Speed limits of two-qubit gates with qudits

• URL: http://arxiv.org/abs/2312.09218v1
• Date: Thu, 14 Dec 2023 18:49:11 GMT
• Title: Speed limits of two-qubit gates with qudits
• Authors: Bora Basyildiz, Casey Jameson, and Zhexuan Gong
• Abstract summary: We find an optimal theoretical bound for the speed limit of a two-qubit gate achieved using two qudits with a bounded interaction strength and arbitrarily fast single-qudit gates. We develop an open-source, machine learning assisted, quantum optimal control algorithm that can achieve a speedup close to the theoretical limit with near-perfect gate fidelity.
• Score: 0.5852077003870417
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The speed of elementary quantum gates ultimately sets the limit on the speed at which quantum circuits can operate. For a fixed physical interaction strength between two qubits, the speed of any two-qubit gate is limited even with arbitrarily fast single-qubit gates. In this work, we explore the possibilities of speeding up two-qubit gates beyond such a limit by expanding our computational space outside the qubit subspace, which is experimentally relevant for qubits encoded in multi-level atoms or anharmonic oscillators. We identify an optimal theoretical bound for the speed limit of a two-qubit gate achieved using two qudits with a bounded interaction strength and arbitrarily fast single-qudit gates. In addition, we find an experimentally feasible protocol using two parametrically coupled superconducting transmons that achieves this theoretical speed limit in a non-trivial way. We also consider practical scenarios with limited single-qudit drive strengths and off-resonant transitions. For such scenarios, we develop an open-source, machine learning assisted, quantum optimal control algorithm that can achieve a speedup close to the theoretical limit with near-perfect gate fidelity. This work opens up a new avenue to speed up two-qubit gates when the physical interaction strength between qubits cannot be easily increased while extra states outside the qubit subspace can be well controlled.

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