Quantum computation: algorithms and implementation in quantum dot devices

Matthew P. Wardrop

Since the mid-20th century it has been understood that a general-purpose quan- tum computer would be able to efficiently solve problems that will forever be out-of-reach for conventional computers. Since then, many quantum algorithms have been developed with applications in a wide range of domains including cryptography, simulations, machine learning and data analysis. While this has resulted in substantial attention being paid to the development of quantum com- puters, the best architectures to use in their fabrication is not yet clear. Semiconductor quantum dot devices are a particularly promising candidate for use in quantum computing architectures, as it is anticipated that once the funda- mental building blocks are implemented, they might be massively scalable using the existing lithography techniques of the semiconductor industry. So far, how- ever, it is not yet clear how best to implement the high-fidelity gates required for general-purpose quantum computation. In this thesis, we present and characterise novel theoretical proposals for fast, simple and high-fidelity two-qubit gates using magnetic (exchange) coupling for specific semiconductor quantum dot qubits; namely, the singlet-triplet and resonant-exchange qubits. These two-qubit operations are simple enough that it is feasible for them to be implemented in experiments of the near future. Success- ful implementations would significantly extend the experimentally demonstrable frontier of semi-conductor quantum dot devices as relevant to their use in uni- versal quantum computing architectures. We also develop simple parameter estimation schemes by which it is possible to substantially mitigate the dominant sources of error for our proposed gates; namely, low-frequency charge and magnetic noise. We develop the techniques in the context of pseudo-static magnetic field gradient fluctuations in singlet- triplet qubits, and demonstrate that these techniques lead to a several orders of magnitude improvement in single-qubit coherence times. With minimal effort this could be ported to other qubit architectures.

Amin Mobasher, Saeed Fathololoumi, Somayyeh Rahimi

Chien‐Hung Cho, Chih-Yu Chen, Kuo-Chin Chen +6 more

Javier Oliva del Moral, Olatz Sanz Larrarte, Reza Dastbasteh +2 more

Spin qubits in quantum dots are a promising technology for quantum computing due to their fast response time and long coherence times. An electromagnetic pulse is applied to the system for a specific duration to perform a desired rotation. To avoid decoherence, the amplitude and gate time must be highly accurate. In this work, we aim to study the impact of leakage during the gate time evolution of a spin qubit encoded in a double quantum dot device. We prove that, in the weak interaction regime, leakage introduces a shift in the phase of the time evolution operator, causing over- or under-rotations. Indeed, controlling the leakage terms is useful for adjusting the time needed to perform a quantum computation and increasing the coherence time of the readout process. This is crucial for running fault-tolerant algorithms and is beneficial for Quantum Error Mitigation techniques.

Hai‐Rui Wei, Fu‐Guo Deng

Parity-check building blocks are useful in quantum algorithms, quantum communications, and quantum computing, and such devices may be helpful in implementing robust universal quantum gates. We propose a scheme to construct a robust deterministic controlled-not gate on static electron-spin qubits with parity-check building blocks, assisted by double-sided-cavity quantum systems. Our device is robust against the polarization-flip errors, and it can work in both the weak coupling and strong coupling regimes, but high fidelity is achieved only when the ratio of the side leakage to the cavity loss is low. Our gate is heralded by the polarization of the single-photon medium. Finally, we assess the feasibility of this device and show it can be implemented with current technology.