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Optimal control and speed limits of two-qubit quantum gates
Basyildiz, Bora
Basyildiz, Bora
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2024
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The speed of elementary quantum gates, especially two-qubit gates, sets a fundamental limit on how fast a quantum computer can run. For current quantum computers that are subject to noise and errors, the speed of quantum gates is even more important as qubits have finite coherence times, and faster quantum gates directly lead to a larger circuit depth. This is crucial in solving real-world problems. For a simple system made of just two qubits, the speed limit of a given two-qubit gate is proportional to the interaction strength between the two qubits, and this can be found exactly, if arbitrarily fast single qubit gates are allowed. The knowledge of such speed limits allows one to design gate protocols that are speed optimized. However, for more complicated scenarios, the exact speed limit of two-qubit gates is generally unknown.
In this thesis, we study the speed limits of two-qubit gates for a system of two interacting qudits. In many quantum computing platforms, there exist extra physical states outside the qubit subspace that can be well controlled, and these states may enable faster implementations of two-qubit gate without increasing the physical interaction strength of the two qubits. However, the exact speedup for this is not known. Thus in this work we derive a rigorous upper bound for this speedup, and we further show that for experimentally relevant systems we can saturate this bound exactly, showing that a time optimal gate protocol exists in the absence of noise and off-resonant transitions. For a practical experiment, we need to consider the off-resonant transitions due to the strong but finite-strength single-qudit drives. We again develop and use quantum optimal control software to generate optimized drive pulses that achieve high-fidelity target two-qubit gates using two qutrits close to their theoretical speed limits. We expect our results to be testable in near-term experiments with parametrically coupled transmons.
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