| Summary: | Quantum computers promise huge speed-up over conventional computers in crucial problems like chemistry and materials simulations, decryption, and even machine learning. However, any imperfect manipulations of the qubits from which the machines are formed and any interactions with the environment can lead to errors and loss of their quantum properties. This thesis will develop practical schemes for fighting such errors in the quantum hardware and discuss possible applications of such noisy machines.
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We can protect the quantum information against noise by employing additional qubits and performing quantum error correction, whose experimental implementation has been brought much closer to reality via the recent rapid advance of quantum hardware, but challenges still remain. One example is coherent errors, which can grow much faster than regular errors. In this thesis, we tackle it by improving upon the conventional scheme that transforms it into regular errors using twirling, and also by developing a new scheme called Pauli conjugation that makes use of its coherent properties to our advantage. Implementations of quantum error correction codes also bring about hardware challenges like wiring packing and leakage errors. For the silicon spin qubit platform, these can be overcome by a surface code architecture we develop.
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It is challenging to use quantum error correction for the applications of near- term quantum hardware due to the constrained qubit count. Instead, we rely on quantum error mitigation to fight noise, which makes use of extra measurements instead of extra qubits. The Fermi-Hubbard variational quantum eigensolver is one of the most promising near-term quantum algorithms, thus we have performed a resource estimation for the task to gauge its feasibility. We then improve and combine the existing error mitigation schemes to boost their performance and thus to enhance the feasibility of near-term quantum algorithms, bringing practical applications of quantum hardware closer to reality.
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