In this thesis we present a spin based QuBit Architecture that implements single-QuBit gates in the QuBit itself and is predicted to have a long coherence time.
This architecture has been physically realized in a Ferromagnetic Double Quantum Dot hosted in a Single Wall Carbon Nanotube, and studied through a coupled Microwave cavity. We present a Linear Response Theory model that ties the transmitted amplitude and phase of the microwave signal through the cavity to the microscopic charge susceptibility of the Double Quantum Dot. We fit those two channels of experimental data to a simple 4 level master equation model that allows us to extract the inter-dot tunneling rate, the charge-photons coupling rate and the charge dephasing rate. We also present a numerical algorithm that allows to evolve in time the quantum state of the device also considering the effect of charge noise. This algorithm is used to study the effect of fast Landau-Zener style pulses on the QuBit, giving the ideal shape of the control pulses.
In this thesis we present a spin based QuBit Architecture that implements single-QuBit gates in the QuBit itself and is predicted to have a long coherence time.
This architecture has been physically realized in a Ferromagnetic Double Quantum Dot hosted in a Single Wall Carbon Nanotube, and studied through a coupled Microwave cavity. We present a Linear Response Theory model that ties the transmitted amplitude and phase of the microwave signal through the cavity to the microscopic charge susceptibility of the Double Quantum Dot. We fit those two channels of experimental data to a simple 4 level master equation model that allows us to extract the inter-dot tunneling rate, the charge-photons coupling rate and the charge dephasing rate. We also present a numerical algorithm that allows to evolve in time the quantum state of the device also considering the effect of charge noise. This algorithm is used to study the effect of fast Landau-Zener style pulses on the QuBit, giving the ideal shape of the control pulses.
This thesis investigates experimentally the coupling mechanism of the charge and spin degrees of freedom in double quantum dots to high finesse superconducting microwave cavities. We use carbon nanotubes as a coherent conductor to host our quantum dots.We conceived an experimental setup and developed new fabrication methods in order to achieve control over these devices. With these methods, we scrutinize the resonant coupling of the dot's charge electronic transitions to a microwave cavity. We drive the system out of equilibrium to characterise its dynamics and extract its relevant intrinsic parameters. We examine a possible coupling of single photons to a single electron spin, using non-collinear exchange fields induced from ferromagnetic interfaces as a key ingredient to engineer this coupling. The preliminary results in this circuit architecture are promising for future spin-based QED experiments with single spins.
In this thesis, we investigate the use of an on-chip micromagnet to control the magnetic-field profile along a carbon nanotube for spin-qubit applications. The nanotube serves as a coherent conductor in which a single electron is confined in a gate-defined double quantum dot shaped by the electrostatic potential along the tube. Quantum information is encoded in the electron's spin state, which serves as the qubit. The quantum-dot circuit is embedded in a circuit quantum electrodynamics (QED) architecture that enables qubit manipulation, readout, and long-range coupling. Coupling of the spin qubit to photons in a microwave resonator is enabled through spin-charge hybridization engineered by controlling the field profile along the nanotube: the electron in the double well experiences different spin-quantization axes in the two dots. Here, magnetic-field control is implemented by integrating a micromagnet into the quantum-dot circuit. Optimal geometries for on-chip field gradients are identified through numerical simulations to maximize the magnetic-field difference between the two quantum dots. Thin-film magnetic characterization and local field sensing of the micromagnet - using NV-center magnetometry - are performed. The experimental data are matched with micromagnetic simulations to predict the magnetic field generated by the magnet at various external fields and positions, and hence to forecast spin-qubit performance. To further enhance spin-photon coupling, the spin-qubit architecture is integrated with a microwave circuit fabricated from niobium nitride (NbN), a high-kinetic-inductance, magnetic-field-resilient superconductor. The design and characterization of a high-impedance resonator are detailed. Finally, we demonstrate on-chip integration of the carbon-nanotube quantum-dot circuit, the micromagnet, and the NbN microwave circuitry.
