Operator complexity for quantum scalar fields and cosmological perturbations

Haque, S. Shajidul; Jana, Chandan; Underwood, Bret

doi:10.1103/physrevd.106.063510

Cited by 11 publications

(3 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Computational complexity, a well-known entity in the context of computer science and associated mathematical subfields like graph theory, is still very much a shiny new concept in high energy physics. While the primary motivation for its introduction in the latter was the understanding of the black hole information-loss paradox, it has proven far more versatile with recent applications to the emergence of spacetime in quantum gravity, early universe cosmology [64][65][66][67] and even condensed matter physics. It is this last aspect that is the focus of this article.…”

Section: Discussionmentioning

confidence: 99%

Spread complexity and topological transitions in the Kitaev chain

Caputa

Gupta

Haque

et al. 2023

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

A number of recent works have argued that quantum complexity, a well-known concept in computer science that has re-emerged recently in the context of the physics of black holes, may be used as an efficient probe of novel phenomena such as quantum chaos and even quantum phase transitions. In this article, we provide further support for the latter, using a 1-dimensional p-wave superconductor — the Kitaev chain — as a prototype of a system displaying a topological phase transition. The Hamiltonian of the Kitaev chain manifests two gapped phases of matter with fermion parity symmetry; a trivial strongly-coupled phase and a topologically non-trivial, weakly-coupled phase with Majorana zero-modes. We show that Krylov-complexity (or, more precisely, the associated spread-complexity) is able to distinguish between the two and provides a diagnostic of the quantum critical point that separates them. We also comment on some possible ambiguity in the existing literature on the sensitivity of different measures of complexity to topological phase transitions.

show abstract

Section: Discussionmentioning

confidence: 99%

Spread complexity and topological transitions in the Kitaev chain

Caputa

Gupta

Haque

et al. 2023

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Similar deformations also appear in the context of cosmological perturbations. One could also study these path integral optimization in de Sitter space. Recently in [122–124] Circuit Complexity, Krylov complexity [ 125,126 ] and entanglement have been explored in the continuous variable system, the open quantum systems, in interacting QFTs and also in the quenched quantum systems. [ 127 ] It is interesting to pursue similar analysis for the quantum complexity and the entanglement in the context of cosmological perturbations.…”

Section: Discussionmentioning

confidence: 99%

Causality Constraint on Circuit Complexity from COSMOEFT

Choudhury

Mukherjee

Pandey

et al. 2023

Fortschritte der Physik

View full text Add to dashboard Cite

In this article, we investigate the physical implications of the causality constraint via the effective speed of sound cs(≤1)$c_s(\le 1)$ on Quantum Circuit Complexity (QCC) in the framework of Cosmological Effective Field Theory (COSMOEFT) using the two‐mode squeezed quantum states. This COSMOEFT setup is constructed using the Stnormalü$\ddot{\text{u}}$ckelberg trick with the help of the lowest dimensional operators, which are broken under time diffeomorphism. In this setup, we consider only the contributions from the two derivative terms in the background quasi‐de Sitter metric. Next, we compute the relevant measures of the circuit complexity and their cosmological evolution for different values of cs$c_s$ by following two different approaches, the Nielsen's approach and the Covariance matrix approach. Using this setup, we also compute the Von‐Neumann and the Rényi entropy, which finally establishes an underlying relationship between the entanglement entropy and the circuit complexity. Considering the scale factor and cs$c_s$ as parameters, our analysis of the circuit complexity measures and the entanglement entropy suggests several interesting unexplored features within the window, 0.024≤cs≤1$0.024\le c_s\le 1$, which is supported by both causality and cosmological observation. Finally, we comment on the connection between the circuit complexity, the entanglement entropy and the equilibrium temperature for different cs$c_s$ values lying within the mentioned window.

show abstract

“…Before proceeding further, it is worthwhile to reflect on the physical expectations for Krylov complexity. The Hamiltonians we consider are similar to harmonic oscillator and inverted harmonic oscillator studied previously in the complexity literature [8,10,34] (see also the su(1, 1) example in [13,35]). Indeed, when using the creation / annihilation operator representation, these systems are related by a shift of the creation / annihilation operators and Bogoliubov transformation.…”

Section: K-complexitymentioning

confidence: 99%

Krylov complexity for Jacobi coherent states

Haque,

Murugan,

Tladi

et al. 2024

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

We develop computational tools necessary to extend the application of Krylov complexity beyond the simple Hamiltonian systems considered thus far in the literature. As a first step toward this broader goal, we show how the Lanczos algorithm that iteratively generates the Krylov basis can be augmented to treat coherent states associated with the Jacobi group, the semi-direct product of the 3-dimensional real Heisenberg-Weyl group H1, and the symplectic group, Sp(2, ℝ) ≃ SU(1, 1). Such coherent states are physically realized as squeezed states in, for example, quantum optics [1]. With the Krylov basis for both the SU(1, 1) and Heisenberg-Weyl groups being well understood, their semi-direct product is also partially analytically tractable. We exploit this to benchmark a scheme to numerically compute the Lanczos coefficients which, in principle, generalizes to the more general Jacobi group Hn ⋊ Sp(2n, ℝ).

show abstract

Operator complexity for quantum scalar fields and cosmological perturbations

Cited by 11 publications

References 45 publications

Spread complexity and topological transitions in the Kitaev chain

Spread complexity and topological transitions in the Kitaev chain

Causality Constraint on Circuit Complexity from COSMOEFT

Krylov complexity for Jacobi coherent states

Contact Info

Product

Resources

About