Nielsen complexity with multiple cost factors
Summary
arXiv:2606.02817v1 Announce Type: new Abstract: We investigate Nielsen's geometric approach to quantum complexity in the presence of multiple cost factors, extending the standard framework where a single penalty distinguishes easy from hard directions of the group manifold. By introducing a hierarchy of penalties associated with different degrees of non-locality, we develop a generalized right-invariant complexity geometry and analyze its implications for geodesic evolution. We derive the modified Euler-Arnold and Jacobi equations and study how multiple cost factors reshape the structure and scaling of conjugate points, where geodesic optimality breaks down.
Why It Matters
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Key Facts
- SectorQuantum
- Market—
- ImpactLow (42/100)
- SignalFunding Research