Related papers: Complexity and Momentum
The concepts of operator size and computational complexity play important roles in the study of quantum chaos and holographic duality because they help characterize the structure of time-evolving Heisenberg operators. It is particularly…
We demonstrate a precise relation between the rate of complexity of quantum states excited by local operators in two-dimensional conformal field theories and the radial momentum of particles in 3-dimensional Anti-de Sitter spacetimes.…
This article discusses the relationship between the boundary spread complexity rate and the radial momentum in the bulk within the framework of AdS/CFT. We demonstrate that the radial momentum of a freely falling particle, as measured by a…
In a recent note I argued that the holographic origin of gravitational attraction is the quantum mechanical tendency for operators to grow under time evolution. In a followup the claim was tested in the context of the SYK theory and its…
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 calculate the operator complexity for the displacement, squeeze and rotation operators of a quantum harmonic oscillator. The complexity of the time-dependent displacement operator is constant, equal to the magnitude of the coherent state…
To O(1/N) we derive, purely from CFT data, the bulk equations of motion for interacting scalar fields and for scalars coupled to gauge fields and gravity. We first uplift CFT operators to mimic local AdS fields by imposing bulk…
The rate of complexification of a quantum state is conjectured to be bounded from above by the average energy of the state. A different conjecture relates the complexity of a holographic CFT state to the on-shell gravitational action of a…
We review some approaches to the Hamiltonian dynamics of (loop) quantum gravity, the main issues being the regularization of the Hamiltonian and the continuum limit. First, Thiemann's definition of the quantum Hamiltonian is presented, and…
Complexity in quantum physics measures how difficult a state can be reached from a reference state and more precisely it is the number of fundamental unitary gates we have to operate to transform the reference state to the state we are…
Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. We seek to…
The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the…
We study the radial quantization of the 3d O(N) vector model. We calculate the higher spin charges whose commutation relations give the higher spin algebra. The Fock states of higher spin gravity in AdS_{4} are realized as the states in the…
We show that the holographic Complexity = Volume proposal satisfies a very general notion of Momentum/Complexity correspondence (PC), based on the Momentum Constraint of General Relativity. It relates the rate of complexity variation with…
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…
In this paper we explore how to describe a bulk moving particle in the dual conformal field theories (CFTs). One aspect of this problem is to construct the dual state of the moving particle. On the other hand one should find the…
A potentially powerful approach to quantum gravity has been developed over the last few years under the name of Causal Dynamical Triangulations. Numerical simulations have given very interesting results in the cases of two, three and four…
The quantum theory of a harmonic oscillator with a time dependent frequency arises in several important physical problems, especially in the study of quantum field theory in an external background. While the mathematics of this system is…
We study a two-dimensional conformal field theory coupled to quantum gravity on a disk. Using the continuum Liouville field approach, we compute three-point correlation functions of boundary operators. The structure of momentum…
We analyze the size and evolution of quantum fluctuations of cosmologically relevant geometric observables, in the context of the effective relational cosmological dynamics of GFT models of quantum gravity. We consider the fluctuations of…