The growing interest in quantum computers has triggered various approaches for the realization of a large-scale quantum processor that can eventually outperform classical high-performance computers. Quantum computers are attracting increasing attention for their potential to enormously accelerate the simulation of quantum systems and the solution of optimization problems, promising an immense impact, particularly in fields such as chemistry, medicine, and cybersecurity. Although it is still a long way to a practical quantum device, the progress over the last decades has shown encouraging results for a so far limited number of quantum bits, or qubits for short, which represent the computational units of the processor. One promising platform for the implementation of qubits is the spin of charge carriers in semiconductor quantum dots. Especially the use of purified silicon as a host material has significantly improved the performance of quantum operations. Advanced fabrication techniques from the established semiconductor industry in principle allow for the manufacturing of a large number of qubits on a small chip, making them specifically competitive from the perspective of scalability. In this thesis, we investigate challenges for electron spin qubits, particularly in the context of scaling to large qubit arrays for quantum computation. We evaluate the performance of quantum gates, present error mitigation strategies, and propose new quantum operations for two particular spin qubit implementations. In a dense array of Loss-DiVincenzo spin qubits on a chip, quantum information can be electrically controlled by microwave pulses. For neighboring qubits, capacitive couplings of nearby electrodes lead to crosstalk that affects the quantum computation. The first examination in this thesis addresses the effect of crosstalk on idling and operating spin qubits due to an interfering microwave drive. After the analysis and characterization of the performance, we suggest mitigation protocols for different constellations of important quantum gates, which can be easily implemented experimentally. We further show how to reduce crosstalk in a two-qubit gate using an asymmetric driving scheme, resulting in an enormous improvement of the gate performance, and may be used to generally overcome the obstacle of crosstalk. An additional source of errors in spin qubit registers originates from the finite residual exchange interaction between neighboring qubits. It arises due to a finite overlap of the electron wave functions and is caused by the limited speed at which the applied voltages can be controlled. We evaluate the fidelity of doing quantum operations under these circumstances with a varying number of neighboring qubits and present robust mitigation schemes with a decent performance also in the presence of noise. Besides crosstalk, another crucial observation in experiments using microwaves is the heating caused by the delivery of high-power radio frequency pulses to the quantum chip and results in a change of the qubit properties. We therefore investigate the impact of phonons on the energy levels in spin qubits to identify a temperature-dependent correction to the qubit state splitting. As microwave pulses are associated with potential errors, exchange-only qubits represent a promising alternative to achieve universal quantum computation only using baseband control. Therefore, we shift our focus towards exchange-only qubits and outline the main error sources in these systems, including residual exchange interactions between spins, charge noise from the applied voltages, and magnetic fluctuations in the material. A consequential complication of this implementation is that the quantum information can leak out of the qubit states. This effect, however, can be reduced in the presence of a finite magnetic field, as we will demonstrate in this thesis. The gate construction for exchange-only qubits usually requires more pulse steps than in the previous qubit type. Nevertheless, if exchange interactions are switched on simultaneously, this can result in faster quantum gates, as we demonstrate in this thesis. Especially the discovery of a quantum operation that introduces relative phases between computational and leakage states can be of interest for the construction of two-qubit gates and will be discussed in an example for a special operation space.
