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

TL;DR

This paper introduces a method to generate numerous analytical solutions for the time-dependent Schrödinger equation in two-level quantum systems, enabling precise quantum control and manipulation.

Contribution

It presents a novel analytical-assisted solution scheme for the Schrödinger equation with time-dependent Hamiltonians, applicable to various qubit systems.

Findings

Provides a near-infinite set of analytical solutions with boundary restrictions.

Enables precise quantum manipulations and control.

Applicable to diverse experimental qubit setups.

Abstract

It is well-known that time-dependent Schr\"{o}dinger 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 Schr\"{o}dinger 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 Schr\"{o}dinger equation, thus provides an alternative and analytical-based routine for precise control over qubits.