Complexity of mixed Gaussian states from Fisher information geometry
Giuseppe Di Giulio, Erik Tonni
Abstract
A bstract We study the circuit complexity for mixed bosonic Gaussian states in harmonic lattices in any number of dimensions. By employing the Fisher information geometry for the covariance matrices, we consider the optimal circuit connecting two states with vanishing first moments, whose length is identified with the complexity to create a target state from a reference state through the optimal circuit. Explicit proposals to quantify the spectrum complexity and the basis complexity are discussed. The purification of the mixed states is also analysed. In the special case of harmonic chains on the circle or on the infinite line, we report numerical results for thermal states and reduced density matrices.
Topics & Concepts
Fisher informationPhysicsGaussianCovarianceState (computer science)HarmonicBasis (linear algebra)Circuit complexitySpectrum (functional analysis)Computational complexity theoryStatistical physicsInformation geometryAlgorithmTopology (electrical circuits)GeometryInformation theoryDegrees of freedom (physics and chemistry)Quantum mechanicsGaussian processApplied mathematicsCurrent (fluid)Theoretical physicsCoherent statesThermalEigenvalues and eigenvectorsQuantum many-body systemsQuantum Information and CryptographyQuantum Mechanics and Non-Hermitian Physics