The growing interest in quantum computers has triggered various approaches for the realization of a large-scale quantum processor that can eventually outperform classical high-performance computers. Quantum computers are attracting increasing attention for their potential to enormously accelerate the simulation of quantum systems and the solution of optimization problems, promising an immense impact, particularly in fields such as chemistry, medicine, and cybersecurity. Although it is still a long way to a practical quantum device, the progress over the last decades has shown encouraging results for a so far limited number of quantum bits, or qubits for short, which represent the computational units of the processor. One promising platform for the implementation of qubits is the spin of charge carriers in semiconductor quantum dots. Especially the use of purified silicon as a host material has significantly improved the performance of quantum operations. Advanced fabrication techniques from the established semiconductor industry in principle allow for the manufacturing of a large number of qubits on a small chip, making them specifically competitive from the perspective of scalability. In this thesis, we investigate challenges for electron spin qubits, particularly in the context of scaling to large qubit arrays for quantum computation. We evaluate the performance of quantum gates, present error mitigation strategies, and propose new quantum operations for two particular spin qubit implementations. In a dense array of Loss-DiVincenzo spin qubits on a chip, quantum information can be electrically controlled by microwave pulses. For neighboring qubits, capacitive couplings of nearby electrodes lead to crosstalk that affects the quantum computation. The first examination in this thesis addresses the effect of crosstalk on idling and operating spin qubits due to an interfering microwave drive. After the analysis and characterization of the performance, we suggest mitigation protocols for different constellations of important quantum gates, which can be easily implemented experimentally. We further show how to reduce crosstalk in a two-qubit gate using an asymmetric driving scheme, resulting in an enormous improvement of the gate performance, and may be used to generally overcome the obstacle of crosstalk. An additional source of errors in spin qubit registers originates from the finite residual exchange interaction between neighboring qubits. It arises due to a finite overlap of the electron wave functions and is caused by the limited speed at which the applied voltages can be controlled. We evaluate the fidelity of doing quantum operations under these circumstances with a varying number of neighboring qubits and present robust mitigation schemes with a decent performance also in the presence of noise. Besides crosstalk, another crucial observation in experiments using microwaves is the heating caused by the delivery of high-power radio frequency pulses to the quantum chip and results in a change of the qubit properties. We therefore investigate the impact of phonons on the energy levels in spin qubits to identify a temperature-dependent correction to the qubit state splitting. As microwave pulses are associated with potential errors, exchange-only qubits represent a promising alternative to achieve universal quantum computation only using baseband control. Therefore, we shift our focus towards exchange-only qubits and outline the main error sources in these systems, including residual exchange interactions between spins, charge noise from the applied voltages, and magnetic fluctuations in the material. A consequential complication of this implementation is that the quantum information can leak out of the qubit states. This effect, however, can be reduced in the presence of a finite magnetic field, as we will demonstrate in this thesis. The gate construction for exchange-only qubits usually requires more pulse steps than in the previous qubit type. Nevertheless, if exchange interactions are switched on simultaneously, this can result in faster quantum gates, as we demonstrate in this thesis. Especially the discovery of a quantum operation that introduces relative phases between computational and leakage states can be of interest for the construction of two-qubit gates and will be discussed in an example for a special operation space.
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 thesis addresses the concept of quantum computing with semiconductor quantum dots. The basic unit of a quantum computer is a quantum mechanical two-level system, the so-called quantum bit (qubit). The qubit can be defined as the spin of an electron confined in a quantum dot or as a two-dimensional subspace of the Hilbert space for several spins. Some semiconductors have several minima in their conduction band, socalled valleys. A two-dimensional valley degree of freedom can also be considered as a qubit. In this thesis, quantum registers storing spin as well as valley qubits are described theoretically. Virtual hopping yields an exchange interaction between neighboring quantum dots, which reduces the energy of antisymmetric spin-valley states according to the Pauli principle. Considering the spin and the valley degrees of freedom of two electrons in neighboring quantum dots as qubits, the exchange interaction is a four-qubit interaction. In this thesis, it will be shown that it is, nevertheless, possible to generate a universal two-qubit gate for spin qubits or for valley qubits by combining the exchange interaction and individual single-qubit gates. The exchange interaction in this two-electron double quantum dot directly provides a universal two-qubit gate for one spin and one valley qubit as well. For this, the qubits are defined as suitable subspaces, spanned by the singlet and one triplet state of the spin and the valley states, respectively, Using those gates, arbitrary quantum operations can be performed for single-spin and single-valley qubits in the same quantum register, where in one double quantum dot the quantum states are restricted to the singlet-triplet subspace. While in this register single-spin and single-valley rotations are required, these gates are dispensable in a quantum register storing spin and valley singlet-triplet qubits. The single-qubit operations, in this case, can be provided by the exchange interaction and a gradient in the energy splitting of spin and valley states when the spin qubit is stored in a double quantum dot with spin degrees of freedom only and when the spin states in the double quantum dot which stores the valley qubit are polarized. For providing the two-qubit gate, the spin and the valley qubits need to be stored in the same double quantum dot. The crucial task for this register is to interchange the spin of a spin-only and a spin-valley quantum dot in order to switch between the single-qubit and the two-qubit operation mode. This interchanging of the spin can be achieved by a valley-depending virtual hopping between the quantum dots. Furthermore, echo sequences for a so-called exchange-only qubit are considered. An exchange-only qubit is defined as a subspace in a system of three electron spins in a triple quantum dot. An inhomogeneous magnetic field, which may be caused by nuclear spins in the semiconductor, can lead to decoherence and leakage, i.e., the state might leave the qubit subspace. Suppressing this effect by an echo sequence which consists of pulses interchanging neighboring spin states, so-called SWAP gates, was proposed. Controllability over these quantum operations is provided via the exchange interaction. In this thesis, the performance of different such sequences is investigated. The analysis shows that optimization strategies developed for single spin echoes can be adapted for the three spin system. The echo sequences can be different in their order of applied SWAP gates interchanging the spins in the first and second dots or in the second and third dots. The noise suppression performance depends slightly on this order of SWAP gates. For two spins in a double quantum dot a scheme for quantum state tomography is presented. The corresponding measurement operators are constructed from a set of mutually unbiased bases of the four-dimensional two-qubit Hilbert space. These measurements are represented by short sequences of no more than three elementary quantum gates and projective measurements by the well-established spin-to-charge conversion.
