Universal quantum logic in hot silicon qubits

In the last decade silicon has emerged as a potential material platform for quantum information. The main attraction comes from the fact that silicon technologies have been developed extensively in the last semiconductor revolution, and this gives hope that quantum dots can be fabricated one day with the same ease transistors are made today. However, building a large-scale quantum computer presents also complications that go beyond fabrication. The heat-dissipation challenge is one of these. As many other qubit platforms, also quantum dot qubits are cooled down at temperatures close to absolute zero in order to overcome the problem of decoherence. While this can be advantageous in few-qubit experiments, it becomes soon impractical as the qubit number increases. The first part of the thesis describes a series of experiments that demonstrate how Si- MOS quantum dot qubits can be successfully operated beyond one Kelvin, where the increase in cooling power is substantial. The first step is to demonstrate that electrons have sufficiently large energy scales to be properly isolated and controlled at these high temperatures. In the first experimental chapter of the thesis we demonstrate a highly uniform double quantum dot system at the temperature of 0.5 K. The on-chip single-electron-transistor (SET) shows very regular oscillations and an exceptional sensitivity to dot-reservoir and interdot transitions. The electrons in the quantum dot can also be completely decoupled from the reservoir, resulting in a fully isolated system. In order to performquantumoperations it is not only crucial to isolate electrons, but also to couple them. While this is routinely achieved in Si-SiGe heterostructures, it is usually more challenging in Si-MOS due to the larger disorder at the Si-SiO2 interface. However, we find that in the same device we can control the tunnel coupling between the electrons, in a range from below 1 Hz up to 13 GHz. This would allow to isolate the electrons for single-qubit operations and to couple them for two-qubit gates or readout using Pauli spin blockade. Part of the challenges concerning operation of ‘hot’ spin qubits lies in the temperature dependence of two parameters: the spin lifetime and the charge noise, which are thoroughly studied in chapter 4. The spin lifetime is usually very long in silicon, due to a weak spin-orbit coupling, and it can approach seconds at low magnetic fields. However, the temperature increases the excitations in the phonon bath and activates two-phonon transitions, which have a steep temperature dependence. These processes, which we experimentally find to start around 500 mK, can ultimately limit qubit performances. However, the spin lifetime can be significantly improved by working in a low magnetic field and high valley splitting regime. Si-MOS quantum dot qubits have a large valley splitting, usually of several hundreds of &eV, and a lowmagnetic field can be set by reading out the qubits with Pauli spin blockade. This guarantees that useful spin lifetimes can still be found at temperatures close to one Kelvin. In particular, in chapter 4 we measure values exceeding 1 ms at 1.1 K, and discuss how they can be further improved in case of a larger valley splitting.QCD/Veldhorst La

A single-hole spin qubit

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.QCD/Veldhorst LabBusiness DevelopmentQCD/Scappucci La

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

Extremely long coherence times, excellent single-qubit gate fidelities, and two-qubit logic have been demonstrated with silicon metal-oxide-semiconductor spin qubits, making it one of the leading platforms for quantum information processing. Despite this, a long-standing challenge in this system has been the demonstration of tunable tunnel coupling between single electrons. Here we overcome this hurdle with gate-defined quantum dots and show couplings that can be tuned on and off for quantum operations. We use charge sensing to discriminate between the (2,0) and (1,1) charge states of a double quantum dot and show excellent charge sensitivity. We demonstrate tunable coupling up to 13 GHz, obtained by fitting charge polarization lines, and tunable tunnel rates down to <1 Hz, deduced from the random telegraph signal. The demonstration of tunable coupling between single electrons in a silicon metal-oxide-semiconductor device provides significant scope for high-fidelity two-qubit logic toward quantum information processing with standard manufacturing.QCD/Veldhorst LabQuTechQCD/Vandersypen LabQN/Vandersypen La

Design and integration of single-qubit rotations and two-qubit gates in silicon above one Kelvin

Spin qubits in quantum dots define an attractive platform for quantum information because of their compatibility with semiconductor manufacturing, their long coherence times, and the ability to operate above one Kelvin. However, despite demonstrations of SWAP oscillations, the integration of this two-qubit gate together with single-qubit control to create a universal gate set as originally proposed for single spins in quantum dots has remained elusive. Here, we show that we can overcome these limitations and execute a multitude of native two-qubit gates, together with single-qubit control, in a single device, reducing the operation overhead to perform quantum algorithms. We demonstrate single-qubit rotations, together with the two-qubit gates CROT, CPHASE, and SWAP, on a silicon double quantum dot. Furthermore, we introduce adiabatic and diabatic composite sequences that allow the execution of CPHASE and SWAP gates on the same device, despite the finite Zeeman energy difference. Both two-qubit gates can be executed in less than 100 ns and, by theoretically analyzing the experimental noise sources, we predict control fidelities exceeding 99%, even for operation above one Kelvin.BUS/Quantum DelftQCD/Vandersypen LabQCD/Veldhorst LabQN/Vandersypen LabQN/Veldhorst La

