相关论文: Complexity Growth in Integrable and Chaotic Models
Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing -- in studying the…
We study operator complexity on various time scales with emphasis on those much larger than the scrambling period. We use, for systems with a large but finite number of degrees of freedom, the notion of K-complexity employed in…
We study the complexity of both time-optimal and time sub-optimal quantum Hamiltonian evolutions connecting arbitrary source and a target states on the Bloch sphere equipped with the Fubini-Study metric. This investigation is performed in a…
We apply a notion of quantum complexity, called "Krylov complexity", to study the evolution of systems from integrability to chaos. For this purpose we investigate the integrable XXZ spin chain, enriched with an integrability breaking…
Under the Heisenberg evolution in chaotic quantum systems, initially simple operators evolve into complicated ones and ultimately cover the whole operator space. We study the growth of the operator ``size'' in this process, which is related…
Simulating the time dynamics of an observable under Hamiltonian evolution is one of the most promising candidates for quantum advantage as we do not expect efficient classical algorithms for this problem except in restricted settings. Here,…
We analyze the dynamical evolution of systems which obey simple growth laws, like diffusion limited aggregation or dielectric breakdown. We show that, if the developing patterns is sufficiently complex, a scale invariant noise spectrum is…
We analyse time evolution of spread complexity (SC) in an isolated interacting quantum many-body system when it is subjected to a sudden quench. The differences in characteristics of the time evolution of the SC for different time scales is…
Self-gravitating systems of $N$ particles are chaotic. We wonder how chaotic the Galaxy is, and what the consequences are. We therefore simulate the dynamical evolution of a galaxy-scale distribution of point masses in order to measure the…
A natural example of evolution can be described by a time-dependent two degrees-of-freedom Hamiltonian. We choose the case where initially the Hamiltonian derives from a general cubic potential, the linearised system has frequencies 1 and…
We study time evolution of a subsystem's density matrix under unitary evolution, generated by a sufficiently complex, say quantum chaotic, Hamiltonian, modeled by a random matrix. We exactly calculate all coherences, purity and…
The Sachdev--Ye--Kitaev (SYK) model is a prominent model of strongly interacting fermions that serves as a toy model of quantum gravity and black hole physics. In this work, we study the Trotter error and gate complexity of the quantum…
Understanding how quantum chaotic systems generate entanglement can provide insight into their microscopic chaotic dynamics and can help distinguish between different classes of chaotic behavior. Using von Neumann entanglement entropy, we…
We study a sparse Sachdev-Ye-Kitaev (SYK) model with $N$ Majoranas where only $\sim k N$ independent matrix elements are non-zero. We identify a minimum $k \gtrsim 1$ for quantum chaos to occur by a level statistics analysis. The spectral…
We consider symplectic time integrators in numerical General Relativity and discuss both free and constrained evolution schemes. For free evolution of ADM-like equations we propose the use of the Stoermer-Verlet method, a standard…
We numerically analyze the complexity of unitary time-evolution and precursor operators in one- and two-qubit systems using the framework of Nielsen complexity geometry. We find that, as expected, the complexities of unitary time evolution…
The SYK model proposed by Sachdev, Ye, and Kitaev consists of Majorana fermions that interact randomly four at a time. The model develops a dense spectrum above the ground state, due to which the model becomes nearly conformal. This…
The circuit complexity for Hamiltonian simulation of the sparsified SYK model with $N$ Majorana fermions and $q=4$ (quartic interactions) which retains holographic features (referred to as `minimal holographic sparsified SYK') with $k\ll…
An evolution equation for a population of strings evolving under the genetic operators: selection, mutation and crossover is derived. The corresponding equation describing the evolution of schematas is found by performing an exact coarse…
The time evolution equations of a simplified isolated ideal gas, the "tetrahe- dral" gas, are derived. The dynamical behavior of the LMC complexity [R. Lopez-Ruiz, H. L. Mancini, and X. Calbet, Phys. Lett. A 209, 321 (1995)] is studied in…