Abstract Spins confined in quantum dots are considered as a promising platform for quantum information processing. While many advanced quantum operations have been demonstrated, experimental as well as theoretical efforts are now focusing on the development of scalable spin quantum bit architectures. One particularly promising method relies on the coupling of spin quantum bits to microwave cavity photons. This would enable the coupling of distant spins via the exchange of virtual photons for two qubit gate applications, which still remains to be demonstrated with spin qubits. Here, we use a circuit QED spin–photon interface to drive a single electronic spin in a carbon nanotube-based double quantum dot using cavity photons. The microwave spectroscopy allows us to identify an electrically controlled spin transition with a decoherence rate which can be tuned to be as low as 250 kHz. We show that this value is consistent with the expected hyperfine coupling in carbon nanotubes. These coherence properties, which can be attributed to the use of pristine carbon nanotubes stapled inside the cavity, should enable coherent spin–spin interaction via cavity photons and compare favorably to the ones recently demonstrated in Si-based circuit QED experiments. Our clean and controlled nano-assembly technique of carbon nanotubes in the cavity could be further improved by purified 12 C growth to get rid of the nuclear spins resulting in an even higher spin coherence.
Quantum physics describes the universe on a microscopic scale. Even though this scale is not accessible without complex experimental setups, quantum effects are respon- sible for the properties of matter and in some instances we have learned to exploit them technologically. A modern computer constituted of transistors passively utilizes the quantum nature of charge carriers in the band structure of semiconductors to encode and process information. Although such a classical computer is a formidable tool already, what could be achieved with active control over the quantum states in the computer is an intriguing question. This is the idea of the quantum computer, which offers an entirely new paradigm of computing by encoding information in quantum binary digits (qubits). Indeed, for several applications it has been shown that a quantum computer is superior to its classical counterpart, even though its realization remains elusive up to date. One candidate to host qubits are gate-defined semiconductor quantum dots, confin- ing single or few charge carriers with spin. The spin of a single confined electron is a quantum two-level system which can be manipulated and measured, allowing the storage and processing of quantum information. This thesis can be viewed as part of the endeavor to give birth to quantum computers based on semiconductor spin qubits. It primarily focuses on the challenge to enable scalable architectures of well-characterized qubits. In the first part, spin shuttling is investigated. This denotes the coherent transport of a single spin between spatially separate nodes of a quantum processor, driven by a time-dependent electric potential. The object of study is a minimal version of a bucket- brigade-like spin shuttling between two quantum dots. The probability of maintaining the spin state is identified as figure of merit and the effect of spin-orbit interaction and the Zeeman effect in an inhomogeneous magnetic field is explored with analytical and numerical methods. Special attention is paid to the repercussions of near-degenerate valleys. The second part of the thesis addresses the challenge to probe the microscopic properties of a quantum dot array, which is a crucial first step before any quantum operation can be performed. The transmission of a microwave resonator coupled to a triple quantum dot occupied by two electrons is investigated, and a scheme to infer the exchange interaction between electrons in adjacent quantum dots is proposed. By means of analytical derivations it is shown that the transmission profile of the resonator directly reveals the value of the exchange coupling strength between two electrons. This holds even if magnetic gradients or a valley splitting comparable to the inter-dot tunnel coupling are included. Subsequently, quantum transport measurements in the Pauli blockade regime are modelled in the presence of a microwave resonator, bringing together two powerful techniques to probe quantum dots. Based on generalized input-output theory, a theoretical framework is derived to investigate how a double quantum dot in a transport setup interacts with a coupled microwave resonator while the current through the double qauntum dot is rectified by Pauli blockade. It is shown that the output field of the resonator can be used to infer the leakage current and thus obtain insight into the blockade mechanisms and to estimate a large number of parameters of the quantum dots. Furthermore, the back-action of the resonator photons on the steady state leakage current is described and quantified. In the context of Pauli blockade, the spin and valley physics of bilayer graphene quantum dots in the few-electron regime is touched upon, describing a situation where spin blockade is observed despite the presence of the valleys. In the final part of the thesis, the attention is shifted towards the readout of the spin qubits. A new paradigm of dispersive readout is devised, which is performed while the qubit dephases, implementing a measurement in the x-basis. Laplace transforming the time dependent cavity response allows a separation of contributions from multiple qubits coupled to the same resonator. Thus, they can be read out simultaneously in a single shot. Modelling silicon spin qubits, as an example, results in in a readout time that compares favourably to conventional dispersive readout with comparable fidelity, even for a single qubit. With an auxiliary qubit the readout scheme can be extended to a quantum non-demolition measurement.
