Classical nature of nuclear spin noise near clock transitions of Bi donors in silicon

Abstract

Whether a quantum bath can be approximated as classical Gaussian noise is a fundamental issue in central spin decoherence and also of practical importance in designing noise-resilient quantum control. Spin qubits based on bismuth donors in silicon have tunable interactions with nuclear spin baths and are first-order insensitive to magnetic noise at so-called clock transitions (CTs). This system is therefore ideal for studying the quantum/classical Gaussian nature of nuclear spin baths since the qubit-bath interaction strength determines the back-action on the baths and hence the adequacy of a Gaussian noise model. We develop a Gaussian noise model with noise correlations determined by quantum calculations and compare the classical noise approximation to the full quantum bath theory. We experimentally test our model through a dynamical decoupling sequence of up to 128 pulses, finding good agreement with simulations and measuring electron spin coherence times approaching 1 s-notably using natural silicon. Our theoretical and experimental study demonstrates that the noise from a nuclear spin bath is analogous to classical Gaussian noise if the back-action of the qubit on the bath is small compared to the internal bath dynamics, as is the case close to CTs. However, far from the CTs, the back-action of the central spin on the bath is such that the quantum model is required to accurately model spin decoherence. Introduction. Central spin decoherence due to coupling to the environment is not only a central issue in understanding quantum-to-classical transitions [1,2], but also one of the key challenges in the realization of quantum computation [3]. There are two distinct models to describe the decoherence processes in such cases: in the semiclassical model, the central spin accumulates random phases due to thermal or quantum fluctuations of the environment [4,5], while in the quantum model, the coupling between the central spin and the environment produces entanglement and results in leakage of the which-way information from the central spin to the environment [6][7][8][9]. The fundamental difference between these two models lies in the fact that the classical noise is independent of the central spin state while the quantum noise is governed by the difference of environmental Hamiltonians conditioned on the qubit state, called the back-action from the central spin [10,11].The classical noise model of quantum baths, especially the Gaussian stochastic noise model, is a useful approximation in designing noise-resilient quantum control [12], which would otherwise require a large amount of numerical simulations of many-body dynamics of quantum baths. Dynamical decoupling has been employed to extract the noise spectra of baths [13][14][15][16][17], which are in turn used to design optimal quantum control for protecting quantum coherence and quantum gates. The viability of such methods critically

29Si nuclear spins as a resource for donor spin qubits in silicon

“…These could be harnessed to perform, for example, a three-qubit QEC protocol using the donor nuclear spin and one strongly coupled 29 Si as ancillae, and one weakly coupled 29 Si for the data qubit. Combined with recent measurements which show that bismuth donor electron spin coherence times can reach a second in natural silicon [48], these results indicate that isotopically enriched 28 Si may not be a panacea for silicon-based qubits, and the more abundant and easily accessible variant may bring benefits for some applications. Although more technically complex, there may also be merits in incorporating 29 Si in the vicinity of the donor (e.g.…”

Decoherence of two entangled spin qubits coupled to an interacting sparse nuclear spin bath: Application to nitrogen vacancy centers

“…When the influence that each of these systems exerts on the qubit is weak, and when there are many systems exerting similar influence, it is clear that the net effect that the environment has on the qubit is then equivalent to that of classical Gaussian noise. However, if there is a certain number of nuclear clusters strongly coupled to the qubits that need to be considered to correctly describe the time dependence of qubits' coherence, the classical Gaussian noise picture breaks down [29][30][31].…”

Noise representations of open system dynamics

“…A commonly entertained hypothesis (e.g., see Refs. 20,22,25,26 ) proposes that for the stochastic modeling of system-environment interaction to work, the coupling between S and E has to cause no back-action. The absence of back-action is understood here as the asymmetry between the system and the environment where E influences S but S does not influence E.…”