REVIEW 8 cited by
A Lanczos approach to the Adiabatic Gauge Potential
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
A Lanczos approach to the Adiabatic Gauge Potential
read the original abstract
The Adiabatic Gauge Potential (AGP) is the generator of adiabatic deformations between quantum eigenstates. There are many ways to construct the AGP operator and evaluate the AGP norm. Recently, it was proposed that a Gram-Schmidt-type algorithm can be used to explicitly evaluate the expression of the AGP. We employ a version of this approach by using the Lanczos algorithm to evaluate the AGP operator in terms of Krylov vectors and the AGP norm in terms of the Lanczos coefficients. It has the advantage of minimizing redundancies in evaluating the nested commutators in the analytic expression for the AGP operator. The algorithm is used to explicitly construct the AGP operator for some simple systems. We derive an integral transform relation between the AGP norm and the autocorrelation function of the deformation operator. We present a modification of the Variational approach to derive the regulated AGP norm. Using this, we approximate the AGP to varying degrees of success. Finally, we compare and contrast the quantum-chaos-probing capacities of the AGP and K-complexity in view of the Operator Growth Hypothesis.
Forward citations
Cited by 8 Pith papers
-
Shortcuts to Adiabaticity for non-Hermitian systems in Krylov Space
A diagonalization-free Krylov (bi-Lanczos/Arnoldi) construction yields exact or truncated adiabatic gauge potentials for non-Hermitian STA, reducing them to sparse matrix equations that suppress nonadiabatic excitatio...
-
Krylov Dynamics and Operator Growth in Time-Dependent Systems via Lie Algebras
The paper establishes a Lie-algebraic framework for exact Krylov dynamics in time-dependent quantum systems and introduces a quantum speed limit for complexity growth that retains its time-independent form but saturat...
-
Krylov Dynamics and Operator Growth in Time-Dependent Systems via Lie Algebras
A Lie-algebraic framework unifies Krylov dynamics for time-dependent Hamiltonians, yielding a quantum speed limit whose saturation requires time-commuting Hamiltonians.
-
Scalable Acceleration of Many-Body Quantum Dynamics via Time-Rescaling
Time-rescaling accelerates many-body quantum dynamics beyond prior regimes, improving Ising-model annealing fidelity and GHZ-state preparation while the Mandelstam-Tamm limit is offset by larger energy fluctuations.
-
Feedback-based quantum optimization and its classical counterpart: quantum advantage and the power of classical algorithms
Classical feedback-based optimization matches or exceeds quantum performance in speed and scalability while quantum retains an edge in final solution quality on tested instances.
-
Partial Reversibility and Counterdiabatic Driving in Nearly Integrable Systems
Slow integrability-breaking ramps in degenerate systems leave a finite irreversible energy spread that local counterdiabatic driving cannot fully remove.
-
Krylov Complexity Under Hamiltonian Deformations and Toda Flows
Certain Hamiltonian deformations preserve the Krylov subspace, yielding generalized Toda equations and allowing imaginary-time dynamics to be recast as real-time unitary evolution, with applications to thermodynamic s...
-
Quantum Dynamics in Krylov Space: Methods and Applications
Krylov subspace methods efficiently describe quantum evolution, operator growth, and chaos in many-body systems, with metrics like Krylov complexity and applications in open systems, QFT, and quantum computing.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.