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arXiv:1510.08944

Quantum-Bath Decoherence of Hybrid Electron-Nuclear Spin Qubits

S. J. Balian

Published Oct 30, 2015• 0 citations
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Abstract

A major problem facing the realisation of scalable solid-state quantum computing is that of overcoming decoherence - the process whereby phase information encoded in a qubit is lost as the qubit interacts with its environment. Due to the vast number of environmental degrees of freedom, it is challenging to accurately calculate decoherence times $T_2$, especially when the qubit and environment are highly correlated. Hybrid or mixed electron-nuclear spin qubits, such as donors in silicon, possess 'optimal working points' (OWPs) which are sweet-spots for reduced decoherence in magnetic fields. Analysis of sharp variations of $T_2$ near OWPs was previously based on insensitivity to classical noise, even though hybrid qubits are situated in highly correlated quantum environments, such as the nuclear spin bath of $^{29}$Si impurities. This presented limited understanding of the decoherence mechanism and gave unreliable predictions for $T_2$. I present quantum many-body calculations of the qubit-bath dynamics, which (i) yield $T_2$ for hybrid qubits in excellent agreement with experiments in multiple regimes, (ii) elucidate the many-body nature of the nuclear spin bath and (iii) expose significant differences between quantum-bath and classical-field decoherence. To achieve these, the cluster correlation expansion was adapted to include electron-nuclear state mixing. In addition, an analysis supported by experiment was carried out to characterise the nuclear spin bath for a bismuth donor as the hybrid qubit, a simple analytical formula for $T_2$ was derived with predictions in agreement with experiment, and the established method of dynamical decoupling was combined with operating near OWPs in order to maximise $T_2$. Finally, the decoherence of a $^{29}$Si spin in proximity to the hybrid qubit was studied, in order to establish the feasibility for its use as a quantum register.

