Exact quantum dynamics for two-level systems with time-dependent driving

Abstract

It is well-known that time-dependent Schrödinger equation can only be exactly solvable in very rare cases, even for two-level quantum systems. Therefore, finding exact quantum dynamics under time-dependent Hamiltonian is not only of fundamental importance in quantum physics but also can facilitate active quantum manipulations for quantum information processing. Here, we present a method which could generate a near infinite number of analytical-assisted solutions of the Schrödinger equation for a qubit with time-dependent driving. This analytical-assisted solution has free parameters with only boundary restrictions, and thus can find many applications in precise quantum manipulations. Due to the general form of the time-dependent Hamiltonian in our scheme, it can be readily implemented in various experimental setups of qubits. Therefore, our scheme provides new solutions for Schrödinger equation, thus provides an alternative and analytical-based routine for precise control over qubits.

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