Quantum Algorithm for Reversing Unknown Unitary Evolutions

Understand

Reversing an unknown quantum evolution is of central importance to quantum information processing and fundamental physics, yet it remains a formidable challenge as conventional methods necessitate an infinite number of queries to fully characterize the quantum process.

• Here we introduce the Quantum Unitary Reversal Algorithm (QURA), a deterministic and exact approach to universally reverse arbitrary unknown unitary transformations using $\mathcal{O}(d^2)$ calls of the unitary, where $d$ is the system dimension.
• Our quantum algorithm resolves a fundamental problem of time-reversal simulations for closed quantum systems by confirming the feasibility of reversing any unitary evolution without knowing the exact process.
• The algorithm also provides the construction of a key oracle for unitary inversion in many quantum algorithm frameworks, such as quantum singular value transformation.