Intrinsic phonon decoherence and quantum gates in coupled lateral quantum-dot charge qubits

Abstract

Recent experiments by Hayashi et al. [Phys. Rev. Lett. 91, 226804 (2003)] demonstrate coherent oscillations of a charge quantum bit (qubit) in laterally defined quantum dots. We study the intrinsic electron-phonon decoherence and gate performance for the next step: a system of two coupled charge qubits. The effective decoherence model contains properties of local as well as collective decoherence. Decoherence channels can be classified by their multipole moments, which leads to different lowenergy spectra. It is shown that due to the super-Ohmic spectrum, the gate quality is limited by the single-qubit Hadamard gates. It can be significantly improved, by using double-dots with weak tunnel coupling.

Decoherence and relaxation of a qubit coupled to an Ohmic bath directly and via an intermediate harmonic oscillator

“…We can not obtain general results on the decoherence and relaxation from some special initial states. Essentially, this limitation is inevitable, because in order to obtain measures of the decoherence and relaxation one should perform the calculations over all possible initial states in general [30,31]. But, we may figure out some information on the trend of the decoherence and relaxation of the qubit from some special results.…”

“…When the bath modes have lower frequencies than Ω 0 , the dynamics of the qubit in the bath with effective spectral density J ef f (ω) is similar to the dynamics of the qubit in Ohmic bath with spectral density J ohm (ω), which is widely investigated in recent years [24,25,26,27,28,29,30]. In this paper we investigate another limited case, namely, the bath modes have higher frequencies than the oscillation frequency Ω 0 of IHO.…”

Improving the Purity of One‐ and Two‐qubit Gates

“…This coupling of each qubit to an individual bath represents a proper model for sufficiently distant qubits [29]. Within the present work, we consider the so-called ohmic spectral density (4) with the dimensionless coupling strength α and the cutoff frequency ω c .…”

“…This relates to the interpretation that the first term of the master equation is responsible for the coherent dynamics, while the second and third term correspond to decoherence and relaxation, respectively. The average over all pure states, which underlies the rate (10), may differ from the average over a discrete set of initial states by a factor of the order unity, due to the particular choice of a discrete ensemble: There, one commonly chooses ensembles which are unsymmetric on the Bloch sphere [27,28] or which do not include entangled states [27][28][29].…”

“…Several proposals to overcome the ensuing decoherence have been put forward, such as the use of decoherence free subspaces [8][9][10][11][12], coherence-preserving qubits [13], quantum Zeno subspaces [14], optimized pulse sequences [15,16], dynamical decoupling [17][18][19][20][21], and coherent destruction of tunneling [22,23]. Theoretical studies of decoherence of two-level systems have been extended to gate operations in the presence of an environment in [24][25][26][27][28][29].…”