A singlet-triplet hole spin qubit in planar Ge

Spin qubits are considered to be among the most promising candidates for building a quantum processor. Group IV hole spin qubits are particularly interesting owing to their ease of operation and compatibility with Si technology. In addition, Ge offers the option for monolithic superconductor–semiconductor integration. Here, we demonstrate a hole spin qubit operating at fields below 10 mT, the critical field of Al, by exploiting the large out-of-plane hole g-factors in planar Ge and by encoding the qubit into the singlet-triplet states of a double quantum dot. We observe electrically controlled g-factor difference-driven and exchange-driven rotations with tunable frequencies exceeding 100 MHz and dephasing times of 1 μs, which we extend beyond 150 μs using echo techniques. These results demonstrate that Ge hole singlet-triplet qubits are competing with state-of-the-art GaAs and Si singlet-triplet qubits. In addition, their rotation frequencies and coherence are comparable with those of Ge single spin qubits, but singlet-triplet qubits can be operated at much lower fields, emphasizing their potential for on-chip integration with superconducting technologies. A singlet-triplet spin qubit using holes in a Ge quantum well is demonstrated, and can be operated at low magnetic fields of a few millitesla.

[1]  H. Riemann,et al.  Engineering long spin coherence times of spin–orbit qubits in silicon , 2018, Nature Materials.

[2]  A. Gossard,et al.  Scaling of dynamical decoupling for spin qubits. , 2011, Physical review letters.

[3]  R Maurand,et al.  A CMOS silicon spin qubit , 2016, Nature Communications.

[4]  R. Ishihara,et al.  Interfacing spin qubits in quantum dots and donors—hot, dense, and coherent , 2017, npj Quantum Information.

[5]  A. Gossard,et al.  A Coherent Beam Splitter for Electronic Spin States , 2010, Science.

[6]  S T Merkel,et al.  Reduced Sensitivity to Charge Noise in Semiconductor Spin Qubits via Symmetric Operation. , 2015, Physical review letters.

[7]  Andreas D. Wieck,et al.  Closed-loop control of a GaAs-based singlet-triplet spin qubit with 99.5% gate fidelity and low leakage , 2019, Nature Communications.

[8]  M. Veldhorst,et al.  Spin and orbital structure of the first six holes in a silicon metal-oxide-semiconductor quantum dot , 2018, Nature Communications.

[9]  Giovanni Isella,et al.  Scattering mechanisms in high-mobility strained Ge channels , 2004 .

[10]  S. Girvin,et al.  0 40 73 25 v 1 1 3 Ju l 2 00 4 Circuit Quantum Electrodynamics : Coherent Coupling of a Single Photon to a Cooper Pair Box , 2022 .

[11]  Saeed Fallahi,et al.  High-fidelity entangling gate for double-quantum-dot spin qubits , 2016, 1608.04258.

[12]  J. Levy.  Universal quantum computation with spin-1/2 pairs and Heisenberg exchange. , 2001, Physical review letters.

[13]  Susheng Tan,et al.  Germanium Quantum-Well Josephson Field-Effect Transistors and Interferometers. , 2018, Nano letters.

[14]  O. Schmidt,et al.  Nature of tunable hole g factors in quantum dots. , 2012, Physical review letters.

[15]  Jacob M. Taylor,et al.  Coherent Manipulation of Coupled Electron Spins in Semiconductor Quantum Dots , 2005, Science.

[16]  S. Tarucha,et al.  A>99.9%-fidelity quantum-dot spin qubit with coherence limited by charge noise , 2017, 1708.01454.

[17]  Fei Gao,et al.  A germanium hole spin qubit , 2018, Nature Communications.

[18]  Tammy Pluym,et al.  Spin-orbit Interactions for Singlet-Triplet Qubits in Silicon. , 2018, Physical review letters.

[19]  R. Schouten,et al.  A four-qubit germanium quantum processor , 2020, Nature.

[20]  Alessandro Virtuani,et al.  Defect imaging of SiGe strain relaxed buffers grown by LEPECVD , 2006 .

[21]  Edwin Barnes,et al.  Composite pulses for robust universal control of singlet–triplet qubits , 2012, Nature Communications.

[22]  G. A. D. Briggs,et al.  Sensitive radiofrequency readout of quantum dots using an ultra-low-noise SQUID amplifier , 2018, Journal of Applied Physics.

[24]  D. DiVincenzo,et al.  Quantum computation with quantum dots , 1997, cond-mat/9701055.

