| Summary: | <p>Quantum computing is considered an emerging technology with promising applications in chemistry, materials, medicine, and cryptography. Superconducting circuits are a leading candidate hardware platform for the realisation of quantum computing, and superconducting devices have now been demonstrated at a scale of hundreds of qubits. Further scale-up faces challenges in wiring, frequency crowding, and the high cost of control electronics. Complementary to increasing the number of qubits, using qutrits (3-level systems) or qudits (d-level systems, d>3) as the basic building block for quantum processors can also increase their computational capability. A commonly used superconducting qubit design, the transmon, has more than two levels. It is a good candidate for a qutrit or qudit processor. Variational quantum algorithms are a type of quantum algorithm that can be implemented on near-term devices. They have been proposed to have a higher tolerance to noise in near-term devices, making them promising for near-term applications of quantum computing. The difference between qubits and qudits makes it non-trivial to translate a variational algorithm designed for qubits onto a qudit quantum processor. The algorithm needs to be either rewritten into a qudit version or an emulator needs to be developed to emulate a qubit processor with a qudit processor.</p>
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<p>This thesis describes research on the implementation of variational quantum algorithms, with a particular focus on utilising more than two computational levels of transmons. The work comprises building a two-qubit transmon device and a multi-level transmon device that is used as a qutrit or a qudit (<i>d</i> = 4). We fully benchmarked the two-qubit and the single qudit devices with randomised benchmarking and gate-set tomography, and found good agreement between the two approaches. The qutrit Hadamard gate is reported to have an infidelity of 3.22 ± 0.11 × 10<sup>−3</sup>, which is comparable to state-of-the-art results. We use the qudit to implement a two-qubit emulator and report that the two-qubit Clifford gate randomised benchmarking result on the emulator (infidelity 9.5 ± 0.7 × 10<sup>−2</sup>) is worse than the physical two-qubit (infidelity 4.0 ± 0.3 × 10<sup>−2</sup>) result. We also implemented active reset for the qudit transmon to demonstrate preparing high-fidelity initial states with active feedback. We found the initial state fidelity improved from 0.900 ± 0.011 to 0.9932 ± 0.0013 from gate set tomography.</p>
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<p>We finally utilised the single qudit device to implement quantum algorithms. First, a single qutrit classifier for the iris dataset was implemented. We report a successful demonstration of the iris classifier, which yields the training accuracy of the qutrit classifier as 0.96 ± 0.03 and the testing accuracy as 0.94 ± 0.04 among multiple trials. Second, we implemented a two-qubit emulator with a 4-level qudit and used the emulator to demonstrate a variational quantum eigensolver for hydrogen molecules. The solved energy versus the hydrogen bond distance is within 1.5 × 10<sup>−2</sup> Hartree, below the chemical accuracy threshold.</p>
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<p>From the characterisation, benchmarking results, and successful demonstration of two quantum algorithms, we conclude that higher levels of a transmon can be used to increase the size of the Hilbert space used for quantum computation with minimal extra cost.</p>
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