This dissertation describes a set of experiments with the goal of creating a super-conductor-semiconductor hybrid circuit quantum electrodynamics architecture with single electron spins. Single spins in silicon quantum dots have emerged as attractive qubits for quantum computation. However, how to scale up spin qubit systems remains an open question. The hybrid architecture considered here could provide a route to realizing large networks of quantum dot–based spin qubit registers. The first experiment in this thesis is aimed at achieving strong coupling between a single electron spin and a single microwave photon. The electron is trapped in a gate-defined double quantum dot in a Si/SiGe heterostructure and the photon is stored in an on-chip superconducting high-impedance NbTiN cavity. The photon is coupled directly to the electron charge, and indirectly to the electron spin, mediated through a synthetic spin-orbit field. We observe a vacuum Rabi splitting that depends on the spin-charge hybridization. The ratio of spin-photon coupling strength to decoherence rates of the spin and cavity combined is larger than unity, confirming the strong coupling regime has been reached. In addition, we find an optimal degree of spin-charge hybridization for which this ratio is maximized. The demonstration of strong spin-photon coupling not only opens a new range of physics experiments, but fulfills also a crucial requirement for coupling spin qubits at a distance via a cavity. The second experiment is focused on spin readout with the on-chip cavity. Instead of the direct dispersive readout of a single spin, we use the cavity to detect whether the electron is allowed to tunnel between the two dots or not. We benchmark the charge sensitivity and bandwidth of the detector and find that rapid detection of the electron charge with high SNR is possible. In the two-electron regime, electron tunneling is contingent on the total spin state (Pauli spin blockade). This spin-to-charge conversion scheme enables single-shot detection of singlet states with high-fidelity. The demonstration of single-shot spin readout with a cavity is an essential step towards readout in dense spin qubit arrays, such as the crossbar network, where it is not possible to integrate electrometers and accompanying reservoirs adjacent to the qubit dots. In the third experiment, we develop on-chip microwave filters to suppress microwave photon leakage from the cavity through the gate electrodes that are necessary to form quantum dots. We introduce a new cavity design that is compatible with long-distance connectivity between spins, but is also more susceptible to microwave leakage. We test and compare two low-pass filter variations in terms of performance, footprint and integrability. They use the same nanowire inductor, but different implementations of the capacitor: one with a planar interdigitated capacitor and one novel design with an overlapping thin-film capacitor. We find that both approaches are effective against microwave leakage. However, the large footprint of the interdigitated capacitor makes this solution inconvenient as the number of gate lines increases. The thin-film capacitor, with its much smaller footprint, is better suited for our devices. The final part of this dissertation contains concluding remarks and possible future directions are proposed.
The double-quantum-dot device benefits from the advantages of both the spin and charge qubits, while offering ways to mitigate their drawbacks. Careful gate voltage modulation can grant greater spinlike or chargelike dynamics to the device, yielding long coherence times with the former and high electrical susceptibility with the latter for electrically driven spin rotations or coherent interactions with microwave photons. As this architecture is a serious contender for the realization of a versatile physical qubit, improving its control is a critical step toward building a large-scale spin-based universal quantum computer. We show that optimal control pulses generated using the gradient ascent pulse engineering algorithm can yield higher fidelity operating regime transfers than can be achieved using linear methods.