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arXiv:0705.1870

High-fidelity, adaptive qubit measurements through repetitive information transfer

David B. Hume, Till Rosenband, David J. Wineland

Published May 14, 2007• 1 citation
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Abstract

Using two trapped ion species ($\rm{^{27}Al^+}$ and $\rm{^9Be^+}$) as primary and ancillary systems, we implement qubit measurements based on the repetitive transfer of information and quantum nondemolition detection. The repetition provides a natural mechanism for an adaptive measurement strategy, which leads to exponentially lower error rates compared to using a fixed number of detection cycles. For a single qubit we demonstrate 99.94 % measurement fidelity. We also demonstrate a technique for adaptively measuring multiple qubit states using a single ancilla, and apply the technique to spectroscopy of an optical clock transition.

DOI
10.48550/arxiv.0705.1870

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Using two trapped ion species (27Al+\rm{^{27}Al^+}27Al+ and 9Be+\rm{^9Be^+}9Be+) as primary and ancillary systems, we implement qubit measurements based on the repetitive transfer of information and quantum nondemolition detection. The repetition provides a natural mechanism for an adaptive measurement strategy, which leads to exponentially lower error rates compared to using a fixed number of detection cycles. For a single qubit we demonstrate 99.94 % measurement fidelity. We also demonstrate a technique for adaptively measuring multiple qubit states using a single ancilla, and apply the technique to spectroscopy of an optical clock transition.
Using two trapped ion species ((27)Al(+) and (9)Be(+)) as primary and ancillary quantum systems, we implement qubit measurements based on the repetitive transfer of information and quantum nondemolition detection. The repetition provides a natural mechanism for an adaptive measurement strategy, which leads to exponentially lower error rates compared to using a fixed number of detection cycles. For a single qubit we demonstrate 99.94% measurement fidelity. We also demonstrate a technique for adaptively measuring multiple qubit states using a single ancilla, and apply the technique to spectroscopy of an optical clock transition.
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.
The computational potential of a quantum processor can only be unleashed if errors during a quantum computation can be controlled and corrected for. Quantum error correction works if imperfections of quantum gate operations and measurements are below a certain threshold and corrections can be applied repeatedly. We implement multiple quantum error correction cycles for phase-flip errors on qubits encoded with trapped ions. Errors are corrected by a quantum-feedback algorithm using high-fidelity gate operations and a reset technique for the auxiliary qubits. Up to three consecutive correction cycles are realized, and the behavior of the algorithm for different noise environments is analyzed.
Quantum error correction is of crucial importance for fault-tolerant quantum computers.As an essential step toward the implementation of quantum error-correcting codes, quantum nondemolition measurements are needed to efficiently detect the state of a logical qubit without destroying it.Here we implement quantum nondemolition measurements in a Si/SiGe two-qubit system, with one qubit serving as the logical qubit and the other serving as the ancilla.Making use of a two-qubit controlled-rotation gate, the state of the logical qubit is mapped onto the ancilla, followed by a destructive readout of the ancilla.Repeating this procedure enhances the logical readout fidelity from 75.5 Æ 0.3% to 94.5 Æ 0.2% after 15 ancilla readouts.In addition, we compare the conventional thresholding method with an improved signal processing method called soft decoding that makes use of analog information in the readout signal to better estimate the state of the logical qubit.We demonstrate that soft decoding leads to a significant reduction in the required number of repetitions when the readout errors become limited by Gaussian noise, for instance, in the case of readouts with a low signal-to-noise ratio.These results pave the way for the implementation of quantum error correction with spin qubits in silicon.
Quantum Information Successful protocols for quantum information processing and quantum computation depend on the reliable storage and manipulation of the quantum state of a qubit. Qubits, however, are prone to errors because complete isolation from the environment is not possible. Methods for correcting these errors must also contend with the fact that direct measurement of a qubit destroys it. Xue et al. describe a repetitive quantum nondemolition method on a two-qubit system in which the state of the main qubit is mapped onto a second qubit that acts as an ancilla. Repeated measurement of the ancilla qubit allows the main qubit to be maintained and read out with higher fidelity. Such a protocol provides a route to robust quantum information processing in solid-state systems. Phys. Rev. X 10 , 021006 (2020).