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Register a new userKeeping a spin qubit alive in natural silicon: Comparing optimal working points and dynamical decoupling
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There are two distinct techniques of proven effectiveness for extending the coherence lifetime of spin qubits in environments of other spins. One is dynamical decoupling, whereby the qubit is subjected to a carefully timed sequence of control pulses; the other is tuning the qubit towards optimal working points (OWPs), which are sweet-spots for reduced decoherence in magnetic fields. By means of quantum many-body calculations, we investigate the effects of dynamical decoupling pulse sequences far from and near OWPs for a central donor qubit subject to decoherence from a nuclear spin bath. Key to understanding the behavior is to analyse the degree of suppression of the usually dominant contribution from independent pairs of flip-flopping spins within the many-body quantum bath. We find that to simulate recently measured Hahn echo decays at OWPs (lowest-order dynamical decoupling), one must consider clusters of three interacting spins, since independent pairs do not even give finite $T_2$ decay times. We show that while operating near OWPs, dynamical decoupling sequences require hundreds of pulses for a single order of magnitude enhancement of $T_2$, in contrast to regimes far from OWPs, where only about ten pulses are required.
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We present rigorous performance bounds for the optimal dynamical decoupling pulse sequence protecting a quantum bit (qubit) against pure dephasing. Our bounds apply under the assumption of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians. We show that if the total sequence time is fixed the optimal sequence can be used to make the distance between the protected and unperturbed qubit states arbitrarily small in the number of applied pulses. If, on the other hand, the minimum pulse interval is fixed and the total sequence time is allowed to scale with the number of pulses, then longer sequences need not always be advantageous. The rigorous bound may serve as testbed for approximate treatments of optimal decoupling in bounded models of decoherence.
Quantum error correction is of crucial importance for fault-tolerant quantum computers. As an essential step towards the implementation of quantum error-correcting codes, quantum non-demolition (QND) measurements are needed to efficiently detect the state of a logical qubit without destroying it. Here we implement QND 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 $75.5pm 0.3%$ to $94.5 pm 0.2%$ 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.
A two-qubit controlled-NOT (CNOT) gate, realized by a controlled-phase (C-phase) gate combined with single-qubit gates, has been experimentally implemented recently for quantum-dot spin qubits in isotopically enriched silicon, a promising solid-state system for practical quantum computation. In the experiments, the single-qubit gates have been demonstrated with fault-tolerant control-fidelity, but the infidelity of the two-qubit C-phase gate is, primarily due to the electrical noise, still higher than the required error threshold for fault-tolerant quantum computation (FTQC). Here, by taking the realistic system parameters and the experimental constraints on the control pulses into account, we construct experimentally realizable high-fidelity CNOT gates robust against electrical noise with the experimentally measured $1/f^{1.01}$ noise spectrum and also against the uncertainty in the interdot tunnel coupling amplitude. Our optimal CNOT gate has about two orders of magnitude improvement in gate infidelity over the ideal C-phase gate constructed without considering any noise effect. Furthermore, within the same control framework, high-fidelity and robust single-qubit gates can also be constructed, paving the way for large-scale FTQC.
Sensing the internal dynamics of individual nuclear spins or clusters of nuclear spins has recently become possible by observing the coherence decay of a nearby electronic spin: the weak magnetic noise is amplified by a periodic, multi-pulse decoupling sequence. However, it remains challenging to robustly infer underlying atomic-scale structure from decoherence traces in all but the simplest cases. We introduce Floquet spectroscopy as a versatile paradigm for analysis of these experiments, and argue it offers a number of general advantages. In particular, this technique generalises to more complex situations, offering physical insight in regimes of many-body dynamics, strong coupling and pulses of finite duration. As there is no requirement for resonant driving, the proposed spectroscopic approach permits physical interpretation of striking, but overlooked, coherence decay features in terms of the form of the avoided crossings of the underlying quasienergy eigenspectrum. This is exemplified by a set of diamond shaped features arising for transverse-field scans in the case of single-spin sensing by NV-centers in diamond. We investigate also applications for donors in silicon showing that the resulting tunable interaction strengths offer highly promising future sensors.
We consider dynamical decoupling schemes in which the qubit is continuously manipulated by a control field at all times. Building on the theory of the Uhrig Dynamical Decoupling sequence (UDD) and its connections to Chebyshev polynomials, we derive a method of always-on control by expressing the UDD control field as a Fourier series. We then truncate this series and numerically optimize the series coefficients for decoupling, constructing the CAFE (Chebyshev and Fourier Expansion) sequence. This approach generates a bounded, continuous control field. We simulate the decoupling effectiveness of our sequence vs. a continuous version of UDD for a qubit coupled to fully-quantum and semi-classical dephasing baths and find comparable performance. We derive filter functions for continuous-control decoupling sequences, and we assess how robust such sequences are to noise on control fields. The methods we employ provide a variety of tools to analyze continuous-control dynamical decoupling sequences.
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