum information processing. We present direct single-shot measurement of an "optical" qubit stored in a single calcium-40 ion by the process of resonance fluorescence with a fidelity of 99.991(1)% (surpassing the level necessary for fault-tolerant quantum computation). A time-resolved maximum likelihood method is used to discriminate efficiently between the two qubit states based on photon-counting information, even in the presence of qubit decay from one state to the other. It also screens out errors due to cosmic ray events in the detector, a phenomenon investigated in this work. An adaptive method allows the 99.99% level to be reached in 145us average detection time. The readout fidelity is asymmetric: 99.9998% is possible for the "bright" qubit state, while retaining 99.98% for the "dark" state. This asymmetry could be exploited in quantum error correction (by encoding the "no-error" syndrome of the ancilla qubits in the "bright" state), as could the likelihood values computed (which quantify confidence in the measurement outcome). We then extend the work to parallel readout of a four-ion string using a CCD camera and achieve the same 99.99% net fidelity, limited by qubit decay in the 400us exposure time. The behaviour of the camera is characterised by fitting experimental data with a model. The additional readout error due to cross-talk between ion images on the CCD is measured in an experiment designed to remove the effect of qubit decay; a spatial maximum likelihood technique is used to reduce this error to only 0.2(1)x10^{-4} per qubit, despite the presence of ~4% optical cross-talk between neighbouring qubits. Studies of the cross-talk indicate that the readout method would scale with negligible loss of fidelity to parallel readout of ~10,000 qubits with a readout time of ~3us per qubit. Monte-Carlo simulations of the readout process are presented for comparison with experimental data; these are also used to explore the parameter space associated with fluorescence detection and to optimise experimental and analysis parameters. Applications of the analysis methods to readout of other atomic and solid-state qubits are discussed.
We report high-fidelity state readout of a trapped ion qubit using a trap-integrated photon detector. We determine the hyperfine qubit state of a single ^{9}Be^{+} ion held in a surface-electrode rf ion trap by counting state-dependent ion fluorescence photons with a superconducting nanowire single-photon detector fabricated into the trap structure. The average readout fidelity is 0.9991(1), with a mean readout duration of 46 μs, and is limited by the polarization impurity of the readout laser beam and by off-resonant optical pumping. Because there are no intervening optical elements between the ion and the detector, we can use the ion fluorescence as a self-calibrated photon source to determine the detector quantum efficiency and its dependence on photon incidence angle and polarization.
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.