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arXiv:2103.05865 · npj Quantum Information

Anisotropy with respect to the applied magnetic field of spin qubit decoherence times

Yujun Choi, Robert Joynt

Published Jun 21, 2022• 8 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/s41534-022-00576-6

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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.
We present our study of decoherence in charge (spin) qubits due to evanescent-wave Johnson noise (EWJN) in a laterally coupled double quantum dot (single quantum dot). The high density of evanescent modes in the vicinity of metallic gates causes energy relaxation and a loss of phase coherence of electrons trapped in quantum dots. We derive expressions for the resultant energy relaxation rates of charge and spin qubits in a variety of dot geometries, and EWJN is shown to be a dominant source of decoherence for spin qubits held at low magnetic fields. Previous studies in this field approximated the charge or spin qubit as a point dipole. Ignoring the finite size of the quantum dot in this way leads to a spurious divergence in the relaxation rate as the qubit approaches the metal. Our approach goes beyond the dipole approximation and remedies this unphysical divergence by taking into account the finite size of the quantum dot. Additionally, we derive an enhancement of EWJN that occurs outside a thin metallic film, relative to the field surrounding a conducting half-space.
Abstract In many quantum computer architectures, the qubits are in close proximity to metallic device elements. The fluctuating currents in the metal give rise to noisy electromagnetic fields that leak out into the surrounding region. These fields are known as evanescent-wave Johnson noise. The noise can decohere the qubits. We review and update the general theory of this effect for charge qubits subject to electric noise and for spin and magnetic qubits subject to magnetic noise. A mapping of the quantum-mechanical problem onto a problem in classical electrodynamics simplifies the calculations. The focus is on relatively simple geometries in which analytical calculations can be done. Results are presented for the local noise spectral density in the vicinity of cylindrical conductors such as small antennae, noise from objects that can be treated as dipoles, and noise correlation functions for several geometries. We summarize the current state of the comparison of theory with experimental results on decoherence times of qubits. Emphasis is placed on qualitative understanding of the basic concepts and phenomena.
Abstract : A key step in the construction of quantum computing technologies is the identification and elimination of unwanted sources of noise and its resulting quantum decoherence. In solid state devices, one important source of noise is the fluctuating electric and magnetic fields that come from the device elements themselves. The ultimate source of these fluctuations is the random electric currents that are strongest in the metallic electrodes and leads. This random motion has both thermal and quantum components, though in most devices presently under investigation, the thermal part dominates. In the past, this important physical effect has generally been modeled by picturing the device using an equivalent RC circuit and applying the Nyquist theorem to this circuit. This approach has limitations, since it depends on global quantities, rather than on the detailed geometry and the local electromagnetic properties of the components. Our aim in this research project was to compute the effect from first principles. We considered the underlying physical law (quantum electrodynamics) governing the devices in question. Given the position- and frequency-dependent dielectric function, the electromagnetic noise spectrum can be calculated, and the decohering effect can be deduced. Semiconducting quantum dot and superconducting flux qubits were investigated.
In many quantum computer architectures, the qubits are in close proximity to metallic device elements. Metals have a high density of photon modes, and the fields spill out of the bulk metal because of the evanescent-wave component. Thus thermal and quantum electromagnetic Johnson-type noise from metallic device elements can decohere nearby qubits. In this Rapid Communication we use quantum electrodynamics to compute the strength of this evanescent-wave Johnson noise as a function of distance zzz from a metallic half space. Previous treatments have shown unphysical divergences at z=0z=0z=0. We remedy this by using a proper nonlocal dielectric function. Decoherence rates of local qubits are proportional to the magnitude of electric or magnetic correlation functions evaluated at the qubit position. We present formulas for the decoherence rates. These formulas serve as an important constraint on future device architectures. Comparison with single-electron spin relaxation measurements shows that evanescent-wave Johnson noise may constitute the dominant relaxation mechanism in experiments performed at low magnetic field.
Mobile spin qubit architectures promise flexible connectivity for efficient quantum error correction and relaxed device layout constraints, but their viability rests on preserving spin coherence during transport. While shuttling transforms spatial disorder into time-dependent noise, its net impact on spin coherence remains an open question. Here we demonstrate systematic noise mitigation during spin shuttling in a linear 28^{28}28Si/SiGe quantum dot device. First, by passively reducing magnetic field gradients, we minimize charge-noise coupling to the spin and double the spatially averaged dephasing time T2∗(xn)T_2^*(x_n)T2∗​(xn​) from 4.44.44.4 to 8.5 μs8.5\,μ\text{s}8.5μs. Next, we exploit motional narrowing by periodically shuttling the qubit, achieving a further enhancement in coherence time up to T2∗,sh=11.5 μsT_{2}^{*,sh} = 11.5\,μ\text{s}T2∗,sh​=11.5μs. Finally, we incorporate dynamical decoupling techniques while periodically shuttling over distances exceeding 200 nm200\,\text{nm}200nm, reaching T2H,sh=32 μsT_\text{2}^{H,sh}= 32\,μ\text{s}T2H,sh​=32μs. For the same setup, we demonstrate that dressed-state shuttling provides robust protection against low-frequency noise with a decay time TRsh=21 μsT_R^{\text{sh}} = 21\,μ\text{s}TRsh​=21μs, without the overhead of pulsed control and allowing protection during one-way spin transport. By preserving coherence over timescales exceeding typical gate and readout operations, the demonstrated strategies establish mobile spin qubits as a viable solution for scalable silicon quantum processors.
Direct phonon spin-lattice relaxation of an electron qubit bound by a donor impurity or quantum dot in SiGe heterostructures is investigated. The aim is to evaluate the importance of decoherence from this mechanism in several important solid-state quantum computer designs operating at low temperatures. We calculate the relaxation rate 1/T1{1/T}_{1}1/T1​ as a function of [100] uniaxial strain, temperature, magnetic field, and silicon/germanium content for Si:P bound electrons and quantum dots. The quantum dot potential is much smoother, leading to smaller splittings of the valley degeneracies. We have estimated these splittings in order to obtain upper bounds for the relaxation rate. In general, we find that the relaxation rate is strongly decreased by uniaxial compressive strain in a SiGe-Si-SiGe quantum well, making this strain an important positive design feature. Ge in high concentrations (particularly over 85%) increases the rate, making Si-rich materials preferable. We conclude that SiGe bound electron qubits must meet certain conditions to minimize decoherence but that spin-phonon relaxation does not rule out the solid-state implementation of error-tolerant quantum computing.