New Measure of Quantum Complexity Could Reshape Computing Design
Physicists have developed a new framework for measuring how quickly quantum information spreads through a system, introducing a metric called "Koherence" that tracks sensitivity to tiny changes in initial conditions. The work reveals fundamental limits in how effectively quantum computers and simulations can scale, with direct implications for hardware design and the viability of certain quantum algorithms in real systems.
Originaltitel: Variations on a theme of Krylov
<p>Spread complexity uses the distribution of support of a time-evolving state in the Krylov basis to quantify dispersal across accessible dimensions of a Hilbert space. Here, we describe how variations in initial conditions, the Hamiltonian, and the dimension of the Hilbert space affect spread complexity and Krylov basis structure. We introduce <em>Koherence</em>, the entropy of coherence between perturbed and unperturbed Krylov bases, which can, e.g., quantify dynamical amplification of differences in initial conditions in chaos. To illustrate, we show that dynamics on SL(2, <em>ℝ</em>), SU(2), and Heisenberg-Weyl group manifolds, often used as paradigmatic settings for contrasting chaotic and integrable (semi-)classical behavior, display distinctively different responses to variations of the initial state or Hamiltonian. We then describe a lattice model that displays linear growth of spread complexity, saturating for bounded lattices and continuing forever in a thermodynamic limit. The latter example illustrates a breakdown of continuum/classical effective descriptions of complexity growth in bounded quantum systems.</p>