Dr Shuxiang Cao

Abstract:

Machine learning is seen as a promising application of quantum computation. For near-term noisy intermediate-scale quantum devices, parametrized quantum circuits have been proposed as machine learning models due to their robustness and ease of implementation. However, the cost function is normally calculated classically from repeated measurement outcomes, such that it is no longer encoded in a quantum state. This prevents the value from being directly manipulated by a quantum computer. To solve this problem, we give a routine to embed the cost function for machine learning into a quantum circuit, which accepts a training dataset encoded in superposition or an easily preparable mixed state. We also demonstrate the ability to evaluate the gradient of the encoded cost function in a quantum state.

Abstract:

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.

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 (d = 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 × 10⁻³, 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 × 10⁻²) is worse than the physical two-qubit (infidelity 4.0 ± 0.3 × 10⁻²) 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.

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 × 10⁻² Hartree, below the chemical accuracy threshold.

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.