Exact Quantum Speed Limits

TL;DR

This paper derives exact quantum speed limits for pure-state systems that outperform traditional bounds, enabling precise evolution time estimates and establishing bounds on quantum circuit complexity, impacting quantum physics and technologies.

Contribution

The authors develop exact quantum speed limits for pure states that surpass existing bounds and relate these limits to quantum circuit complexity.

Findings

Exact quantum speed limits outperform traditional bounds.

Derived an improved Mandelstam-Tamm bound saturating for self-inverse Hamiltonians.

Established an upper bound on quantum circuit complexity.

Abstract

The traditional quantum speed limits are not attainable for many physical processes, as they tend to be loose and fail to determine the exact time taken by quantum systems to evolve. To address this, we derive exact quantum speed limits for the unitary dynamics of pure-state quantum system that outperform the existing quantum speed limits. Using these exact quantum speed limits, we can precisely estimate the evolution time for two- and higher-dimensional quantum systems. Additionally, for both finite- and infinite-dimensional quantum systems, we derive an improved Mandelstam-Tamm bound for pure states and show that this bound always saturates for any unitary generated by self-inverse Hamiltonians. Furthermore, we show that our speed limits establish an upper bound on the quantum computational circuit complexity. These results will have a significant impact on our understanding of quantum physics as well as rapidly developing quantum technologies, such as quantum computing, quantum control and quantum thermal machines.