arXiv:1906.02731 · Physical review. B./Physical review. B
Spatial noise correlations in a Si/SiGe two-qubit device from Bell state coherences
Jelmer M. Boter, Xiao Xue, Tobias Krähenmann, Thomas F. Watson, Vickram N. Premakumar, Daniel R. Ward, D. E. Savage, M. G. Lagally, Mark G. Friesen, S. N. Coppersmith, M. A. Eriksson, Robert Joynt, Lieven M. K. Vandersypen
We study spatial noise correlations in a Si/SiGe two-qubit device with integrated micromagnets. Our method relies on the concept of decoherence-free subspaces, whereby we measure the coherence time for two different Bell states, designed to be sensitive only to either correlated or anticorrelated noise, respectively. From these measurements we find weak correlations in low-frequency noise acting on the two qubits, while no correlations could be detected in high-frequency noise. We expect nuclear spin noise to have an uncorrelated nature. A theoretical model and numerical simulations give further insight into the additive effect of multiple independent (anti)correlated noise sources with an asymmetric effect on the two qubits as can result from charge noise. Such a scenario in combination with nuclear spins is plausible given the data and the known decoherence mechanisms. This work is highly relevant for the design of optimized quantum error correction codes for spin qubits in quantum dot arrays, as well as for optimizing the design of future quantum dot arrays.
We study spatial noise correlations in a Si/SiGe two-qubit device with integrated micromagnets. Our method relies on the concept of decoherence-free subspaces, whereby we measure the coherence time for two different Bell states, designed to be sensitive only to either correlated or anticorrelated noise, respectively. From these measurements we find weak correlations in low-frequency noise acting on the two qubits, while no correlations could be detected in high-frequency noise. We expect nuclear spin noise to have an uncorrelated nature. A theoretical model and numerical simulations give further insight into the additive effect of multiple independent (anti)correlated noise sources with an asymmetric effect on the two qubits as can result from charge noise. Such a scenario in combination with nuclear spins is plausible given the data and the known decoherence mechanisms. This work is highly relevant for the design of optimized quantum error correction codes for spin qubits in quantum dot arrays, as well as for optimizing the design of future quantum dot arrays.
Probing Residual Noise at a Decoherence Sweet Spot in a 28Si/SiGe Spin Qubit
In 28Si/SiGe spin qubits with micromagnets, the longitudinal stray field gradient transduces charge noise into qubit frequency noise and limits coherence. We compare two neighboring qubits in the same device with 800 ppm residual 29Si, one near a decoherence sweet spot where the gradient is locally minimized and the other at a position with a larger gradient. At the sweet spot, T2∗ reaches 67 μs and the Carr-Purcell-Meiboom-Gill coherence time reaches 4.6 ms, whereas T2∗ is 5.2 μs at the neighboring qubit. Near 1 Hz, the frequency noise power spectral density at the sweet spot is nearly two orders of magnitude lower than at the neighboring qubit. The magnitude and low-frequency decay of the residual spectrum are compatible with the prediction for 29Si nuclear spin noise, and the weak interqubit correlation indicates that local noise becomes important for dephasing at the sweet spot. Despite a finite correlation with the charge sensor, sweet-spot operation strongly reduced the transduction of charge noise, bringing the residual frequency noise close to the level predicted for 29Si nuclear spin fluctuations.
Correlated noise across multiqubit architectures is known to be highly detrimental to the operation of error-correcting codes and the long-term feasibility of quantum processors. The recent discovery of spatially dependent correlated noise in multiqubit architectures of superconducting qubits arising from the impact of cosmic radiation and high-energy particles giving rise to quasiparticle poisoning within the substrate has led to intense investigations of mitigation strategies to address this. Correlated noise in semiconductor spin qubits is also now receiving attention, as this platform begins to scale. Here we report the magnitude, frequency, and spatial dependence of noise correlations between four silicon quantum dot pairs as a function of interdot distance at frequencies from 0.3 to 1 mHz. We find the magnitude of charge-noise correlations, quantified by the magnitude square coherence C x y , are significantly suppressed from > 0.5 to < 0.1 as the interdot distance increases from 75 to 300 nm. Using an analytical model we confirm that, in contrast to superconducting qubits, the dominant source of correlated noise arises from low-frequency charge noise from the presence of two level fluctuators (TLFs) at the native silicon-silicon dioxide surface. Knowing this, we conclude with a timely discussion of charge-noise mitigation strategies.
