Circuit QED with hole-spin qubits in Ge/Si nanowire quantum dots

Abstract

We propose a setup for universal and electrically controlled quantum information processing with hole spins in Ge/Si core/shell nanowire quantum dots (NW QDs). Single-qubit gates can be driven through electric-dipoleinduced spin resonance, with spin-flip times shorter than 100 ps. Long-distance qubit-qubit coupling can be mediated by the cavity electric field of a superconducting transmission line resonator, where we show that operation times below 20 ns seem feasible for the entangling √ iSWAP gate. The absence of Dresselhaus spinorbit interaction (SOI) and the presence of an unusually strong Rashba-type SOI enable precise control over the transverse qubit coupling via an externally applied, perpendicular electric field. The latter serves as an on-off switch for quantum gates and also provides control over the g factor, so single-and two-qubit gates can be operated independently. Remarkably, we find that idle qubits are insensitive to charge noise and phonons, and we discuss strategies for enhancing noise-limited gate fidelities. PACS numbers: 73.21.Hb, 73.21.La, 42.50.Pq, 03.67.Lx In the past decade, the idea of processing quantum information with spins in quantum dots (QDs) [1] was followed by remarkable progress [2]. While the workhorse systems are highly advanced, such as self-assembled (In)GaAs QDs [3-10] and negatively charged, lateral GaAs QDs [11][12][13][14][15][16][17], an emerging theme is the search for systems that allow further optimization. In particular, Ge and Si have attracted attention because they can be grown nuclear-spin-free, which eliminates a major source of decoherence [18][19][20] Prime examples for novel qubits are hole spins in Ge/Si NW QDs [25, 26, 31,42,48], because they combine all the advantages of group-IV materials, VB states, and strong confinement along two axes. The Si shell provides a large VB offset ∼0.5 eV [22], induces strain, and removes dangling bonds from the core. Furthermore, the holes feature an unusually strong Rashba-type spin-orbit interaction (SOI), referred to as direct Rashba SOI (DRSOI), that is not suppressed by the band gap [48]. We show here that these properties are highly useful for implementing spin qubits.In this work, we propose a setup for quantum information processing with holes in Ge/Si core/shell NW QDs. In stark contrast to previous systems [13,[43][44][45][46][47]49], where the EDSR relies on conventional Dresselhaus and Rashba SOI [50], the dynamics in our setup are governed by the DRSOI whose origin fundamentally differs. We find that EDSR allows flipping of hole spins within less than 100 ps. Two-qubit gates can be realized via circuit quantum electrodynamics (CQED), i.e., with an on-chip cavity [51][52][53], where we estimate that operation times below 20 ns are feasible for √ iSWAP. The long-range spin-spin interactions [49,[54][55][56] enable upscaling. Compared to the original proposal for electron spins in InAs [49], which was recently followed by encouraging results [46], we find several new and striking features. First, because o...

Electric-field dependentg-factor anisotropy in Ge-Si core-shell nanowire quantum dots

“…We point out that the spin states are mixtures of heavy and light hole states and therefore m s = 1/2, which is accounted for by the introduction of g as an effective g factor. Note that g may differ significantly from transition to transition due to the varying heavy-hole light-hole mixing of subbands and quantum dot states [19] at the valence band edge of the nanowire [21,23].…”

“…The band mixing gives rise to an enhanced Rashba-type spin-orbit interaction [19], leading to strongly anisotropic and electric-field dependent g factors [20]. This makes quantum dots in Ge-Si coreshell nanowires promising candidates for robust spin-orbit qubits that can be electrically controlled via circuit quantum electrodynamics [21].…”

Heavy-Hole States in Germanium Hut Wires

“…9−11 This fact together with the rather weak hyperfine interaction, already in nonpurified materials, make Ge quantum dots (QDs) a promising platform for the realization of high-fidelity spin qubits. 12 …”

Charge-Insensitive Single-Atom Spin-Orbit Qubit in Silicon

“…[22] Here, the spin state shifts the cavity resonance by ∆f = g [72,73] g c κ = 6.7 (33) Rabi cycles can be obtained for z 0 = 4.6 nm (6.9 nm), where κ = f /Q is the cavity loss rate.…”