Error rate of a charge qubit coupled to an acoustic phonon reservoir

Abstract

We analyze decoherence of an electron in a double-dot due to the interaction with acoustic phonons. For large tunneling rates between the quantum dots, the main contribution to decoherence comes from the phonon emission relaxation processes, while for small tunneling rates, the virtual-phonon, dephasing processes dominate. Our results show that in common semiconductors, such as Si and GaAs, the latter mechanism determines the upper limit for the double-dot charge qubit performance measure.PACS numbers: 03.67. Lx, 85.35.Be, 73.20.Hb Recently, there has been a lot of interest in implementation of quantum logic gates by manipulating two-level electron systems in semiconductor quantum dots (artificial atoms) [1]. Several designs for solid state quantum information processing have been suggested [2,3,4]. Quantum-dot architecture of a quantum computer is very attractive because it is possibly scalable and the most compatible with the recent microelectronics technology. However, it is a great challenge to maintain a satisfactory level of coherence of an electron in semiconductor to perform even elementary quantum gates [5]. Hopefully, coherence can be enhanced by encoding of the logical qubit states into a subspace of the electron states in a large quantum dot array (artificial crystal) [6]. It is also noted that in a gate-engineered structure of two coupled identical quantum dots one can control decoherence rates by several orders of magnitude [3]. Recent advances in technology of fabrication of double-dot [7,8] and doubledonor [4] qubits have been reported. Coherent oscillations in double-dot qubit are observed [9]. It have been demonstrated that scattering by phonons can significantly influence electron transport through double-dot system [10] and qubit dynamics during measurement [11].In this work, we analyze decoherence of an electron in a double-dot potential due to acoustic phonons during one qubit gate cycle.We consider a single electron in the double well potential shown schematically in Fig. 1. Such a structure can be fabricated as two gate-engineered quantum dots [7,8,9], whose geometry is determined by the pattern of external metallic gates and electric potential at them, or by the coupling the two nearby phosphorus donors embedded in silicon [4]. The resulting qubit is supposed to evolve in the basis spanned by the states |0 and |1 which describe the electron localized around the left and right minima of the potential, respectively. We assume that the parameters of the double-dot qubit structure are selected appropriately and the temperature is low enough such that the effects of the electron transitions to the higher energy levels can be neglected. Inves- tigation of decoherence due to acoustic phonons is the primary goal of our work. Below, we will present the model and describe the two main mechanisms of decoherence. We will introduce the appropriate approximations schemes, quantify the overall error rate and discuss the ways to minimize it.The Hamiltonian of the electron and the phonon bath isHere q...

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

“…(see for example Refs. [31,32,33]). However, essentially, the decoherence of an open quantum system is reflected through the decays of the off-diagonal coherent terms of its reduced density matrix [34].…”

Orbital and spin relaxation in single and coupled quantum dots

“…[4][5][6] On the other hand, at higher fields ͑Teslas͒ the relaxation is due to phonon-induced spin-flip transitions. [7][8][9][10][11][12][13][14][15][16][17][18][19] These are allowed due to the presence of spin-orbit coupling. Variants of the phonon-induced spin relaxation has been proposed, such as ripple coupling, 20,21 important in very small quantum dots ͑10 nm͒, or fluctuations in spin-orbit parameters, important when underlying heterostructure inhomogeneities 22 are present.…”

Non-Markovian dynamics and phonon decoherence of a double quantum dot charge qubit

“…As in Refs. [11,12] in this paper we set the sound velocity in the GaAs crystal s ≈ 5 × 10 3 m/s. With the parameters of GaAs in Ref.…”

“…This kind of processing introduces an new approximation which has not been estimated to the affects of the dynamics. Fedichkin et al [12,13] studied the error rate of DQD charge qubit with short-time approximation. This method is accurate enough in adequate short time.…”