DOI
10.48550/arxiv.1510.08944

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A major problem facing the realisation of scalable solid-state quantum computing is that of overcoming decoherence - the process whereby phase information encoded in a qubit is lost as the qubit interacts with its environment. Due to the vast number of environmental degrees of freedom, it is challenging to accurately calculate decoherence times T2T_2T2​, especially when the qubit and environment are highly correlated. Hybrid or mixed electron-nuclear spin qubits, such as donors in silicon, possess 'optimal working points' (OWPs) which are sweet-spots for reduced decoherence in magnetic fields. Analysis of sharp variations of T2T_2T2​ near OWPs was previously based on insensitivity to classical noise, even though hybrid qubits are situated in highly correlated quantum environments, such as the nuclear spin bath of 29^{29}29Si impurities. This presented limited understanding of the decoherence mechanism and gave unreliable predictions for T2T_2T2​. I present quantum many-body calculations of the qubit-bath dynamics, which (i) yield T2T_2T2​ for hybrid qubits in excellent agreement with experiments in multiple regimes, (ii) elucidate the many-body nature of the nuclear spin bath and (iii) expose significant differences between quantum-bath and classical-field decoherence. To achieve these, the cluster correlation expansion was adapted to include electron-nuclear state mixing. In addition, an analysis supported by experiment was carried out to characterise the nuclear spin bath for a bismuth donor as the hybrid qubit, a simple analytical formula for T2T_2T2​ was derived with predictions in agreement with experiment, and the established method of dynamical decoupling was combined with operating near OWPs in order to maximise T2T_2T2​. Finally, the decoherence of a 29^{29}29Si spin in proximity to the hybrid qubit was studied, in order to establish the feasibility for its use as a quantum register.
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The dynamics of a nuclear spin bath generates magnetic noise that is a key contributor to the decoherence of electron spin qubits in electrostatically-defined quantum dots. In this paper, we extend the cluster correlation expansion (CCE) technique, which has proven useful for predicting solid-state qubit coherence times across various settings but is limited to shorter time scales, to incorporate stochastic treatments of cluster dynamics in order to efficiently predict slow drifting Overhauser fields over longer time scales. This approach combines quantum evolution with classical rate matrices to enable simulation across a wide range of temporal regimes required to simulate, for example, the long-time convergence of the ergodic T2∗T_2^*T2∗​ from Ramsey experiments. Our methodology is validated against experimental data from various silicon spin qubit systems, demonstrating a strong agreement between simulation and measurement of Ramsey experiments presented in the form of T2∗T_2^*T2∗​ versus averaging time, autocorrelation functions, as well as power spectral densities. Furthermore, we demonstrate significant back-action effects through modeling and experiment; specifically, the dynamics of the nuclear spin bath depends upon the electron spin occupation schedule. Finally, our modeling quantitatively predicts the benefits from compensating for the slow drift of Overhauser fields in qubit operations. Our findings indicate that compensating for an Overhauser rotation measured ΔtΔtΔt in the past results in an effective T2∗T_2^*T2∗​, which we denote T~2∗(Δt)\tilde{T}_2^*(Δt)T~2∗​(Δt) for clarity, under certain scenarios of interest, can be one or two orders of magnitude larger than the ergodic T2∗T_2^*T2∗​ if the Overhauser rotation is re-characterized every 100 milliseconds; that is, T~2∗(Δt=100 ms)\tilde{T}_2^*(Δt = 100~{\rm ms})T~2∗​(Δt=100 ms) can be 101010 to 100100100 times larger than T2∗T_2^*T2∗​.
Pulsed magnetic resonance allows the quantum state of electronic and nuclear spins to be controlled on the timescale of nanoseconds and microseconds respectively. The time required to flip dilute spins is orders of magnitude shorter than their coherence times, leading to several schemes for quantum information processing with spin qubits. Instead, we investigate 'hybrid nuclear-electronic' qubits consisting of near 50:50 superpositions of the electronic and nuclear spin states. Using bismuth-doped silicon, we demonstrate quantum control over these states in 32 ns, which is orders of magnitude faster than previous experiments using pure nuclear states. The coherence times of up to 4 ms are five orders of magnitude longer than the manipulation times, and are limited only by naturally occurring 29 Si nuclear spin impurities. We find a quantitative agreement between our experiments and an analytical theory for the resonance positions, as well as their relative intensities and Rabi oscillation frequencies. These results bring spins in a solid material a step closer to research on ion-trap qubits. © 2013 Macmillan Publishers Limited.
Donors in silicon, which combine an electron and nuclear spin, are some of the most promising candidates for quantum information. The electron spin has been proposed as a register with fast manipulation and the nuclear spin as a memory with long coherence times. However, this division reduces the complexity of the donor system, in particular behaviors emerging from their interaction. In natural silicon, there is also the presence of 29Si nuclear spins in the donor environment; though they are generally seen as a source of decoherence, they are quantum systems that can be investigated too. The main subject of this thesis is the study of the interactions between these various spins, using different methods to probe and control them. I first concentrate on the coupling between the donor and the 29Si spins. This coupling can be perturbed by the application of dynamical decoupling on the donor electron spin, whose evolution can be made sensitive to the number of 29Si spins interacting together. I then propose an error correction scheme using the donor and 29Si spins, showing key requirements such as coherence times and methods for manipulation and initialization. Secondly, I focus on the donor itself, in a regime where the hyperfine and Zeeman couplings compete with each other. Here, the spin transitions can have different sensitivities to the magnetic environment, and can even be suppressed to first order, resulting in coherence times up to seconds with electron spin-like manipulation times. Controlling this sensitivity was also used to probe the effect of the donor on the 29Si spin bath evolution. Finally, I use electric fields to modulate the hyperfine coupling within the donor. I first characterize the spins’ sensitivity to the electric field, and then demonstrate electrical switching of the nuclear spin response to an external magnetic excitation.
Decoherence of electron spins in nanoscale systems is important to quantum technologies such as quantum information processing and magnetometry. It is also an ideal model problem for studying the crossover between quantum and classical phenomena. At low temperatures or in light-element materials where the spin-orbit coupling is weak, the phonon scattering in nanostructures is less important and the fluctuations of nuclear spins become the dominant decoherence mechanism for electron spins. Since the 1950s, semi-classical noise theories have been developed for understanding electron spin decoherence. In spin-based solid-state quantum technologies, the relevant systems are in the nanometer scale and nuclear spin baths are quantum objects which require a quantum description. Recently, quantum pictures have been established to understand the decoherence and quantum many-body theories have been developed to quantitatively describe this phenomenon. Anomalous quantum effects have been predicted and some have been experimentally confirmed. A systematically truncated cluster-correlation expansion theory has been developed to account for the many-body correlations in nanoscale nuclear spin baths that are built up during electron spin decoherence. The theory has successfully predicted and explained a number of experimental results in a wide range of physical systems. In this review, we will cover this recent progress. The limitations of the present quantum many-body theories and possible directions for future development will also be discussed.
Spin-12\frac{1}{2}21​ 119^{119}119Sn nuclei in a silicon semiconductor could make excellent qubits. Nuclear spins in silicon are known to have long coherence times. Tin is isoelectronic with silicon, so we expect electrons can easily shuttle from one Sn atom to another to propagate quantum information via a hyperfine interaction that we predict, from all-electron linearized augmented plane wave density functional theory calculations, to be roughly ten times larger than intrinsic 29^{29}29Si. A hyperfine-induced electro-nuclear controlled-phase (e-n-CPhase) gate operation, generated (up to local rotations) by merely holding an electron at a sweet-spot of maximum hyperfine strength for a specific duration of time, is predicted to be exceptionally resilient to charge/voltage noise. Diabatic spin flips are suppressed with a modest magnetic field (>15 >15~>15 mT for <10−6<10^{-6}<10−6 flip probabilities) and nuclear spin bath noise may be avoided via isotopic enrichment or mitigated using dynamical decoupling or through monitoring and compensation. Combined with magnetic resonance control, this operation enables universal quantum computation.