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arXiv:1503.08673 · Physical review. B./Physical review. B

Open quantum system description of singlet-triplet qubits in quantum dots

L. K. Castelano, F. F. Fanchini, K. Berrada

Published Dec 23, 2016• 38 citations
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Abstract

We develop a theoretical model to describe the dissipative dynamics of singlet-triplet qubits in GaAs quantum dots. Using the concurrence experimentally obtained [Shulman et al., Science 336, 202 (2012)] as a guide, we assume that each logical qubit fluctuates under the action of a random telegraph noise (RTN) that simulates the $1/{f}^{\ensuremath{\alpha}}$ noise. We also study the dynamics of concurrence as a function of the amplitude of the RTN, the correlation time of the RTN, the preparation time of states, and the two-qubit coupling. Furthermore, we show that the two-qubit coupling together with the preparation time strongly affect the entanglement dissipative dynamics and both physical quantities can be employed to enhance the entanglement between singlet-triplet qubits.

DOI
10.1103/physrevb.94.235433

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We develop a theoretical model to describe the dissipative dynamics of singlet-triplet qubits in GaAs quantum dots. Using the concurrence experimentally obtained [Shulman et al., Science 336, 202 (2012)] as a guide, we assume that each logical qubit fluctuates under the action of a random telegraph noise (RTN) that simulates the 1/f\ensuremathα1/{f}^{\ensuremath{\alpha}}1/f\ensuremathα noise. We also study the dynamics of concurrence as a function of the amplitude of the RTN, the correlation time of the RTN, the preparation time of states, and the two-qubit coupling. Furthermore, we show that the two-qubit coupling together with the preparation time strongly affect the entanglement dissipative dynamics and both physical quantities can be employed to enhance the entanglement between singlet-triplet qubits.
Abstract We analyze in detail a procedure of entangling of two singlet–triplet (S– T0T_{0}T0​ T 0 ) qubits operated in a regime when energy associated with the magnetic field gradient, ΔBz\Delta B_{z}ΔBz​ Δ B z , is an order of magnitude smaller than the exchange energy, J, between singlet and triplet states (Shulman et al. in Science 336:202, 2012). We have studied theoretically a single S– T0T_{0}T0​ T 0 qubit in free induction decay and spin echo experiments. We have obtained analytical expressions for the time dependence of components of its Bloch vector for quasistatic fluctuations of ΔBz\Delta B_{z}ΔBz​ Δ B z and quasistatic or dynamical 1/fβ1/f^{\beta }1/fβ 1 / f β -type fluctuations of J. We have then considered the impact of fluctuations of these parameters on the efficiency of the entangling procedure which uses an Ising-type coupling between two S– T0T_{0}T0​ T 0 qubits. In particular, we have obtained an analytical expression for evolution of two qubits affected by 1/fβ1/f^{\beta }1/fβ 1 / f β -type fluctuations of J. This expression indicates the maximal level of entanglement that can be generated by performing the entangling procedure. Our results deliver also an evidence that in the above-mentioned experiment S– T0T_{0}T0​ T 0 qubits were affected by uncorrelated 1/fβ1/f^{\beta }1/fβ 1 / f β charge noises.
Entangled qubit pairs can serve as a quantum memory or as a resource for quantum communication. The utility of such pairs is measured by how long they take to disentangle or decohere. To answer the question of whether qubit-qubit interactions can prolong entanglement, we calculate the dissipative dynamics of a pair of qubits coupled via the exchange interaction in the presence of random telegraph noise and 1/f1/f1/f noise. We show that for maximally entangled (Bell) states, the exchange interaction generally suppresses decoherence and disentanglement. This suppression is more apparent for random telegraph noise if the noise is non-Markovian, whereas for 1/f1/f1/f noise the exchange interaction should be comparable in magnitude to the strongest noise source. The entangled singlet-triplet superposition state of two qubits (${\ensuremath{\psi}}_{\ifmmode\pm\else\textpm\fi{}}$ Bell state) can be protected by the interaction, while for the triplet-triplet state (${\ensuremath{\phi}}_{\ifmmode\pm\else\textpm\fi{}}$ Bell state), it is less effective. Thus the former is more suitable for encoding quantum information.
We analyze theoretically the decoherence of two interacting electrons in a double self-assembled quantum dot due to a random telegraph noise. For this purpose we have examined the pure dephasing rate by evaluating the decoherence factor. The latter has been shown to be different from that calculated within the Gaussian approximation in the strong coupling regime. In order to determine the influence of the random telegraph noise on the entanglement of the system states, the concurrence, the populations, and the entropy are evaluated as well. Our results show that telegraph noise can severely impact the coherence of charge qubits.
In the present paper, the joint effects of two kinds of classical environmental noises, without direct interaction among each other, on the dynamics of quantum correlations (QCs) of a three-qubit system coupled in independent environments is investigated. More precisely, we join the random telegraph noise (RTN) and the static noise (SN) and focus on the dynamics of entanglement and quantum discord (QD) when the qubits are initially prepared in the GHZ- and W-type states. The overall noise affecting the qubits is obtained by combining the RTN and SN in two different setups. The results show that the disorder of the environmental noise as well as its memory qualities and the purity of the initial state considered play a crucial role in the time evolution of the system in such a way that the dynamics of QCs can be controlled by varying them. In fact, we show that, depending on the initial state and noise regime considered, the rate of collapse of QCs may either decrease or increase with the increase of the degree of disorder of the SN, the switching rate of the RTN and the purity of the initial state.
Electron spins confined in semiconductor quantum dots are emerging as a promising system to study quantum information science and to perform sensitive metrology. Their weak interaction with the environment leads to long coherence times and robust storage for quantum information, and the intrinsic tunability of semiconductors allows for controllable operations, initialization, and readout of their quantum state. These spin qubits are also promising candidates for the building block for a scalable quantum information processor due to their prospects for scalability and miniaturization. owever, several obstacles limit the performance of quantum information experiments in these systems. For example, the weak coupling to the environment makes inter-qubit operations challenging, and a fluctuating nuclear magnetic field limits the performance of single-qubit operations.\n\n\n\nThe focus of this thesis will be several experiments which address some of the outstanding problems in semiconductor spin qubits, in particular, singlet-triplet (S-T0) qubits. We use these qubits to probe both the electric field and magnetic field noise that limit the performance of these qubits. The magnetic noise bath is probed with high bandwidth and precision using novel techniques borrowed from the field of Hamiltonian learning, which are effective due to the rapid control and readout available in S-T0 qubits. These findings allow us to effectively undo the undesired effects of the fluctuating nuclear magnetic field by tracking them in real-time, and we demonstrate a 30-fold improvement in the coherence time T2*.\n\n\n\nWe probe the voltage noise environment of the qubit using coherent qubit oscillations, which is partially enabled by control of the nuclear magnetic field. We find that the voltage noise bath is frequency- dependent, even at frequencies as high as 1MHz, and it shows surprising and, as of yet, unexplained temperature dependence. We leverage this knowledge of the voltage noise environment, the nuclear magnetic field control, as well as new techniques for calibrated measurement of the density matrix in a singlet-triplet qubit to entangle two adjacent single-triplet qubits. We fully characterize the generated entangled states and prove that they are, indeed, entangled.\n\n\n\nThis work opens new opportunities to use qubits as sensors for improved metrological capabilities, as well as for improved quantum information processing. The singlet-triplet qubit is unique in that it can be used to probe two fundamentally different noise baths, which are important for a large variety of solid state qubits. More specifically, this work establishes the singlet-triplet qubit as a viable candidate for the building block of a scalable quantum information processor.