Optimization of Postselection in Quantum Algorithms: A Two-Way Quantum Computing Approach

Abstract: Postselection is an operation that allows the selection of specific measurement outcomes. It serves as a powerful theoretical tool for enhancing the performance of existing quantum algorithms. Despite recent developments such as time reversal in quantum measurements and IBM's mid-circuit measurements, postselection continues to face significant challenges, most notably poor, often exponential, scaling. This study investigates how Two-Way Quantum Computing (2WQC) offers potential solutions to these challenges. By introducing the concept of postparation and enabling dynamic quantum state control, 2WQC has the potential to mitigate scaling issues and improve the practicality of postselection, thereby fostering advancements in the field of quantum algorithms.