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Multiseed Krylov complexity
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Multiseed Krylov complexity
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Krylov complexity is an attractive measure for the rate at which quantum operators spread in the space of all possible operators under dynamical evolution. One expects that its late-time plateau would distinguish between integrable and chaotic dynamics, but its ability to do so depends precariously on the choice of the initial seed. We propose to apply such considerations not to a single operator, but simultaneously to a collection of initial seeds in the manner of the block-Lanczos algorithm. We furthermore suggest that this collection should comprise all simple (few-body) operators in the theory, which echoes the applications of Nielsen complexity to dynamical evolution. The resulting construction, unlike the conventional Krylov complexity, reliably distinguishes integrable and chaotic Hamiltonians without any need for fine-tuning.
Forward citations
Cited by 10 Pith papers
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Polynomial Initial-State Jumps and Christoffel Transforms in Krylov Complexity
Changing the initial state to Q(H)|K0⟩ is exactly a Christoffel reweighting of the spectral measure by |Q|²; Krylov complexity then transfers from the reference problem through finite-band connectors and finite-rank k...
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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...
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Holographic Krylov Complexity for Charged, Composite and Extended Probes
Holographic Krylov complexity for charged composite and extended probes retains universal leading large-time growth but acquires structure-dependent subleading corrections.
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Holographic Spread Complexity from Branes and Strings
D0-branes in ABJM, rotating D3-branes, and wound strings realize holographic spread complexity via proper momentum and Routhian prescriptions that match short-time Krylov behavior.
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Controlled Chaos in 4D SCFTs
Orbifolds of N=4 SYM produce SCFTs whose dilatation operator in a subsector is realized by a tunable spin chain whose eigenvalue statistics exhibit chaos for specific marginal couplings.
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Bridging Krylov Complexity and Universal Analog Quantum Simulator
Generalized Krylov complexity predicts the minimum time to realize target operations in analog quantum simulators such as Rydberg atom arrays.
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Black Hole States in Quantum Spin Chains
An equal-weight superposition of all non-crossing singlet pairings in a Heisenberg chain shows logarithmic entanglement growth (c≈5.2) and near-infinite-temperature thermalization.
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Quantum Cosmology in Krylov Space: Complexity and Entropy
In a sharply peaked Gaussian state of a flat FLRW universe with a massless scalar clock, Krylov state complexity grows as σ²(φ−φ0)²/4 and operator complexity is exactly twice that, in both Wheeler-DeWitt and loop quan...
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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.
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A Quantum Computational Perspective on Spread Complexity
Spread complexity is recovered as the infinitesimal-time limit of a circuit complexity defined by minimal-cost synthesis with time-evolution and beam-splitting operations.
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