Abstract
Benchmarking the performance of a quantum computer is of key importance in identifying and reducing the error sources, and therefore in achieving faulttolerant quantum computation. In the last decade, qubits made of electron spins in silicon emerged as promising candidates for practical quantum computers. To understand their physical properties and the engineering challenges behind, a complete characterization of coupled spin qubits is highly demanded. This dissertation presents extensive studies on performance benchmarking of silicon quantum processors, covering the aspects of quantum logic, quantum measurement, crosstalk and error correlations, and cryogenic quantum control.
The first experiment presented in this dissertation reports the complete characterization of a universal set of quantum gates for silicon spin qubits. As a powerful alternative to conventional Cliffordbased single and twoqubit randomized benchmarking, we introduce a new approach named character randomized benchmarking. We use it to extract a fidelity of 92% for a controlledZ gate, and show that the crosstalk and error correlations between simultaneous singlequbit gates can be quantified in the same experiment.
The second experiment is focused on the spatial noise correlation between two idling spin qubits. Such correlated noise is critical in quantum error correction. We characterize such correlations by measuring the coherence times of two different twoqubit Bell states with parallel and antiparallel spins respectively, and find only modest correlations. This is likely due to the existence of uncorrelated nuclear noise arising from ^29Si atoms.
In the third experiment, we observe strong nonlinear effects in electricdipole spin resonance, which is the key mechanism for implementing singlequbit gates in all works presented in this dissertation. Importantly, this induces a novel crosstalk effect between simultaneously driven qubits. The valleyorbit hybridization is investigated and found to give a phenomenological explanation of such nonlinearity. Further studies in material properties and microwave heating effects are needed to explain the discrepancy.
The fourth experiment is about quantum nondemolition measurement of a spin qubit, which is an essential building block of quantum error correction codes. Helped by an ancilla qubit, we can significantly improve the readout fidelity of the data qubit from ∼75% to ∼95% after 15 repetitive measurements. We experimentally test an improved signal processing method, namely soft decoding, and showcase its advantage when Gaussian noise dominates the readout errors.
In the fifth experiment, we finally break the barrier of 99% for the fidelity of the twoqubit gate for semiconductor spin qubits. Combining isotopically purified silicon, careful Hamiltonian engineering of exchange interactions, and error diagnosis from gate set tomography, we achieve fidelities of all single and twoqubit gates of over 99.5%, well above the popular surface code error threshold. Powered by the highfidelity universal gate set, we are able to execute a variational quantum eigensolver routine for computing the dissociation energy of molecular hydrogen with the silicon quantum processor.
The last experiment steers the focus towards the interface between quantum processor and classical control electronics, known as a major bottleneck in scaling. We propose to solve the problem by utilizing control circuits working at a few Kelvin. A control chip named "Horse Ridge'' is therefore tested at 3 Kelvin and demonstrated to match the same control fidelities obtained using bulky commercial instruments working at room temperature, at a cost of only a few hundred milliwatts. The functionality of this control chip is further tested by operating universal twoqubit logic as well as executing a twoqubit DeutschJosza algorithm.
At the end of this dissertation, we propose a few possible nextsteps to further explore the error sources in spin qubits and approaches for scalable operations.
The first experiment presented in this dissertation reports the complete characterization of a universal set of quantum gates for silicon spin qubits. As a powerful alternative to conventional Cliffordbased single and twoqubit randomized benchmarking, we introduce a new approach named character randomized benchmarking. We use it to extract a fidelity of 92% for a controlledZ gate, and show that the crosstalk and error correlations between simultaneous singlequbit gates can be quantified in the same experiment.
The second experiment is focused on the spatial noise correlation between two idling spin qubits. Such correlated noise is critical in quantum error correction. We characterize such correlations by measuring the coherence times of two different twoqubit Bell states with parallel and antiparallel spins respectively, and find only modest correlations. This is likely due to the existence of uncorrelated nuclear noise arising from ^29Si atoms.
In the third experiment, we observe strong nonlinear effects in electricdipole spin resonance, which is the key mechanism for implementing singlequbit gates in all works presented in this dissertation. Importantly, this induces a novel crosstalk effect between simultaneously driven qubits. The valleyorbit hybridization is investigated and found to give a phenomenological explanation of such nonlinearity. Further studies in material properties and microwave heating effects are needed to explain the discrepancy.
The fourth experiment is about quantum nondemolition measurement of a spin qubit, which is an essential building block of quantum error correction codes. Helped by an ancilla qubit, we can significantly improve the readout fidelity of the data qubit from ∼75% to ∼95% after 15 repetitive measurements. We experimentally test an improved signal processing method, namely soft decoding, and showcase its advantage when Gaussian noise dominates the readout errors.
In the fifth experiment, we finally break the barrier of 99% for the fidelity of the twoqubit gate for semiconductor spin qubits. Combining isotopically purified silicon, careful Hamiltonian engineering of exchange interactions, and error diagnosis from gate set tomography, we achieve fidelities of all single and twoqubit gates of over 99.5%, well above the popular surface code error threshold. Powered by the highfidelity universal gate set, we are able to execute a variational quantum eigensolver routine for computing the dissociation energy of molecular hydrogen with the silicon quantum processor.
The last experiment steers the focus towards the interface between quantum processor and classical control electronics, known as a major bottleneck in scaling. We propose to solve the problem by utilizing control circuits working at a few Kelvin. A control chip named "Horse Ridge'' is therefore tested at 3 Kelvin and demonstrated to match the same control fidelities obtained using bulky commercial instruments working at room temperature, at a cost of only a few hundred milliwatts. The functionality of this control chip is further tested by operating universal twoqubit logic as well as executing a twoqubit DeutschJosza algorithm.
At the end of this dissertation, we propose a few possible nextsteps to further explore the error sources in spin qubits and approaches for scalable operations.
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  31 May 2022 
Print ISBNs  9789085935278 
DOIs  
Publication status  Published  2022 
Keywords
 quantum dots
 spin qubits
 quantum computation
 quantum benchmarking