Fast two-qubit logic with holes in germanium

Abstract

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 singlequbit 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.Gate-defined quantum dots were recognized early on as a promising platform for quantum information [1] and a plethora of materials stacks has been investigated as host material. Initial research mainly focused on the low disorder semiconductor gallium arsenide [2,3]. Steady progress in the control and understanding of this system culminated in the initial demonstration and optimization of spin qubit operations [4,5] and the realization of rudimentary analog quantum simulations [6]. However, the omnipresent hyperfine interactions in group III-V materials seriously deteriorate the spin coherence, despite attempts to mitigate this by nuclear polarization [7]. Drastic improvements to the coherence times could be achieved by switching to the group IV semiconductor silicon, in particular when defining spin qubits in isotopically purified host crystal with vanishing concentrations of nonzero nuclear spin [8]. This enabled single qubit rotations with fidelities beyond 99.9% [9] and the execution of two-qubit logic gates with fidelities up to 98% [10-13], 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 requires the inclusion of microscopic components such as onchip striplines or nanomagnets close to each qubit, which seriously complicates the design of large and dense 2D-structures. This, combined with the limited control over the location and coupling of the dots, remains an outstanding challenge for the scalability of these systems and a platform that can overcome these limitations would be highly desirable. * These two authors contributed equally to this work Hole states in semiconductors typically exhibit strong spinorbit coupling, which has enabled the demonstration of fast single qubit rotations [14,15] and additionally, unlike electrons, holes do not suffer from nearby valley states. In silicon, unfavorable band alignment...

Site‐Controlled Uniform Ge/Si Hut Wires with Electrically Tunable Spin–Orbit Coupling

“…Among them, Ge is attracting more and more attention due to its high hole mobility, [ 10–13 ] low effective mass in 2D hole gases, [ 14,15 ] good contacts with metals, [ 16–18 ] strong spin–orbit interactions, [ 19–22 ] capability of isotopic purification, [ 23 ] and compatibility with Si. These attractive features make Ge a promising candidate not only as a transistor channel material but also as a host for spin [ 6,24,25 ] and even topological qubits. [ 26,27 ] Excitingly, the first hole spin qubit [ 6 ] and proximity‐induced superconductivity with a hard gap [ 28 ] have been realized recently in 1D Ge.…”

A single-hole spin qubit

“…Early research demonstrated the feasibility of using the SOC for allelectric driving 17,18 , but these experiments were limited by nuclear spins and the coherent driving of a single-hole spin remained an open challenge. More recently, hole spins in group-IV materials have gained attention as a platform for quantum information processing [19][20][21][22] . In particular, hole states in germanium can provide a high degree of quantum dot tunability [23][24][25] , fast and all-electrical driving 20,21 and Ohmic contacts to superconductors for hybrids 26,27 .…”

“…More recently, hole spins in group-IV materials have gained attention as a platform for quantum information processing [19][20][21][22] . In particular, hole states in germanium can provide a high degree of quantum dot tunability [23][24][25] , fast and all-electrical driving 20,21 and Ohmic contacts to superconductors for hybrids 26,27 . These experiments culminated in the recent demonstration of full two-qubit logic 21 .…”

Tunable Coupling and Isolation of Single Electrons in Silicon Metal-Oxide-Semiconductor Quantum Dots

“…The exchange interaction is set by the tunnel coupling and detuning, and gaining precise control over these parameters enables to define and operate qubits at their optimal points [5][6][7][8]. Excellent control has already been reported in GaAs [5,6,9], strained silicon [10,11], and more recently in strained germanium [12,13]. Reaching this level of control in silicon metal-oxide-semiconductor (SiMOS) quantum dots is highly desired as this platform has a high potential for complete integration with classical manufacturing technology [14][15][16].…”