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arXiv:0906.3304 · Physical Review A

Scalable simultaneous multiqubit readout with 99.99% single-shot fidelity

Alice Heather Burrell, D. J. Szwer, S. C. Webster, D. M. Lucas

Published Apr 5, 2010• 62 citations
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Abstract

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 $400$ $\ensuremath{\mu}$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 $4%$ 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 $~$$10 000$ qubits at a density of $\ensuremath{\lesssim}$$1$ qubit/$\ensuremath{\mu}$m${}^{2}$, with a readout time of $~1$ $\ensuremath{\mu}$s/qubit.

DOI
10.1103/physreva.81.040302

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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×\else\texttimes\fi10\ensuremath−40.9(3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}0.9(3)\ifmmode×\else\texttimes\fi10\ensuremath−4 readout error in 400400400 \ensuremathμ\ensuremath{\mu}\ensuremathμs 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×\else\texttimes\fi10\ensuremath−40.1(1)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}0.1(1)\ifmmode×\else\texttimes\fi10\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 ~$$10 000 qubits at a density of \ensuremath{\lesssim}$$1 qubit/\ensuremathμ\ensuremath{\mu}\ensuremathμm2{}^{2}2, with a readout time of  1~1 1 \ensuremathμ\ensuremath{\mu}\ensuremathμs/qubit.
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.
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 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.
Fast, high-fidelity, and low back-action readout plays a crucial role in the advancement of quantum error correction (QEC). Here, we demonstrate high-performance multiplexed readout of superconducting qubits using a tunable broadband Purcell filter, effectively resolving the fundamental trade-off between measurement speed and photon-noise-induced dephasing. By dynamically tuning the filter parameters, we suppress photon-noise-induced dephasing by a factor of 7 in idle status, while enabling rapid, high-fidelity readout in measurement status. We achieve 99.6\% single-shot readout fidelity with 100~ns readout pulse, limited primarily by relaxation errors during readout. Using a multilevel readout protocol, we further attain 99.9\% fidelity in 50~ns. Simultaneous readout of three qubits using 100~ns pulses achieves an average fidelity of 99.5\% with low crosstalk. Additionally, the readout exhibits high quantum-nondemolition (QND) performance: 99.4\% fidelity over repeated measurements and a low leakage rate below 0.1\%. Building on the tunable broadband filter, we further propose a scalable readout scheme for surface code QEC with enhanced multiplexing capability, offering a promising solution for fast and scalable QEC.
Measuring the state of a qubit is a key fundamental operation of a quantum computer. High-fidelity single-shot readout of superconducting qubits can be achieved using parametric amplifiers at millikelvin temperatures. However, scaling parametric amplifiers beyond hundreds of qubits is challenging due to practical size and power limitations. Nanobolometers can, in contrast, offer scalability, sensitivity and speed suitable for qubit readout. Here we show that a bolometer can provide single-shot qubit readout with a readout duration of 13.9 μs and a single-shot fidelity of 0.618. The fidelity is mainly limited by the energy relaxation time of the qubit (28 μs), and a fidelity of 0.927 is found after removing errors arising from this relaxation. In the future, higher-fidelity single-shot readout may be achieved through improvements in chip design and experimental setup, as well as a change in the bolometer absorber material to reduce the readout time to the level of hundreds of nanoseconds and below.
Measuring the state of qubits is one of the fundamental operations of a quantum computer. Currently, state-of-the-art high-fidelity single-shot readout of superconducting qubits relies on parametric amplifiers at the millikelvin stage. However, parametric amplifiers are challenging to scale beyond hundreds of qubits owing to practical size and power limitations. Nanobolometers have a multitude of properties that are advantageous for scalability and have recently shown sensitivity and speed promising for qubit readout, but such thermal detectors have not been demonstrated for this purpose. In this work, we utilize an ultrasensitive bolometer in place of a parametric amplifier to experimentally demonstrate single-shot qubit readout. With a readout duration of 13.9 μs13.9~μ\mathrm{s}13.9 μs, we achieve a single-shot fidelity of 0.618 which is mainly limited by the energy relaxation time of the qubit, T1=28 μsT_1 = 28~μ\mathrm{s}T1​=28 μs. Without the T1T_1T1​ errors, we find the fidelity to be 0.927. In the future, high-fidelity single-shot readout may be achieved by straightforward improvements to the chip design and experimental setup, and perhaps most interestingly by the change of the bolometer absorber material to reduce the readout time to the hundred-nanosecond level and beyond.