All-electric qubit control in heavy hole quantum dots via non-Abelian geometric phases

Abstract

We demonstrate how non-Abelian geometric phases can be used to universally process a spin qubit in heavy hole quantum dots in the absence of magnetic fields. A time dependent electric quadrupole field is used to perform any desired single qubit operation by virtue of non-Abelian holonomy. During the proposed operations, the degeneracy of the time dependent two level system representing the qubit is not split. Since time reversal symmetry is preserved and hyperfine coupling is known to be weak in spin qubits based on heavy holes, we expect very long coherence times in the proposed setup.PACS numbers: 03.67. Lx,03.65.Vf,81.07.Ta Coherent spin control by all-electric means (without breaking time reversal symmetry (TRS)) is among the major goals of spintronics. One of the reasons why is that the presence of TRS is known to forbid several dephasing mechanisms, for example, in spin qubits [1], due to the interplay of electron phonon coupling and Rashba spin orbit coupling [2]. In the original work by Loss and DiVincenzo [1], the proposed scheme for universal quantum computing based on spin qubits in quantum dots (QDs) relied, on the one hand, on all-electric two qubit operations but, on the other hand, on single qubit operations based on magnetic fields or ferromagnetic auxiliary devices that both break TRS. A few years later, electric-dipole-induced spin resonance (EDSR) has been proposed [3] and experimentally realized [4] as a way to process spins electrically in presence of a static magnetic field which is still breaking TRS. Rather recently, it has been theoretically shown that in spin qubits based on carbon nanotube QDs it is indeed possible to accomplish allelectric single qubit operations using EDSR [5,6]. This is true because the specific spin orbit interaction in carbon nanotubes provides a way to split spin up and spin down states in the absence of magnetic fields. However, spin qubits based on carbon nanotubes face other problems and it is fair to say that all host materials for spin qubits have advantages and disadvantages.In this work, we are interested in spin qubits based on heavy hole (HH) QDs. We show how universal single qubit operations can be performed by all-electric means in the framework of holonomic quantum computing [7] in these systems. The adiabatic evolution in presence of a time dependent electric quadrupole field is employed to control the HH qubit (see Fig. 1 for a schematic). For our purposes, HH spin qubits (composed of J = 3 2 states) are the simplest two level system that can be manipulated in the desired way. However, HH spin qubits are, of course, a very active research area by itself beyond holonomic quantum computing. Two reasons why HH QDs are promising and interesting candidates for spin qubits FIG. 1. (Color online) Schematic of single particle (red ball) with a HH (pseudo)spin (yellow arrow) in a J = 3 2 valence band QD. The three-dimensional QD is surrounded by 18 gates that allow to generate an electrostatic potential with quadrupole symmetry in any direction in space. T...

Spin-Orbit-Mediated Manipulation of Heavy-Hole Spin Qubits in Gated Semiconductor Nanodevices

“…Not only long coherence times but also the possibility to initialize the hole spin state even without a magnetic field [25], and the recent realization of a coherent control of a hole spin state in single and double coupled quantum dots [32][33][34] has promoted the hole as a very good candidate as carrier of quantum bit information. There are also a few theoretical proposals how the HH spin state can be manipulated [35][36][37].In this paper we demonstrate by using a four band HH-LH model that the motion of the valence hole in gated semiconductor nanostructures can induce the rotation of the HH spin in the presence of the Dresselhaus spin-orbit interaction (DSOI). Supported by these results we present an efficient scheme which can be used to realize any rotation of the HH spin and propose a nanodevice which acts as a quantum logic NOT gate on a HH spin qubit.…”

“…Not only long coherence times but also the possibility to initialize the hole spin state even without a magnetic field [25], and the recent realization of a coherent control of a hole spin state in single and double coupled quantum dots [32][33][34] has promoted the hole as a very good candidate as carrier of quantum bit information. There are also a few theoretical proposals how the HH spin state can be manipulated [35][36][37].…”

Maximizing the purity of a qubit evolving in an anisotropic environment

“…45,46 In addition to optical coherent control of hole spins in self-assembled quantum dots, 39,41,47,48 there are several suggestions for electrical manipulation of hole spins. [49][50][51] Such electrical control has recently been demonstrated for hole spins in III-V nanowire quantum dots, 52 and coherence times have now been measured for hole spins in Ge-Si core-shell nanowire quantum dots. 53 The very recent achievement of the few-hole regime in lateral gated double-dot devices, 54 suggests that previous highly successful measurements performed for electron spins [55][56][57][58][59][60] can now be performed for hole spins, which show promise for much longer coherence times.…”

Symmetry-induced hole-spin mixing in quantum dot molecules

“…In recent years, heavy-hole spin qubits have emerged as a robust and long-lived alternative to electron spins, as they can be less sensitive to dephasing from nuclear spins [1][2][3][4][5][6][7][8][9]. Significant advances have been reported on hole spin initialization, control, and readout by means of optical excitations [2-4,10-13], and different proposals for electrical control have been put forward [14][15][16][17][18].…”

“…In recent years, heavy-hole spin qubits have emerged as a robust and long-lived alternative to electron spins, as they can be less sensitive to dephasing from nuclear spins [1][2][3][4][5][6][7][8][9]. Significant advances have been reported on hole spin initialization, control, and readout by means of optical excitations [2-4,10-13], and different proposals for electrical control have been put forward [14][15][16][17][18].Although most works so far have focused on QDs grown along [001], it has been noted that the C 2 point symmetry of such systems gives rise to a splitting of bright exciton states that limits the fidelity of optical hole spin preparation [12,19]. No such splitting is expected, however, in [111] grown QDs due to their higher (C 3 ) symmetry [20,21], which hence become an alternative worth exploring.…”