Fault tolerant quantum computation with superconducting elements
MetadataShow full item record
Quantum computing with superconducting elements promises scalability and is widely regarded as a viable approach to develop a fault-tolerant architecture for a quantum computer. In this thesis, I address some hardware-related theoretical challenges encountered in realizing a quantum computer with superconducting devices. I first discuss how to design high-fidelity two-qubit entangling gates, especially the controlled-Z (CZ) operation, and then explore the performance of some existing fault-tolerant superconducting architectures under a realistic multi-parameter error model. Assuming phase or transmon qubits and using only low frequency qubit-bias control, our CZ operation exhibits threshold fidelity (intrinsic) with a realistic two-parameter pulse profile. In addition, we develop an analytic model that estimates the fidelities of CZ gates as a function of pulse parameters as well as quantifies the error due to any perturbation over an optimal pulse shape. Our analysis shows that leakage of population to non-computational states remains the dominant source of intrinsic error for such quantum operations. The effect of such leakage errors on the fault-tolerance of standard topological codes has remained largely unknown so far. We therefore explore the signature and consequences of such leakage errors on ancilla-assisted Pauli operator measurement, which is a central ingredient for any standard topological error correction scheme. We consider a realistic coupled-qutrit model, parameterize the non-ideal CZ gate, and simulate the repeated ancilla-assisted measurement of a single Pauli Z operator. We find that there is the possibility of a less typical but dangerous type of leakage event in the data qubit, where ancilla becomes paralyzed, rendering it oblivious to data-qubit errors for many consecutive measurement cycles. The consequences of such paralysis on the fault-tolerance of standard topological codes are also discussed in this context. Next we consider a realistic, multi-parameter error model and investigate the performance of surface code error correction for some possible superconducting architectures. We map amplitude and phase damping to the Pauli channel via the Pauli Twirling Approximation, and obtain the logical error rate as a function of the qubit coherence time, intrinsic state preparation, and gate and readout errors. A numerical Monte Carlo simulation is performed to obtain the logical error rates and a leading order analytic model is constructed to estimate their scaling behavior below threshold. Our results suggest that large-scale fault-tolerant quantum computation should be possible with existing superconducting devices.