There is currently a worldwide effort towards the realisation of large-scale quantum computers that exploit quantum phenomena for information processing. While these computing systems could potentially redefine the technological landscape, harnessing quantum effects is challenging due to their inherently fragile nature and the experimentally demanding environments in which they arise. In order for quantum computation to be viable it is first necessary to demonstrate the operation of two-level quantum systems (qubits) which have long coherence times, can be quickly read out, and can be controlled with high fidelity. Focusing on these key requirements, this thesis presents four experiments towards scalable solid state quantum computing using gate-defined quantum dot devices based on gallium arsenide (GaAs) heterostructures. The first experiment investigates a phonon emission process that limits the charge coherence in GaAs and potentially complicates the microwave control of multi-qubit devices. We show that this microwave analogy to Raman spectroscopy can provide a means of detecting the unique phonon spectral density created by a nanoscale device. Experimental results are compared to a theoretical model based on a non-Markovian master equation and approaches to suppressing electron-phonon coupling are discussed. The second experiment demonstrates a technique involving in-situ gate electrodes coupled to lumped-element resonators to provide high-bandwidth dispersive read-out of the state of a double quantum dot. We characterise the charge sensitivity of this method in the few-electron regime and benchmark its performance against quantum point contact charge sensors. The third experiment implements a low-loss, chip-level frequency multiplexing scheme for the readout of scaled-up spin qubit arrays. Dispersive gate-sensing is realised in combination with charge detection based on two radio frequency quantum point contacts to perform multiplexed readout of a double quantum dot in the few-electron regime. Demonstration of a 10-channel multiplexing device is achieved and limitations in scaling spin qubit readout to large numbers using multiplexed channels discussed. The final experiment ties previously presented results together by realising a micro-architecture for controlling and reading out qubits during the execution of a quantum algorithm. The basic principles of this architecture are demonstrated via the manipulation of a semiconductor qubit using control pulses that are cryogenically routed using a high-electron mobility transistor switching matrix controlled by a field programmable gate array. Finally, several technical results are also presented including the development of printed circuit board solutions to allow the high-frequency measurement of nanoscale devices at cryogenic temperatures and the design of on-chip interconnects used to suppress electromagnetic crosstalk in high-density spin qubit device architectures.
Quantum information processing in semiconductor quantum dots using single and multi-spin qubitsThe idea of a quantum computer, a device capable of processing information using quantum bits (qubit) instead of classical bits that outperforms classical computer in terms of computation speed, is still science ction. However, recent advances in quantum information processing showed that this ction may come true faster than anticipated. A promising platform for the physical realization of a qubit are spin qubits where the information is encoded in the quantum mechanical spin of an electron con ned in a semiconductor quantum dot. There are a variety of di erent implementations how the logical qubit is physically encoded, the use of a single electron spin or the use of the spins of multi electrons. This thesis focuses on the implementation of the spin- 1/2 qubit using the spin of a single electron in a single quantum dot, the exchangeonly (EO) qubit using three electron spins distributed in three quantum dots, and the novel quadrupolar exchange-only (QUEX) qubit using four electron spins distributed in three quantum dots. In this thesis we investigate several theoretical aspects of the physical implementation of the aforementioned qubit encodings. Since all three qubit encodings are allelectric controlled these implementations su er decoherence, the loss of information, from electric uctuations of the environment commonly called charge noise. Typically, the use of more quantum dots increases the decoherence due to charge noise while it decreases the decoherence due to magnetic noise. The rst main aspect investigated in this thesis is the protection of the quantum information encoded in the di erent qubit implementations against charge noise. Special attention is paid to the multi-electron spin implementations where high-symmetry points of operation are discovered which are less sensitive to the charge noise. Protection against charge noise is even better by increasing the number of electrons while keeping the number of quantum dots making the QUEX qubit superior to the EO qubit. So far the main direction in this thesis is the reduction of the qubit sensitivity to electric uctuations. However, coherent electromagnetic elds in form of microwaves v can be used to interconnect qubits. In this thesis also a high-performance coupling between two spin-1/2 is investigated. The use of a resonator, subsequently, allows for a coupling of qubits over macroscopic distances as well as to extract valuable information about the physical system. Because of the larger susceptibility of multi-spin qubits to the electric eld of the resonator, this thesis focuses on the coupling between an EO or a QUEX qubit and a microwave resonator. Points of operations are discovered for both qubit implementations which o er a strong coupling towards a microwave resonator while maintaining their protection against charge noise. Subsequently, a series of measurements are proposed to extract information about the microscopic structure of the quantum dots. Finally, a promising high-performance protocol for coupling two qubits remotely via the resonator is investigated in detail.
