Efficient Fully-Coherent Quantum Signal Processing Algorithms for Real-Time Dynamics Simulation

Understand

Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts.

• One prominent such instance is the simulation of electronic dynamics, which plays an essential role in chemical reactions, non-equilibrium dynamics, and material design.
• These systems are often time-dependent, which requires that the corresponding simulation algorithm can be successfully concatenated with itself over different time intervals to reproduce the overall coherent quantum dynamics of the system.
• In this paper, we quantify such simulation algorithms by a property called fully-coherent: the algorithm succeeds with arbitrarily high success probability $1-\delta$, while only requiring a single copy of the initial state.