Nature | Vol 577 | 23 January 2020 | 487Article
Fast two-qubit logic with holes in
germanium
N. W. Hendrickx1,2,4, D. P. Franke1,2,4, A. Sammak1,3, G. Scappucci1,2 & M. Veldhorst1,2*Universal quantum information processing requires the execution of single-qubit and
two-qubit logic. Across all qubit realizations^1 , spin qubits in quantum dots have great
promise to become the central building block for quantum computation^2. Excellent
quantum dot control can be achieved in gallium arsenide^3 –^5 , and high-fidelity qubit
rotations and two-qubit logic have been demonstrated in silicon^6 –^9 , but universal
quantum logic implemented with local control has yet to be demonstrated. Here we
make this step by combining all of these desirable aspects using hole quantum dots in
germanium. Good control over tunnel coupling and detuning is obtained by
exploiting quantum wells with very low disorder, enabling operation at the charge
symmetry point for increased qubit performance. Spin–orbit coupling obviates the
need for microscopic elements close to each qubit and enables rapid qubit control
with driving frequencies exceeding 100 MHz. We demonstrate a fast universal
quantum gate set composed of single-qubit gates with a fidelity of 99.3 per cent and a
gate time of 20 nanoseconds, and two-qubit logic operations executed within
75 nanoseconds. Planar germanium has thus matured within a year from a material
that can host quantum dots to a platform enabling two-qubit logic, positioning itself
as an excellent material for use in quantum information applications.Gate-defined quantum dots were recognized early on as a promising
platform for quantum information^2 and many materials have been
investigated as hosts for the quantum dots. Initial research mainly
focused on the low-disorder semiconductor gallium arsenide^10 ,^11. Steady
progress in the control and understanding of this system culminated in
the initial demonstration and optimization of spin qubit operations^12
and the realization of rudimentary analogue quantum simulations^3.
However, the omnipresent hyperfine interactions in group III–V mate-
rials seriously deteriorate the spin coherence. Considerable improve-
ments to the coherence times could be achieved by switching to the
group IV semiconductor silicon, in particular when defining spin qubits
in an isotopically purified host crystal with vanishing concentrations
of non-zero nuclear spins^13. This enabled single-qubit rotations with
fidelities beyond 99.9%^7 and the execution of two-qubit logic gates
with fidelities up to 98%^6 ,^8 ,^9 , underlining the potential of spin qubits
for quantum computation. Nevertheless, quantum dots in silicon are
often formed at unintended locations, and control over the tunnel
coupling determining the strength of two-qubit interactions is limited.
Moreover, the absence of a sizable spin–orbit coupling for electrons
in silicon requires the inclusion of microscopic components such as
on-chip striplines or nanomagnets close to each qubit, which compli-
cates the design of large and dense two-dimensional (2D) structures.
Scalability thus remains a challenge for these systems, and a platform
that can overcome these limitations would be highly desirable.
Hole states in semiconductors^14 typically exhibit strong spin–
orbit coupling (SOC), which has enabled the demonstration of fast
single-qubit rotations^15 –^17. Furthermore, whereas valley degeneracy
complicates qubit definition for electrons in silicon, this is absent for
holes, and excited states can be well separated in energy. In silicon,
unfavourable band alignment prevents strain engineering of low-
disorder quantum wells for holes, restricting experiments to metal–
oxide–semiconductor structures^18. Research on germanium has mostly
focused on self-assembled nanowires^19 and has demonstrated single-
shot spin readout^20 and coherent spin control^17. However, strained
germanium can reach hole mobilities^21 of μ > 10^6 cm^2 V−1 s−1, and undoped
germanium quantum wells were recently shown to support the forma-
tion of gate-controlled hole quantum dots^22. Now, the crucial chal-
lenge is the demonstration of coherent control in this platform and the
implementation of qubit–qubit gates for scalable quantum information
with holes.
Here we make this step and demonstrate single- and two-qubit
logic with holes in planar germanium. We fabricate devices on sili-
con substrates, using standard manufacturing materials. We grow
undoped strained germanium quantum wells, measured to have high
hole mobilities μ > 5 × 10^5 cm^2 V−1 s−1 and a low effective hole mass^22 ,^23
mh = 0.09me, extrapolated to reach mh = 0.05me at zero density^24 , with
me the electron rest mass. This allows us to define quantum dots of com-
paratively large size, and we find excellent control over the exchange
interaction between the two dots. We operate in a multi-hole mode,
reducing challenges in tuning and characterization, which is advanta-
geous for scaling. We make use of the spin–orbit interaction for qubit
driving and perform single-qubit rotations at frequencies exceed-
ing 100 MHz. This advantage of fast driving becomes further appar-
ent in coherently accessing the Hilbert space of a two-qubit system.https://doi.org/10.1038/s41586-019-1919-3
Received: 17 June 2019
Accepted: 8 October 2019
Published online: 13 January 2020
(^1) QuTech, Delft University of Technology, Delft, The Netherlands. (^2) Kavli Institute of Nanoscience, Delft University of Technology, Delft, The Netherlands. (^3) Netherlands Organisation for Applied
Scientific Research (TNO), Delft, The Netherlands.^4 These authors contributed equally: N. W. Hendrickx, D. P. Franke. *e-mail: [email protected]