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Register a new userFast two-qubit logic with holes in germanium
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The promise of quantum computation with quantum dots has stimulated widespread research. Still, a platform that can combine excellent control with fast and high-fidelity operation is absent. Here, we show single and two-qubit operations based on holes in germanium. A high degree of control over the tunnel coupling and detuning is obtained by exploiting quantum wells with very low disorder and by working in a virtual gate space. Spin-orbit coupling obviates the need for microscopic elements and enables rapid qubit control with Rabi frequencies exceeding 100 MHz and a single-qubit fidelity of 99.3 %. We demonstrate fast two-qubit CX gates executed within 75 ns and minimize decoherence by operating at the charge symmetry point. Planar germanium thus matured within one year from a material that can host quantum dots to a platform enabling two-qubit logic, positioning itself as a unique material to scale up spin qubits for quantum information.
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Quantum computation requires qubits that can be coupled and realized in a scalable manner, together with universal and high-fidelity one- and two-qubit logic gates cite{DiVincenzo2000, Loss1998}. Strong effort across several fields have led to an impressive array of qubit realizations, including trapped ions cite{Brown2011}, superconducting circuits cite{Barends2014}, single photonscite{Kok2007}, single defects or atoms in diamond cite{Waldherr2014, Dolde2014} and silicon cite{Muhonen2014}, and semiconductor quantum dots cite{Veldhorst2014}, all with single qubit fidelities exceeding the stringent thresholds required for fault-tolerant quantum computing cite{Fowler2012}. Despite this, high-fidelity two-qubit gates in the solid-state that can be manufactured using standard lithographic techniques have so far been limited to superconducting qubits cite{Barends2014}, as semiconductor systems have suffered from difficulties in coupling qubits and dephasing cite{Nowack2011, Brunner2011, Shulman2012}. Here, we show that these issues can be eliminated altogether using single spins in isotopically enriched siliconcite{Itoh2014} by demonstrating single- and two-qubit operations in a quantum dot system using the exchange interaction, as envisaged in the original Loss-DiVincenzo proposal cite{Loss1998}. We realize CNOT gates via either controlled rotation (CROT) or controlled phase (CZ) operations combined with single-qubit operations. Direct gate-voltage control provides single-qubit addressability, together with a switchable exchange interaction that is employed in the two-qubit CZ gate. The speed of the two-qubit CZ operations is controlled electrically via the detuning energy and we find that over 100 two-qubit gates can be performed within a two-qubit coherence time of 8 textmu s, thereby satisfying the criteria required for scalable quantum computation.
The possibility of quantum computing with spins in germanium nanoscale transistors has recently attracted interest since it promises highly tuneable qubits that have encouraging coherence times. We here present the first complete theory of the orbital states of Ge donor electrons, and use it to show that Ge could have significant advantages over silicon in the implementation of a donor-based quantum processor architecture. We show that the stronger spin-orbit interaction and the larger electron donor wave functions for Ge donors allow for greater tuning of the single qubit energy than for those in Si crystals, thus enabling a large speedup of selective (local) quantum gates. Further, exchange coupling between neighboring donor qubits is shown to be much larger in Ge than in Si, and we show that this greatly relaxes the precision in donor placement needed for robust two-qubit gates. To do this we compare two statistical distributions for Ge:P and Si:P pair couplings, corresponding to realistic donor implantation misplacement, and find that the spin couplings in Ge:P have a $33%$ chance of being within an order of magnitude of the largest coupling, compared with only $10%$ for the Si:P donors. This allows fast, parallel and robust architectures for quantum computing with donors in Ge.
We engineer planar Ge/SiGe heterostructures for low disorder and quiet hole quantum dot operation by positioning the strained Ge channel 55~nm below the semiconductor/dielectric interface. In heterostructure field effect transistors, we measure a percolation density for two-dimensional hole transport of $2.1times10^{10}~text{cm}^{-2}$, indicative of a very low disorder potential landscape experienced by holes in the buried Ge channel. These Ge heterostructures support quiet operation of hole quantum dots and we measure charge noise levels that are below the detection limit $sqrt{S_text{E}}=0.2~mu text{eV}/sqrt{text{Hz}}$ at 1 Hz. These results establish planar Ge as a promising platform for scaled two-dimensional spin qubit arrays.
The prospect of building quantum circuits using advanced semiconductor manufacturing positions quantum dots as an attractive platform for quantum information processing. Extensive studies on various materials have led to demonstrations of two-qubit logic in gallium arsenide, silicon, and germanium. However, interconnecting larger numbers of qubits in semiconductor devices has remained an outstanding challenge. Here, we demonstrate a four-qubit quantum processor based on hole spins in germanium quantum dots. Furthermore, we define the quantum dots in a two-by-two array and obtain controllable coupling along both directions. Qubit logic is implemented all-electrically and the exchange interaction can be pulsed to freely program one-qubit, two-qubit, three-qubit, and four-qubit operations, resulting in a compact and high-connectivity circuit. We execute a quantum logic circuit that generates a four-qubit Greenberger-Horne-Zeilinger state and we obtain coherent evolution by incorporating dynamical decoupling. These results are an important step towards quantum error correction and quantum simulation with quantum dots.
The four-level exciton/biexciton system of a single semiconductor quantum dot acts as a two qubit register. We experimentally demonstrate an exciton-biexciton Rabi rotation conditional on the initial exciton spin in a single InGaAs/GaAs dot. This forms the basis of an optically gated two-qubit controlled-rotation (CROT) quantum logic operation where an arbitrary exciton spin is selected as the target qubit using the polarization of the control laser.
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