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

We investigate hole spin relaxation in the single- and multihole regime in a 2 × 2 germanium quantum dot array. We find spin relaxation times T1 as high as 32 and 1.2 ms for quantum dots with single- and five-hole occupations, respectively, setting benchmarks for spin relaxation times for hole quantum dots. Furthermore, we investigate qubit addressability and electric field sensitivity by measuring resonance frequency dependence of each qubit on gate voltages. We can tune the resonance frequency over a large range for both single and multihole qubits, while simultaneously finding that the resonance frequencies are only weakly dependent on neighboring gates. In particular, the five-hole qubit resonance frequency is more than 20 times as sensitive to its corresponding plunger gate. Excellent individual qubit tunability and long spin relaxation times make holes in germanium promising for addressable and high-fidelity spin qubits in dense two-dimensional quantum dot arrays for large-scale quantum information.QCD/Veldhorst LabQuTechQCD/Vandersypen LabBusiness DevelopmentQCD/Scappucci La

A crossbar network for silicon quantum dot qubits

The spin states of single electrons in gate-defined quantum dots satisfy crucial requirements for a practical quantum computer. These include extremely long coherence times, high-fidelity quantum operation, and the ability to shuttle electrons as a mechanism for on-chip flying qubits. To increase the number of qubits to the thousands or millions of qubits needed for practical quantum information, we present an architecture based on shared control and a scalable number of lines. Crucially, the control lines define the qubit grid, such that no local components are required. Our design enables qubit coupling beyond nearest neighbors, providing prospects for nonplanar quantum error correction protocols. Fabrication is based on a three-layer design to define qubit and tunnel barrier gates. We show that a double stripline on top of the structure can drive high-fidelity single-qubit rotations. Self-aligned inhomogeneous magnetic fields induced by direct currents through superconducting gates enable qubit addressability and readout. Qubit coupling is based on the exchange interaction, and we show that parallel two-qubit gates can be performed at the detuning-noise insensitive point. While the architecture requires a high level of uniformity in the materials and critical dimensions to enable shared control, it stands out for its simplicity and provides prospects for large-scale quantum computation in the near future.QCD/Veldhorst LabQuTechQCD/Vandersypen LabQuantum Information and SoftwareQID/Wehner GroupQuantum Internet DivisionQN/Vandersypen La

Spin Lifetime and Charge Noise in Hot Silicon Quantum Dot Qubits

We investigate the magnetic field and temperature dependence of the single-electron spin lifetime in silicon quantum dots and find a lifetime of 2.8 ms at a temperature of 1.1 K. We develop a model based on spin-valley mixing and find that Johnson noise and two-phonon processes limit relaxation at low and high temperature, respectively. We also investigate the effect of temperature on charge noise and find a linear dependence up to 4 K. These results contribute to the understanding of relaxation in silicon quantum dots and are promising for qubit operation at elevated temperatures.QCD/Veldhorst LabQCD/Vandersypen LabGeneralQID/Dobrovitski GroupQN/Vandersypen La

Quantum dot arrays in silicon and germanium

Electrons and holes confined in quantum dots define excellent building blocks for quantum emergence, simulation, and computation. Silicon and germanium are compatible with standard semiconductor manufacturing and contain stable isotopes with zero nuclear spin, thereby serving as excellent hosts for spins with long quantum coherence. Here, we demonstrate quantum dot arrays in a silicon metal-oxide-semiconductor (SiMOS), strained silicon (Si/SiGe), and strained germanium (Ge/SiGe). We fabricate using a multi-layer technique to achieve tightly confined quantum dots and compare integration processes. While SiMOS can benefit from a larger temperature budget and Ge/SiGe can make an Ohmic contact to metals, the overlapping gate structure to define the quantum dots can be based on a nearly identical integration. We realize charge sensing in each platform, for the first time in Ge/SiGe, and demonstrate fully functional linear and two-dimensional arrays where all quantum dots can be depleted to the last charge state. In Si/SiGe, we tune a quintuple quantum dot using the N + 1 method to simultaneously reach the few electron regime for each quantum dot. We compare capacitive crosstalk and find it to be the smallest in SiMOS, relevant for the tuning of quantum dot arrays. We put these results into perspective for quantum technology and identify industrial qubits, hybrid technology, automated tuning, and two-dimensional qubit arrays as four key trajectories that, when combined, enable fault-tolerant quantum computation.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.QCD/Veldhorst LabQuTechQCD/Vandersypen LabQCD/Scappucci LabBUS/Quantum DelftQN/Vandersypen La

How to Utilise the Knowledge of Causal Responses? Physical and Physiological Forest Ecology

Our physical and physiological theory provides causal explanations of various phenomena in forests. This causal nature of the theory enables versatile applications in forestry and in the research of the interactions between climate change and forests. We treat the effects of thinnings and whole-tree harvesting on wood production and the responses of forest ecosystem to nitrogen deposition in more detail. The forests react to the increasing CO2 concentration and also to temperature increase generating feedbacks from forests to climate change. The changes in the carbon storages in forest ecosystems and in the emission of volatile organic compounds are evidently the most important feedbacks from forest ecosystems to the climate change