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Understanding and Suppressing Dephasing Noise in Semiconductor Qubits

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Understanding and Suppressing Dephasing Noise in Semiconductor Qubits Understanding and suppressing dephasing noise in semiconductor qubits Félix Beaudoin Department of Physics McGill University, Montréal July 2016 A thesis submitted to McGill University in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics ©2016 – Félix Beaudoin all rights reserved. Thesis advisor: Professor William A. Coish Félix Beaudoin Understanding and suppressing dephasing noise in semiconductor qubits Abstract Magnetic-field gradients and microwave resonators are promising tools to realize a scalable quantum-computing architecture with spin qubits. Indeed, magnetic-field gradients allow fast se- lective manipulation of distinct qubits through electric-dipole spin resonance and coherent coupling of spin qubits to a microwave resonator. On the other hand, microwave resonators are useful for quantum state transfer and two-qubit gates between distant qubits, and qubit readout. In this thesis, we take a theoretical approach to understand and suppress pure-dephasing mecha- nisms relevant to spin qubits in the presence of the above-mentioned devices, recently introduced to improve scalability. We first focus on dephasing of a spin qubit in the presence of a magnetic-field gradient. We predict that hyperfine coupling of the qubit to an environment of nuclear spins pre- cessing under the influence of a magnetic-field gradient leads to a new qubit dephasing mechanism. We show that in realistic conditions, this new mechanism can dominate over the usual dephasing processes occurring in the absence of a gradient. This result is relevant to spin qubits in GaAs or silicon quantum dots, or at single phosphorus donors in silicon. A magnetic-field gradient may also expose spin qubits to charge noise. We thus also study microscopic charge dephasing mechanisms coming from two-level fluctuators. These mechanisms α typically lead to qubit coherence decay of the form exp[−(t=T2) ]. Focusing on processes coupling charge fluctuators to electron or phonon baths, we find distinct dependencies of T2 and α on tem- perature depending on the nature of the fluctuator-bath interaction. These predictions may be useful for experimental identification of physical processes leading to charge dephasing of semicon- ductor qubits, and offer a new perspective to better understand the results of a recent experiment [Dial et al. Phys. Rev. Lett. 110:146804 (2013)]. Finally, we develop and assess a new protocol for quantum state transfer between a qubit and a resonator that has a high fidelity even in the presence of strong dephasing from low-frequency noise caused, e.g., by nuclear-spin or charge noise. In addition, upon a small modification of our state-transfer protocol, we obtain a method for fast quantum nondemolition readout of a qubit through the resonator output field. This new approach leads to a high-fidelity readout even when resonator damping is stronger than the qubit-resonator coupling. These two improved quantum operations (state transfer and readout) are particularly relevant for spin qubits coupled to microwave resonators, since spin-resonator coupling is typically weaker than qubit dephasing and resonator damping. i Thesis advisor: Professor William A. Coish Félix Beaudoin Understanding and suppressing dephasing noise in semiconductor qubits résumé Les gradients de champ magnétique et les résonateurs micro-ondes sont des outils prometteurs pour la réalisation d’une architecture extensible de calcul quantique fondée sur les qubits de spin. En effet, les gradients de champ magnétique permettent la manipulation rapide et sélective de qubits distincts grâce à la résonance dipolaire électrique de spin, ainsi que le couplage cohérent à un résonateur micro-ondes. Pour leur part, les résonateurs micro-ondes sont utiles pour réaliser des transferts d’états quantiques et des portes logiques entre qubits éloignés, ainsi que pour lire l’état quantique des qubits. Dans cette thèse, on entreprend une approche théorique pour comprendre et réduire le déphasage des qubits de spin en présence des outils mentionnés ci-dessus, favorables à l’extensibilité. On s’intéresse d’abord au déphasage d’un qubit de spin en présence d’un gradient de champ magnétique. On prédit que le couplage hyperfin du qubit à un environnement de spins nucléaires en précession sous l’effet du gradient mène à un nouveau mécanisme de déphasage. Dans des conditions réalistes, ce mécanisme peut dominer les processus de déphasage habituels qui surviennent sans le gradient. Ce résultat s’applique aux qubits de spin dans des boîtes quantiques en GaAs ou en silicium, ainsi qu’aux qubits de spin dans des donneurs uniques de phosphore dans le silicium. Un gradient de champ magnétique peut également exposer les qubits de spin au bruit de charge. On s’intéresse donc aux mécanismes microscopiques de déphasage de charge provenant de fluctua- teurs à deux niveaux. Ces mécanismes mènent typiquement à un amortissement de la cohérence du α qubit de la forme exp[−(t=T2) ]. En se concentrant sur les processus couplant les fluctuateurs de charge à des bains d’électrons ou de phonons, on trouve des dépendances en température pour T2 et α qui se distinguent selon la nature de l’interaction fluctuateur-bain. Ces prédictions pourraient être utiles à l’identification expérimentale des processus physiques menant au déphasage de charge dans les qubits semiconducteurs, et offrent une nouvelle perspective pour mieux comprendre les résultats d’une expérience récente [Dial et al. Phys. Rev. Lett. 110:146804 (2013)]. Enfin, on développe et on caractérise un protocole pour réaliser un transfert d’états quantiquesde haute fidélité entre un résonateur et un qubit même en présence d’un fort déphasage provenant de bruit à basse fréquence causé, par exemple, par des spins nucléaires ou du bruit de charge. Grâce à une légère modification du protocole de transfert d’états proposé, on obtient de surcroît une méthode de lecture rapide et non destructive d’un qubit à travers le champ sortant du résonateur auquel il est couplé. Cette approche mène à une lecture haute fidélité même lorsque l’amortissement du résonateur est plus fort que son couplage au qubit. Ces deux opérations quantiques améliorées (le transfert d’états et la lecture) conviennent particulièrement aux qubits de spin couplés à un résonateur micro-ondes, puisque les couplages spin-résonateur sont typiquement faibles par rapport au déphasage du qubit et à l’amortissement du résonateur. ii Statement of Originality The author declares that the following elements of this thesis constitute original scholarship and an advancement of knowledge: • The analytical expressions for the qubit coherence factor in the presence of hyperfine coupling to a nuclear-spin environment exposed to an inhomogeneous magnetic field. All the specific predictions resulting from these expressions for realistic devices (quantum dots in GaAs or silicon, phosphorus donors in silicon). • The expression for the critical longitudinal magnetic field above which the motional-averaging regime is reached, again due to the presence of an inhomogeneous magnetic field. The expression for the critical transverse magnetic-field gradient beyond which dephasing ofa spin qubit in a single quantum dot becomes Markovian. • The prediction that, for nuclear spins in an ideal narrowed state, a magnetic-field gradient can cause dephasing of a spin qubit in a GaAs or silicon quantum dot that is faster than dephasing due to the usual flip-flop and dipolar mechanisms. • The prediction that, in a realistic setting, a magnetic-field gradient can reduce the Hahn-echo dephasing time by almost an order of magnitude for a spin qubit in a GaAs double quantum dot. • The prediction of a Markovian regime for dephasing of a spin qubit in a silicon single quantum dot due to nuclear spins in an inhomogeneous magnetic field. The prediction of a breakdown of the Gaussian approximation for dephasing of a spin qubit at a single phosphorus donor impurity in silicon, again in the presence of a magnetic-field gradient. • The result that the coherence factor of a qubit undergoing charge dephasing due to Gaussian noise from two-level fluctuators approximately takes the form of a compressed exponential α exp[−(t=T2) ], and the evaluation of the error that follows from this approximation. The universal relation between α for Hahn echo and α for free-induction decay in the fast-noise regime. • The analytical temperature dependencies (in the slow-noise and fast-noise regimes) of T2 and α for charge dephasing of a qubit due to fluctuators whose switching dynamics is caused by any of the following mechanisms: direct tunneling and cotunneling with an electron reservoir, and direct, sum, and Raman phonon emission and absorption processes (through either piezoelectric or deformation coupling mechanisms). iii • The Hamiltonian-engineering protocol (named SQUADD in the manuscript) that leads to high-fidelity quantum state transfer between a qubit and a resonator even under strong dephasing due to inhomogeneous broadening. The exact and large-np analytical expressions for the fidelity of the state transfer as a function of the number of decoupling π pulses np (neglecting cavity damping). • The result that, under SQUADD, the dynamics of a state transfer between a resonator and × a collective mode of an ensemble of pN qubits is well approximated within a closed 4 4 subspace, up to corrections ∼ O(1= N). The analytical expression that follows for the fidelity of the state transfer. • The analytical expression for error
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