Maximizing the purity of a qubit evolving in an anisotropic environment

Wang, Xiaoya Judy; Chesi, Stefano; Coish, W. A.

doi:10.1103/physrevb.92.115424

Cited by 7 publications

(8 citation statements)

References 84 publications

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“…( 12) with the spin operators given in Eqs. ( 14), ( 15), (16). If the electronic state is well-described by an s-like band, the isotropic contact interaction dominates, giving the well-known result for an electron spin in a quantum dot, 6,7…”

Section: B Summary Of Key Resultsmentioning

confidence: 99%

“…[9][10][11][12][13] Because the hole hyperfine interaction is anisotropic, it may be possible to further reduce or eliminate the effects of the hole hyperfine coupling through motionalaveraging. 9, [14][15][16] An additional benefit of hole spins over electrons is a stronger spin-orbit coupling, leading to robust all-electric hole-spin manipulation. [17][18][19][20][21] This advantage afforded by a stronger spin-orbit coupling does not necessarily come at the cost of significantly shorter spin-relaxation (T 1 ) times in confined nanostructures.…”

Section: Introductionmentioning

confidence: 99%

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First-principles hyperfine tensors for electrons and holes in GaAs and silicon

2020

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Understanding (and controlling) hyperfine interactions in semiconductor nanostructures is important for fundamental studies of material properties as well as for quantum information processing with electron, hole, and nuclear-spin states. Through a combination of first-principles densityfunctional theory (DFT) and k · p theory, we have calculated hyperfine tensors for electrons and holes in GaAs and crystalline silicon. Accounting for relativistic effects near the nuclear core, we find contact hyperfine interactions for electrons in GaAs that are consistent with Knight-shift measurements performed on GaAs quantum wells and are roughly consistent with prior estimates extrapolated from measurements on InSb. We find that a combination of DFT and k · p theory (DFT+k · p) is necessary to accurately determine the contact hyperfine interaction for electrons at a conduction-band minimum in silicon that is consistent with bulk Knight-shift measurements. For hole spins in GaAs, the overall magnitude of the hyperfine couplings we find from DFT is consistent with previous theory based on free-atom properties, and with heavy-hole Overhauser shifts measured in GaAs (and InGaAs) quantum dots. In addition, we theoretically predict that the heavy-hole hyperfine coupling to the As nuclear spins is stronger and almost purely Ising, while the (weaker) coupling to the Ga nuclear spins has significant non-Ising corrections. In the case of hole spins in silicon, we find (surprisingly) that the strength of the hyperfine interaction in the valence band is comparable to that in the conduction band and that the hyperfine tensors are highly anisotropic (Ising) in the heavy-hole subspace. These results suggest that the hyperfine coupling cannot be ruled out as a limiting mechanism for coherence (T * 2 ) times recently measured for heavy holes in silicon quantum dots. arXiv:2001.05963v2 [cond-mat.mes-hall]

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Section: B Summary Of Key Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

First-principles hyperfine tensors for electrons and holes in GaAs and silicon

2020

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“…12 and 13). This effect is distinct from modulations arising from non-secular hyperfine couplings for heavy-hole spin qubits, 19,20 or from measurement feedback effects. 21 There are several issues that distinguish the case of HSEEM from the more conventional ESEEM.…”

Section: Introductionmentioning

confidence: 85%

Hole spin echo envelope modulations

et al. 2019

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Hole spins in semiconductor quantum dots or bound to acceptor impurities show promise as potential qubits, partly because of their weak and anisotropic hyperfine couplings to proximal nuclear spins. Since the hyperfine coupling is weak, it can be difficult to measure. However, an anisotropic hyperfine coupling can give rise to a substantial spin-echo envelope modulation that can be Fourieranalyzed to accurately reveal the hyperfine tensor. Here, we give a general theoretical analysis for hole-spin-echo envelope modulation (HSEEM), and apply this analysis to the specific case of a boron-acceptor hole spin in silicon. For boron acceptor spins in unstrained silicon, both the hyperfine and Zeeman Hamiltonians are approximately isotropic leading to negligible envelope modulations. In contrast, in strained silicon, where light-hole spin qubits can be energetically isolated, we find the hyperfine Hamiltonian and g-tensor are sufficiently anisotropic to give spin-echo-envelope modulations. We show that there is an optimal magnetic-field orientation that maximizes the visibility of envelope modulations in this case. Based on microscopic estimates of the hyperfine coupling, we find that the maximum modulation depth can be substantial, reaching ∼ 10%, at a moderate laboratory magnetic field, B 200 mT. arXiv:1906.11953v2 [cond-mat.mes-hall]

