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Krylov Spread Complexity of Quantum-Walks
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Krylov Spread Complexity of Quantum-Walks
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Given the recent advances in quantum technology, the complexity of quantum states is an important notion. The idea of the Krylov spread complexity has come into focus recently with the goal of capturing this in a quantitative way. The present paper sheds new light on the Krylov complexity measure by exploring it in the context of continuous-time quantum-walks on graphs. A close relationship between Krylov spread complexity and the concept of limiting-distributions for quantum-walks is established. Moreover, using a graph optimization algorithm, quantum-walk graphs are constructed that have minimal and maximal long-time average Krylov $\bar C$-complexity. This reveals an empirical upper bound for the $\bar C$-complexity as a function of Hilbert space dimension and an exact lower bound.
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Cited by 1 Pith paper
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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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