[25]  J. R. Petta,et al.  Fast charge sensing of a cavity-coupled double quantum dot using a Josephson parametric amplifier , 2015, 1502.01283.

[26]  A. C. Gossard,et al.  Relaxation and readout visibility of a singlet-triplet qubit in an Overhauser field gradient , 2011, 1108.4210.

[27]  F. Zwanenburg,et al.  Depletion-mode Quantum Dots in Intrinsic Silicon. , 2017, 1709.07361.

[28]  D. Culcer,et al.  Suppressing charge-noise sensitivity in high-speed Ge hole spin-orbit qubits , 2019, 1911.11143.

[29]  J. Wendt,et al.  Probing low noise at the MOS interface with a spin-orbit qubit , 2017, 1707.04357.

[30]  Z. R. Wasilewski,et al.  Enhanced charge detection of spin qubit readout via an intermediate state , 2012, 1206.0778.

[31]  D. Loss,et al.  Heavy-Hole States in Germanium Hut Wires , 2016, Nano letters.

[32]  O. Schmidt,et al.  Observation of spin-selective tunneling in SiGe nanocrystals. , 2011, Physical review letters.

[33]  Amir Yacoby,et al.  Dephasing time of GaAs electron-spin qubits coupled to a nuclear bath exceeding 200 μs , 2011 .

[34]  I. Prieto,et al.  Assessing the potential of Ge/SiGe quantum dots as hosts for singlet-triplet qubits , 2019, 1910.05841.

[35]  S. Girvin,et al.  Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics , 2004, Nature.

[36]  A. C. Doherty,et al.  Suppressing qubit dephasing using real-time Hamiltonian estimation , 2014, Nature Communications.

[37]  G. Capellini,et al.  Light effective hole mass in undoped Ge/SiGe quantum wells , 2019, Physical Review B.

[38]  D. Culcer,et al.  Optimal operation points for ultrafast, highly coherent Ge hole spin-orbit qubits , 2021 .

[39]  G. Capellini,et al.  Shallow and Undoped Germanium Quantum Wells: A Playground for Spin and Hybrid Quantum Technology , 2018, Advanced Functional Materials.

[40]  M. Veldhorst,et al.  Fast two-qubit logic with holes in germanium , 2019, Nature.

[41]  D. Loss,et al.  Strong spin-orbit interaction and helical hole states in Ge/Si nanowires , 2011, 1107.4870.

[42]  M. Myronov,et al.  Reverse graded relaxed buffers for high Ge content SiGe virtual substrates , 2008 .

[43]  E. Bakkers,et al.  Ultrafast Hole Spin Qubit with Gate-Tunable Spin-Orbit Switch , 2020, 2006.11175.

[44]  G. Burkard,et al.  Superconductor-semiconductor hybrid cavity quantum electrodynamics , 2019 .

[45]  Tammy Pluym,et al.  A silicon metal-oxide-semiconductor electron spin-orbit qubit , 2018, Nature Communications.

[46]  A. Yacoby,et al.  Charge noise spectroscopy using coherent exchange oscillations in a singlet-triplet qubit. , 2012, Physical review letters.

[47]  Zhan Shi,et al.  Two-axis control of a singlet–triplet qubit with an integrated micromagnet , 2014, Proceedings of the National Academy of Sciences.

[48]  Alexander Opremcak,et al.  Digital Coherent Control of a Superconducting Qubit , 2018, Physical Review Applied.

[49]  Dino Sejdinovic,et al.  Machine learning enables completely automatic tuning of a quantum device faster than human experts , 2020, Nature Communications.

[50]  K. Itoh,et al.  A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9% , 2018, Nature Nanotechnology.

[51]  Adele E. Schmitz,et al.  Coherent singlet-triplet oscillations in a silicon-based double quantum dot , 2012, Nature.

[52]  D. Loss,et al.  The germanium quantum information route , 2020, Nature Reviews Materials.

[53]  M. Vinet,et al.  Gate-reflectometry dispersive readout and coherent control of a spin qubit in silicon , 2018, Nature Communications.

[54]  M. Manfra,et al.  Readout of singlet-triplet qubits at large magnetic field gradients , 2018, Physical Review B.

[55]  G. Guo,et al.  Ultrafast Operations of a Hole Spin Qubit in Ge Quantum Dot , 2020 .

[56]  Ting Wang,et al.  A germanium hole spin qubit , 2018, Nature Communications.

[57]  Saeed Fallahi,et al.  Noise Suppression Using Symmetric Exchange Gates in Spin Qubits. , 2015, Physical review letters.