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“…For alternative approaches to describing general types of classical noise, see Refs. [17][18][19][20].In developing our extension of the filter function formalism, we focus on the context of FID experiments with ST qubits in order to keep the discussion concrete, although the approach we develop has broad applicability and can be easily adapted to other systems or to include external control pulses. ST qubits [10,[21][22][23][24][25] are defined to live in the S z = 0 subspace of the two-spin Hilbert space of two separated electrons residing in a double quantum dot.…”

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confidence: 99%

“…For alternative approaches to describing general types of classical noise, see Refs. [17][18][19][20].…”

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confidence: 99%

Filter function formalism beyond pure dephasing and non-Markovian noise in singlet-triplet qubits

et al. 2016

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The filter function formalism quantitatively describes the dephasing of a qubit by a bath that causes Gaussian fluctuations in the qubit energies with an arbitrary noise power spectrum. Here, we extend this formalism to account for more general types of noise that couple to the qubit through terms that do not commute with the qubit's bare Hamiltonian. Our approach applies to any power spectrum that generates slow noise fluctuations in the qubit's evolution. We demonstrate our formalism in the case of singlet-triplet qubits subject to both quasistatic nuclear noise and 1/ω α charge noise and find good agreement with recent experimental findings. This comparison shows the efficacy of our approach in describing real systems and additionally highlights the challenges with distinguishing different types of noise in free induction decay experiments.Decoherence presents an important challenge for quantum-based technologies and is particularly relevant for solid state nanoscale devices. A crucial step in overcoming this challenge is to understand how various noise sources affect a qubit's evolution. It is often the case that noise caused by e.g., nuclear spin or charge fluctuations in quantum dots, or flux noise in superconducting circuits, can be well described by a classical Gaussian ensemble characterized by an appropriate power spectrum [1][2][3]. In the case of pure dephasing where the noise creates fluctuations in the qubit energy levels, considerable progress has been made in understanding how the qubit responds to a given noise spectrum [4][5][6][7]. However, it is often the case that noise induces not only energy fluctuations but also rotations between the qubit states. A quantitative theory of how the qubit evolves in the presence of this more general type of decoherence could be used to better understand noise sources and develop new approaches to dynamical decoupling [8][9][10][11] and dynamically corrected gates [12][13][14][15].In this work, we take an important step toward addressing this problem by extending the filter function approach to treat more general types of decoherence beyond the case of pure dephasing. Our approach utilizes the fact that environmental noise fluctuations are often slow compared to qubit dynamics, enabling us to solve for the qubit evolution analytically using the adiabatic theorem. Finding an analytical solution is crucial as it allows us to average these fluctuations with respect to any noise power spectrum by performing a Gaussian path integral. Consistency with the adiabatic approximation imposes constraints on the types of power spectra that may be treated in this way, which we derive below. We demonstrate our theory in the context of free induction decay (FID) in singlet-triplet (ST) qubits and obtain an analytical formula for the singlet return probability in the presence of both nuclear spin and charge noise. We compare our results with recent experiments reported in Ref. [16], finding excellent agreement. In addition, we show that a purely static noise model is also con...

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Maximizing the purity of a qubit evolving in an anisotropic environment

Cited by 7 publications

References 84 publications

First-principles hyperfine tensors for electrons and holes in GaAs and silicon

First-principles hyperfine tensors for electrons and holes in GaAs and silicon

Hole spin echo envelope modulations

Filter function formalism beyond pure dephasing and non-Markovian noise in singlet-triplet qubits

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