Exact solution for the dynamical decoupling of a qubit with telegraph noise

Bergli, Joakim; Faoro, Lara

doi:10.1103/physrevb.75.054515

Cited by 42 publications

(72 citation statements)

References 41 publications

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“…33 Here we reproduce these results using a simple procedure described below and extend them to treat the more commonly used CarrPurcell-Meiboom-Gill (CPMG) protocol and an asymmetric TLF with different switching rates between its states in each direction (γ + = γ − ). Working at low temperatures as compared with the TLF level splitting results in longer stays in the lower state.…”

Section: A Single Fluctuatormentioning

confidence: 91%

“…Previous works studied the weak and strong coupling limits of a single TLF at the OP, 33 and at a general working position. 32 In this section we extend these studies to treat any number of TLFs.…”

Section: General Working Pointmentioning

confidence: 99%

“…The signal decay is calculated by dividing the probability distribution to partial probabilities, p(φ, t) = p + (φ, t) + p − (φ, t), to accumulate phase φ while the TLF is in the up or down state: 33,45 χ(t) = dφp(φ, t)e iφ .…”

Section: A Single Fluctuatormentioning

confidence: 99%

“…23 Although the efficacy of control pulses in mitigating charge noise in the pure dephasing regime is indifferent to their axis within the x − y plane, π y pulses, used here, were shown to be more effective when operating at a general position. 32,33 In addition, π y pulses should be equally effective in correcting nuclear-induced noise, as compared with the traditionally employed π z pulses. We note that our theory can be applied straightforwardly to analyze any sequence of composite pulses, such as the XY − 4 self-correcting protocol that has been suggested to be more robust against pulse errors.…”

Section: Introductionmentioning

confidence: 99%

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Non-Gaussian signatures and collective effects in charge noise affecting a dynamically decoupled qubit

Ramon

2015

Phys. Rev. B

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The effects of a collection of classical two-level charge fluctuators on the coherence of a dynamicallydecoupled qubit are studied. Distinct dynamics are found at different qubit working positions. Exact analytical formulae are derived at pure dephasing and approximate solutions are found at the general working position, for weakly-and strongly-coupled fluctuators. Analysis of these solutions, combined with numerical simulations of the multiple random telegraph processes, reveal the scaling of the noise with the number of fluctuators and the number of control pulses, as well as dependence on other parameters of the qubit-fluctuators system. These results can be used to determine potential microscopic models for the charge environment by performing noise spectroscopy.

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Section: A Single Fluctuatormentioning

confidence: 91%

Section: General Working Pointmentioning

confidence: 99%

Section: A Single Fluctuatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Non-Gaussian signatures and collective effects in charge noise affecting a dynamically decoupled qubit

Ramon

2015

Phys. Rev. B

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“…As pointed out in Ref. 86 for the analogous problem of a Josephson charge qubit coupled to two-level fluctuators, this result actually holds to all orders in a Magnus expansion. Of course, pure dephasing due to exchange fluctuations would lead to a finite decay even in this case.…”

Section: Two-axis Dynamical Decouplingmentioning

confidence: 52%

Maximizing the purity of a qubit evolving in an anisotropic environment

2015

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We provide a general method to calculate and maximize the purity of a qubit interacting with an anisotropic non-Markovian environment. Counter to intuition, we find that the purity is often maximized by preparing and storing the qubit in a superposition of non-interacting eigenstates. For a model relevant to decoherence of a heavy-hole spin qubit in a quantum dot or for a singlettriplet qubit for two electrons in a double quantum dot, we show that preparation of the qubit in its non-interacting ground state can actually be the worst choice to maximize purity. We further give analytical results for spin-echo envelope modulations of arbitrary spin components of a hole spin in a quantum dot, going beyond a standard secular approximation. We account for general dynamics in the presence of a pure-dephasing process and identify a crossover timescale at which it is again advantageous to initialize the qubit in the non-interacting ground state. Finally, we consider a general two-axis dynamical decoupling sequence and determine initial conditions that maximize purity, minimizing leakage to the environment.

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