Fully Tunable Longitudinal Spin-Photon Interactions in Si and Ge Quantum Dots

Abstract

Spin qubits in silicon and germanium quantum dots are promising platforms for quantum computing, but entangling spin qubits over micrometer distances remains a critical challenge. Current prototypical architectures maximize transversal interactions between qubits and microwave resonators, where the spin state is flipped by nearly resonant photons. However, these interactions cause backaction on the qubit that yields unavoidable residual qubit-qubit couplings and significantly affects the gate fidelity. Strikingly, residual couplings vanish when spin-photon interactions are longitudinal and photons couple to the phase of the qubit. We show that large and tunable spin-photon interactions emerge naturally in state-of-the-art hole spin qubits and that they change from transversal to longitudinal depending on the magnetic field direction. We propose ways to electrically control and measure these interactions, as well as realistic protocols to implement fast high-fidelity two-qubit entangling gates. These protocols work also at high temperatures, paving the way toward the implementation of large-scale quantum processors.

Longitudinal coupling between electrically driven spin-qubits and a resonator

“…Furthermore, it allows for fast and high-fidelity two-qubit gates. [46][47][48] In the following we turn the discussion to the driven QDs and demonstrate the emergence of such longitudinal terms and how they can be selectively activated.…”

“…We note that the SOI can be strongly altered by electrical fields in the case of holes. 24,48,57,58 For electrons confined in typical GaAs QDs, λ 0 = 50 nm λ 0 /λ SO ∼ 0.1, giving R c /λ SO ≈ 5 × 10 −5 and g z ∼ 0.1 MHz. While smaller than in the case of holes, this coupling can be increased by considering cavities with higher frequencies.…”

“…Using the same QD systems discussed in the previous section, and assuming state-of-the art resonators with Q ∼ 10 5 , the average photon number for Ge hole-spin qubits encoded in squeezed dots in Ge/SiGe heterostructures, 56 n ph ≈ 10 2 , while for Ge/Si core/shell nano wires 56 n ph ≈ 10 6 . For Si hole-spin qubits encoded in square fin (FETs) 56 n ph ≈ 10 4 , while for electron spin qubits in gate-defined GaAs QDs n ph ≈ 10 2 . Such photonic populations are easily distinguishable by homodyne detection in current experiments.…”

“…III, at Ω = ω c , with a bath temperature T= 40 mK, and γ Ω = 10 −4 . 56 In Fig. 3 we show the relaxation rate T −1 1 (left), and the pure dephasing rate Γ z (right) for for Ge hole-spin encoded in squeezed dots, Ge/Si core/shell nanowires QDs,…”

Enhanced orbital magnetic field effects in Ge hole nanowires

“…Semiconducting nanostructures based on holes are emerging as frontrunner candidates to process quantum information because of their large spin-orbit interaction (SOI) [1][2][3][4][5][6], that enables ultrafast and coherent manipulations of spin qubits [7][8][9][10][11][12], strong coupling to resonators [13][14][15], and is an essential ingredient to host exotic particles such as Majorana bound states (MBSs) [16,17]. In hole nanostructures, the SOI is not only surprisingly strong, orders of magnitude larger than in electronic systems [1,18,19], but it is also highly tunable by external electromagnetic fields and it can be engineered by the confinement potential and by strain [20][21][22][23][24][25][26][27][28], resulting in sweet spots where the charge noise plaguing state-of-the-art spin qubits is strongly suppressed [29][30][31].…”