Fast quantum oscillations of a charge qubit in a double quantum dot fabricated in a Si/SiGe heterostructure are demonstrated and characterized experimentally. The measured inhomogeneous dephasing time T2∗ ranges from 127 ps to 2.1 ns; it depends substantially on how the energy difference of the two qubit states varies with external voltages, consistent with a decoherence process that is dominated by detuning noise (charge noise that changes the asymmetry of the qubit's double-well potential). In the regime with the shortest T2∗, applying a charge-echo pulse sequence increases the measured inhomogeneous decoherence time from 127 to 760 ps, demonstrating that low-frequency noise processes are an important dephasing mechanism.
Abstract Electron spin qubits are a promising platform for quantum computation. Environmental noise impedes coherent operations by limiting the qubit relaxation (T1) and dephasing (Tϕ) times. There are multiple sources of such noise, which makes it important to devise experimental techniques that can detect the spatial locations of these sources and determine the type of source. In this paper, we propose that anisotropy in T1 and Tϕ with respect to the direction of the applied magnetic field can reveal much about these aspects of the noise. We investigate the anisotropy patterns of charge noise, evanescent-wave Johnson noise, and hyperfine noise in hypothetical devices. It is necessary to have a rather well-characterized sample to get the maximum benefit from this technique. The general anisotropy patterns are elucidated. We calculate the expected anisotropy for a particular model of a Si/SiGe quantum dot device.
The path to fault-tolerant quantum computing hinges on hardware that scales while remaining compatible with quantum error correction (QEC). Silicon spin qubits are a leading hardware candidate because they combine industrial fabrication compatibility with a nanoscale footprint that could accommodate millions of qubits on a chip. However, their suitability for QEC remains uncertain since spatially correlated noise naturally emerges from the resulting close proximity of qubits. These correlations increase the likelihood of simultaneous errors and erode the redundancy that QEC depends on. Here we quantify the spatial extent of noise correlations in a five-qubit silicon array and assess their impact on QEC. We identify two distinct sources of correlated noise: global magnetic field drifts that generate perfectly correlated fluctuations, and charge noise from two-level fluctuators that produces short-range correlations decaying within neighboring qubits. While magnetic drifts represent a critical correlated noise source that can compromise QEC, they can be mitigated. In contrast, the measured charge noise correlations are moderate, electrically tunable, and compatible with fault-tolerant operation with minimal qubit overhead. Our results establish quantitative benchmarks for correlated noise and clarify how such correlations impact the viability of quantum error correction in scalable qubit arrays.
A key ingredient for fault-tolerant quantum computers are sufficiently accurate logic gates on single and multiple qubits in the presence of decohering noise. In this thesis, we theoretically develop and experimentally demonstrate such high-fidelity quantum gates for semiconductor-based quantum computing. Specifically, we consider a qubit encoded in the singlet and one triplet state of two electron spins in GaAs. While its potential for optical coupling makes GaAs an attractive material, highly auto-correlated magnetic field noise from fluctuating nuclear spins leads to considerably lower coherence times than for Si-based devices, where nuclear spins can be removed by isotopic purification. In addition to noise, the control methods used in earlier experiments are based on unrealistic approximations. For these reasons, fidelities well above 99 %, as required by current quantum error correction (QEC) schemes, have not been obtained before this thesis. To tackle these issues, we extend the filter function formalism to describe quantum gates and processes in the presence of experimentally relevant non-Markovian noise. Since this formalism can consider all relevant noise sources in a computationally efficient manner, it can be used to find optimal control pulses by numerical optimization, leading to predicted single-qubit gate fidelities of 99.9 %. Furthermore, we deal with the considerable control challenges associated with this qubit type by experimental calibration of the optimized control pulses. To this end, we extend our previous experimental gate set calibration (GSC) routine to remove systematic gate errors on an arbitrary number of qubits. We apply the numerically optimized single-qubit control pulses to our GaAs sample and experimentally calibrate them with GSC. This procedure yields an average gate fidelity of 99.50 ± 0.04 % and a low leakage rate of 0.13 ± 0.03 % out of the computational subspace, characterized by randomized benchmarking. We also optimize realistic two-qubit control pulses, considering current control hardware as well as interqubit Coulomb and exchange coupling that cannot be fully turned off. Using measured noise spectra, we show that two-qubit gate fidelities of 99.90 % can be reached in GaAs, while 99.99 % can be achieved in Si. These results demonstrate that high-fidelity gates can be realized even in the presence of nuclear spins as in GaAs.