Physics Practical Magic

One mathematical formula can teleport any quantum state no matter how big the system is.

April 20, 2026

Original Paper

How to unitarily map between any two pure states with a single closed-form exponential

Peter T. J. Bradshaw, Marcus Gouveia, Jonte R. Hance

arXiv · 2604.16285

The Takeaway

Quantum states are notoriously difficult to manipulate because the math usually gets exponentially harder as the system grows larger. Most transformations require specific, complex calculations tailored to the number of particles involved. This new closed-form exponential method works exactly the same way for two particles as it does for two trillion. It provides a universal shortcut for mapping between states without needing to know the underlying dimensions of the system. This efficiency could drastically speed up quantum computing operations and state preparation in complex laboratories. It effectively turns a specialized engineering hurdle into a simple, universal calculation.

From the abstract

It is well-known that any two pure quantum states (in the same Hilbert space) can be mapped to any other using unitary transformations. However, previous approaches to this problem required two explicit bases for the Hilbert space, one each for the initial and target states, and thus their complexity necessarily scales with the dimension of the Hilbert space. In this Letter, we show how to utilize novel algebraic methods to construct a closed-form exponential unitary transformation which achieve