A single-hole spin qubit

Abstract

Qubits based on quantum dots have excellent prospects for scalable quantum technology due to their compatibility with standard semiconductor manufacturing. While early research focused on the simpler electron system, recent demonstrations using multi-hole quantum dots illustrated the favourable properties holes can offer for fast and scalable quantum control. Here, we establish a single-hole spin qubit in germanium and demonstrate the integration of single-shot readout and quantum control. We deplete a planar germanium double quantum dot to the last hole, confirmed by radio-frequency reflectrometry charge sensing. To demonstrate the integration of single-shot readout and qubit operation, we show Rabi driving on both qubits. We find remarkable electric control over the qubit resonance frequencies, providing great qubit addressability. Finally, we analyse the spin relaxation time, which we find to exceed one millisecond, setting the benchmark for hole quantum dot qubits. The ability to coherently manipulate a single hole spin underpins the quality of strained germanium and defines an excellent starting point for the construction of quantum hardware.

Spin Relaxation Benchmarks and Individual Qubit Addressability for Holes in Quantum Dots

“…We note that these dot-reservoir couplings do not represent the actual tunnelling times at the point of measurement, which are expected to be orders of magnitude longer. The spin relaxation decay shown in Figure 3 c has been analyzed using the above-mentioned double exponential fit and we find an significantly increased single-hole spin relaxation time T 1,| n =1⟩ = 32 ms. By limiting the dot-reservoir tunnel coupling, we have demonstrated spin relaxation lifetimes significantly longer than results previously reported for planar germanium quantum dots ( T 1,| n =1⟩ = 1.2 ms 28 ), hut wires ( T 1 = 90 μs 38 ), nanowires ( T 1 = 600 μs 39 ), and even holes in gallium arsenide ( T 1 = 60 μs 40 ) and silicon ( T 1 = 8.3 μs 41 ) at similar magnetic fields. We expect that the main cause for the observation of longer spin relaxation times for single-hole spins compared to many hole spins originates from the tighter confinement of the quantum dot under P 3 .…”

“…These values are comparable to those measured in a previous work on the same device under different electrostatic tuning parameters, and therefore we expect the coherence times of each qubit to be on the order of 300 ns as measured earlier. 28 This corresponds to a cross talk ratio of about 1:30 for the five-hole qubit and about 1:4 for the single-hole qubit. The cross talk for the single-hole qubit is comparable to the lever arm ratio (see Supporting Information Section II) α P 3 /P 4 ( f 2 ) = 0.11.…”

The germanium quantum information route

“…A particularly attractive property of holes, which is found in various structures, is a strong dependence of the effective g factor on the applied electric field 13,53,71,74,[99][100][101][102] . This property can be used, e.g., to electrically tune the Zeeman splitting and, hence, the resonance condition of hole-spin qubits 20 . Furthermore, it allows for electrically driven spin rotations via g-matrix modulation 99,101,103,104 .…”

“…4c), highlighting the beneficial aspects of planar systems for scalability. Owing to the high mobility 9 and light mass of holes 45 , comparatively large quantum dots (diameter of ≈ 100 nm) can be defined 18 and tuned to contain only a single hole 20,194 in Ge/SiGe quantum wells. Furthermore, these devices are compatible with electric gate fabrication using single-layer technology 18 .…”

Vanishing Zeeman energy in a two-dimensional hole gas

“…Holes can also host superconducting pairing correlations, a key ingredient for the emergence of Majorana zero modes [6][7][8][9][10] for topological quantum computing. Because of its attractive properties [1,[11][12][13][14][15][16][17][18][19][20][21][22], the strained Ge low-dimensional system has been proposed as an effective building block to develop these emerging quantum devices. Interestingly, the simplicity of this system makes it a textbook model to uncover and elucidate subtle hole spin-related phenomena leading, for instance, to the recent observation of pure cubic Rashba spin-orbit coupling [23].…”