REVIEW 7 cited by
Ultimate Speed Limits to the Growth of Operator Complexity
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
In an isolated system, the time evolution of a given observable in the Heisenberg picture can be efficiently represented in Krylov space. In this representation, an initial operator becomes increasingly complex as time goes by, a feature that can be quantified by the Krylov complexity. We introduce a fundamental and universal limit to the growth of the Krylov complexity by formulating a Robertson uncertainty relation, involving the Krylov complexity operator and the Liouvillian, as generator of time evolution. We further show the conditions for this bound to be saturated and illustrate its validity in paradigmatic models of quantum chaos.
Forward citations
Cited by 7 Pith papers
-
Polynomial Initial-State Jumps and Christoffel Transforms in Krylov Complexity
Polynomial changes of the initial state in Krylov complexity are solved exactly via Christoffel transforms of the spectral measure, yielding finite-band amplitude transfer and projected-kernel complexity formulas with...
-
Recursion Coefficients and Krylov Dynamics in Polynomial Random Matrix Models
Recursion coefficients for high-degree asymmetric polynomial random matrix models are computed efficiently via a moment recursion, with large-n asymptotics reproducing Freud's conjecture and transition regions mapped ...
-
Krylov Complexity in Mixed Phase Space
The Krylov complexity peak height correlates with the Brody parameter in mixed-phase-space quantum systems, diminishing as the spectrum becomes Poissonian.
-
Krylov Complexity in the Schr\"odinger Field Theory
For bosonic and fermionic Schrödinger fields with chemical potential μ≤0, the Lanczos coefficients grow linearly and the Krylov complexity grows exponentially with an extracted rate near 2.75/β, below the 4/β slope pr...
-
Emergence of Krylov complexity through quantum walks: An exploration of the quantum origins of complexity
Reducing a graph walk to distance-layers reproduces Krylov/spread complexity, yielding analytic finite-q SYK Lanczos coefficients and hypercube complexity D sin²(t/D), with faster saturation than classical-walk circuits.
-
Statistics and Complexity of Wavefunction Spreading in Quantum Dynamical Systems
The moments of the spreading-operator measurement distribution are generalized spread complexities, which for GUE Hamiltonians peak more sharply at higher order and obey a norm bound.
-
Revisit the relationship between spread complexity rate and radial momentum
The paper shows that two proposed bulk momentum and boundary spread complexity correspondences are consistent, and that the match extends to any particle mass in AdS3.
Discussion (0). Continue with ORCID to comment.