Related papers: Dependence of Krylov complexity on the initial ope…
Considering the large-$q$ expansion of the Sachdev-Ye-Kitaev (SYK) model in the two-stage limit, we compute the Lanczos coefficients, Krylov complexity, and the higher Krylov cumulants in subleading order, along with the $t/q$ effects. The…
The disorder and a simple convex measure of complexity are studied for rank ordered power law distributions, indicative of criticality, in the case where the total number of ranks is large. It is found that a power law distribution may…
We initiate an investigation into a notion of state complexity for discrete-variable quantum systems. Specifically, we propose an information-theoretic quantifier for the complexity of quantum states within the stabilizer formalism of…
Complexity is a fundamental characteristic of states within a quantum system. Its use is however mostly limited to bosonic systems, inhibiting its present applicability to supersymmetric theories. This is also relevant to its application to…
We investigate minimal two-body Hamiltonians with random interactions that generate spectra resembling those of Gaussian random matrices, a phenomenon we term quadratic quantum chaos. Unlike integrable two-body fermionic systems, the…
The symmetry-resolved Krylov complexity is a useful tool in studying chaotic properties of systems that are endowed with symmetries. We investigate the conditions under which an invariant operator would have the symmetry-resolved Krylov…
This work provides a nonasymptotic error analysis of quantum Krylov algorithms based on real-time evolutions, subject to generic errors in the outputs of the quantum circuits. We prove upper and lower bounds on the resulting ground state…
We investigate Krylov spread complexity for the ground state of two-band Hamiltonians, where the reference state is a generic state on the Bloch sphere. The spread complexity is obtained by using a purely geometric formulation in terms of…
One of the important open problems in quantum black hole physics is a dual interpretation of holographic complexity proposals. To date the only quantitative match is the equality between the Krylov spread complexity in triple-scaled SYK at…
We study quantum-to-classical correspondence of the Krylov space for evolutions driven by unitary maps with a classical limit. This entails a proper definition of corresponding quantum and classical operators, inner products and initial…
The notion of complexity of quantum states is quite different from uncertainty or information contents, and involves the tradeoff between its classical and quantum features. In this work, we we introduce a quantifier of complexity of…
We study the operator growth problem and its complexity in the many-body localization (MBL) system from the Lanczos algorithm perspective. Using the Krylov basis, the operator growth problem can be viewed as a single-particle hopping…
In this work, we investigate the relation between different notions of quantum complexity, namely, circuit and spread complexity and physically meaningful quantities such as the particle content of the quantum state and the variances of…
This paper presents a study of the inherent structural properties of Krylov subspaces, in particular for the self-adjoint class of operators, and how they relate with the important phenomenon of `Krylov solvability' of linear inverse…
We analyze the consequences of iterative measurement-induced nonlinearity on the dynamical behavior of qubits. We present a one-qubit scheme where the equation governing the time evolution is a complex-valued nonlinear map with one complex…
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…
In this paper we continue to develop our approach to the chaoticity properties of the quantum Hamiltonian systems. Our earlier suggested chaoticity criterion characterizes the initial symmetry breaking and the destruction of the…
The nonintegrable transverse-field Ising model is a common platform for studying ergodic quantum dynamics. In this work, we introduce a simple variant of the model in which this ergodic behaviour is suppressed by introducing a spatial…
We present a Krylov space based theoretical framework for modeling inhomogeneous spin ensembles with arbitrary distributions of spin frequencies and couplings. The framework is then used to asymptotically large spin ensemble. In the…
Operator scrambling is a crucial ingredient of quantum chaos. Specifically, in the quantum chaotic system, a simple operator can become increasingly complicated under unitary time evolution. This can be diagnosed by various measures such as…