Noise analysis of qubits implemented in triple quantum dot systems in a Davies master equation approach

Abstract

We analyze the influence of noise for qubits implemented using a triple quantum dot spin system. We give a detailed description of the physical realization and develop error models for the dominant external noise sources. We use a Davies master equation approach to describe their influence on the qubit. The triple dot system contains two meaningful realizations of a qubit: We consider a subspace and a subsystem of the full Hilbert space to implement the qubit. The main goal of this paper is to test if one of these implementations is favorable when the qubit interacts with realistic environments. When performing the noise analysis, we extract the initial time evolution of the qubit using a Nakajima-Zwanzig approach. We find that the initial time evolution, which is essential for qubit applications, decouples from the long time dynamics of the system. We extract probabilities for the qubit errors of dephasing, relaxation, and leakage. Using the Davies model to describe the environment simplifies the noise analysis. It allows us to construct simple toy models, which closely describe the error probabilities.

Three-electron spin qubits

“…The corresponding spin Hilbert space H 3spin = H 3/2 ⊕ H 1/2 ⊕ H 1/2 can be divided into a quadruplet H 3/2 with effective spin-3/2 and two degenerate doublets H 1/2 which combined with different orbits and restricted to the total spin S = 1/2 subspace gives rise to a two-fold degenerate subspace H +1/2 ⊕ H -1/2 . This subspace is effectively decoupled from the S = 3/2 subspace considering weak magnetic field gradients [22] and weak spin orbit interaction [21]. Leakage into the S = 3/2 and S z = ±1/2 states is suppressed by exchange [22].…”

“…Since the doubly occupied states |2 , |3 , |4 , and |5 are obtained from |0 and |1 via the motion of a single electron and the states |6 and |7 require the motion of two electrons, the latter two states are neglected in most studies. [9,10,21,23,19,15,3] The resulting matrix representation of the Hamiltonian Eq. (1) in this basis up to a global energy shift, is [3]…”

“…The price to pay for this improvement is an increase in gate complexity. We also take into account the decoherence of the qubit through the influence of magnetic noise [20,21,22], in particular dephasing due to the presence of nuclear spins, as well as dephasing due to charge noise [9,10,23,19,15], fluctuations of the energy levels on each dot due to noisy gate voltages or the environment. Several techniques are discussed which partly decouple the qubit from magnetic noise [24,12,25] while for charge noise it is shown that it is favorable to operate the qubit on the so-called "sweet spots" [10,19] or better "double sweet spots" [23,19,15], which are least susceptible to noise, thus providing a longer lifetime of the qubit.…”

Readout and dynamics of a qubit built on three quantum dots

“…In GaAs/AlGaAs quantum dots the exchange interaction J is estimated in the range 0.02 ÷ 0.3 meV [31,32] and in a molecular magnet as 0.43 meV [21]. The doublet splitting for a linear TQD is the order ∆ ∼ 0.1µ ÷ 1 µeV [16,33]. This parameter can be even larger ∆ ∼ 21.6 µeV in Si/SiGe quantum dots [34].…”

Characterizing gate operations near the sweet spot of an exchange-only qubit

“…15, we provided a detailed account of magnetic noise from the Overhauser fields of nuclear spins on the decoherence of an exchange-only qubit. Here, we simulate realistic gate operations including quasistatic random Overhauser fields 20 and charge noise. 14 In certain regimes we find that the main limit on the gate fidelities arises from the Overhauser fields, as consistent with experimental observations.…”