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arXiv:2006.12801 · Physical Review A

High-fidelity simultaneous detection of a trapped-ion qubit register

Liudmila A. Zhukas, P. Švihra, ANDREI NOMEROTSKI, B. B. Blinov

Published Jun 23, 2021• 18 citations
arXivHTMLPDF

Abstract

Qubit state detection is an important part of a quantum computation. As the number of qubits in a quantum register increases, it is necessary to maintain high-fidelity detection to accurately measure the multiqubit state. Here we present experimental demonstration of high-fidelity detection of a multiqubit trapped-ion register with an average single-qubit detection error of 4.2(1.5) ppm and a four-qubit state detection error of 17(2) ppm, limited by the decay lifetime of the qubit, using a single-photon-sensitive camera with fast data collection, excellent temporal and spatial resolution, and low instrumental crosstalk.

DOI
10.1103/physreva.103.062614

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Qubit state detection is an important part of a quantum computation. As the number of qubits in a quantum register increases, it is necessary to maintain high-fidelity detection to accurately measure the multiqubit state. Here we present experimental demonstration of high-fidelity detection of a multiqubit trapped-ion register with an average single-qubit detection error of 4.2(1.5) ppm and a four-qubit state detection error of 17(2) ppm, limited by the decay lifetime of the qubit, using a single-photon-sensitive camera with fast data collection, excellent temporal and spatial resolution, and low instrumental crosstalk.
We describe single-shot readout of a trapped-ion multiqubit register using space- and time-resolved camera detection. For a single qubit we measure $0.9(3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ readout error in 400400400 $\ensuremath{\mu}$s exposure time, limited by the qubit's decay lifetime. For a four-qubit register (a ``qunybble''), we measure an additional error of only $0.1(1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ per qubit, despite the presence of 44%4 optical cross-talk between neighboring qubits. A study of the cross-talk indicates that the method would scale with a negligible loss of fidelity to  ~ 1000010 00010000 qubits at a density of $\ensuremath{\lesssim}$111 qubit/$\ensuremath{\mu}$m2{}^{2}2, with a readout time of  1~1 1 $\ensuremath{\mu}$s/qubit.
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.
Fast and efficient detection of the qubit state in trapped ion systems is critical for implementing quantum error correction and performing fundamental tests such as a loophole-free Bell test. In this work we present a simple qubit state detection protocol for a (171)Yb+ hyperfine atomic qubit trapped in a microfabricated surface trap, enabled by high collection efficiency of the scattered photons and low background photon count rate. We demonstrate average detection times of 10.5, 28.1, and 99.8 μs, corresponding to state detection fidelities of 99%, 99.856(8)%, and 99.915(7)%, respectively.
Trapped ion systems are the leading candidate for quantum information processing because many of the critical components have already been demonstrated. Scaling trapped ion systems to large numbers of ions is currently believed possible, but much work remains to prove it. Microfabricated surface ion traps are increasing in popularity for their ease of mass production and their ability to manipulate individual ions and interact arbitrary pairs of ions. Even with the advent of scalable ion traps, detection of an individual ion trapped in a high vacuum poses a challenge. The internal state of the ion chosen for a quantum bit can be measured via exposure to a probe beam that causes one state to scatter light (a "bright" state), but not the other state (a "dark" state). In free space, a single ion acts like a point source that emits in all directions; a standard two inch lens system can only collect about 2% of the light emitted by the ion. Poor light collection results in a high error rate and slow determination of the internal state of the ion. Fast, high fidelity state detection is necessary for quantum error correction and loophole-free Bell experiments at short (less than 100\\,km) distances, and high efficiency collection is necessary to rapidly interconnect separate quantum computers. We demonstrate state detection fidelities of 99%, 99.856(8)% and 99.915(7) % which correspond to detection times of 10.5, 28.1 and 99.8 us, respectively.
Simultaneous measurement of multiple qubits stored in hyperfine levels of trapped 111Cd+ ions is realized with an intensified charge-coupled device (CCD) imager. A general theory of fluorescence detection for hyperfine qubits is presented and applied to experimental data. The use of an imager for photon detection allows for multiple qubit state measurement with detection fidelities of greater than 98%. Improvements in readout speed and fidelity are discussed in the context of scalable quantum computation architectures.
Simultaneous measurement of multiple qubits stored in hyperfine levels of trapped ^{111}Cd^+ ions is realized with an intensified charge-coupled device (CCD) imager. A general theory of fluorescence detection for hyperfine qubits is presented and applied to experimental data. The use of an imager for photon detection allows for multiple qubit state measurement with detection fidelities of greater than 98%98\%98%. Improvements in readout speed and fidelity are discussed in the context of scalable quantum computation architectures.