Modern society increasingly depends on ever more capable computing devices. Yet some important problems remain beyond the reach of classical computers due to their inherent computational complexity. At the same time, the energy required to power this growing computational demand is an important concern. Over the past decade, quantum computers have received increased attention, not as a replacement for classical systems, but as a complementary technology with the potential to tackle complex problems more efficiently and significantly boost computational performance. This is made possible by leveraging the principles of quantum mechanics. To achieve this, quantum computers rely on a fundamental basic block called a qubit. There are several different technologies for realizing qubits, and no single approach has yet established itself as the definitive choice. In this work, we focus on silicon spin qubits in quantum dots, which use the intrinsic spin states of an electron as the computational basis states. This platform offers notable advantages including long coherence times, compatibility with the existing semiconductor industry and scalability. However, this technology is still very immature and substantial progress is still required. Just like for the design of classical electronics, simulations can play a crucial role by reducing development cycles, lowering costs, and improving overall efficiency. Throughout this thesis, we will propose a comprehensive simulation framework that allows to study and design spin qubit systems focusing on key aspects of the system architecture. First, a spin qubit compact model is presented that enables the co-simulation of spin qubits together with the classical CMOS control and readout circuitry that will significantly impact the performance of the qubits. We show that the model is capable of including all elements to build an elementary quantum gate set and illustrate its use by co-simulating a spin qubit coupled to a readout resonator with a complete cryo-CMOS readout chip design in a commercial electronic design automation tool. Next, we discuss a hybrid-Hamiltonian simulation approach that is aimed at simulating spin qubit microarchitectures that are suited for running quantum error correction protocols, which protect the encoded information against the errors that unavoidably happen due to the inherently noisy physical qubit devices. This simulation approach incorporates several novel strategies to tackle the challenge of the required computing power that grows exponentially with the size of the simulated system. Furthermore, additional functionality is incorporated to evaluate and track the performance of the implemented error correction protocols. Finally, we propose a characterization protocol for constructing a correlated noise model of the charge noise that is an important factor affecting spin qubit performance. The sources of charge noise are modelled as two-level fluctuators and the entire qubit array is characterized by dividing it into patches and running batches of benchmarking quantum gate sequences. The resulting noise model enables to scale the simulations to larger system sizes and to study the system performance and hardware demands of error correction protocols. Together, these models form a multi-layer simulation framework that enables detailed analysis and optimization of future spin qubit microarchitectures, with particular emphasis on error correction protocols. As such, the framework contributes to the realization of practical large-scale quantum computing.
Electron spins in semiconductor devices are highly promising building blocks for quantum processors (QPs). Commercial semiconductor foundries can create QPs using the same processes used for conventional chips, once the QP design is suitably specified. There is a vast accessible design space; to identify the most promising options for fabrication, one requires predictive modeling of interacting electrons in real geometries and complex nonideal environments. In this work we explore a modeling method based on real-space grids, an approach without assumptions relating to device topology and therefore with wide applicability. Given an electrode geometry, we determine the exchange coupling between quantum dot qubits, and model the full evolution of a SWAP gate to predict qubit loss and infidelity rates for various voltage profiles. We determine full, three-dimensional solutions and introduce a method that can obtain near-identical predictions using far more efficient two-dimensional computations. Moreover we explore the impact of unwanted charge defects (static and dynamic) in the environment, and test robust pulse sequences. As an example we exhibit a sequence correcting both systematic errors and (unknown) charge defects, observing an order of magnitude boost in fidelity. The technique can thus identify the most promising device designs for fabrication, as well as bespoke control sequences for each such device.