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تسجيل مستخدم جديدAn upper bound on the time required to implement unitary operations
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We derive an upper bound for the time needed to implement a generic unitary transformation in a $d$ dimensional quantum system using $d$ control fields. We show that given the ability to control the diagonal elements of the Hamiltonian, which allows for implementing any unitary transformation under the premise of controllability, the time $T$ needed is upper bounded by $Tleq frac{pi d^{2}(d-1)}{2g_{text{min}}}$ where $g_{text{min}}$ is the smallest coupling constant present in the system. We study the tightness of the bound by numerically investigating randomly generated systems, with specific focus on a system consisting of $d$ energy levels that interact in a tight-binding like manner.
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