Spread and circuit complexity as a measure of particle content and phase space fluctuations

• URL: http://arxiv.org/abs/2511.02013v1
• Date: Mon, 03 Nov 2025 19:37:45 GMT
• Title: Spread and circuit complexity as a measure of particle content and phase space fluctuations
• Authors: Satyaki Chowdhury,
• Abstract summary: We show that circuit and spread complexity at any instant is determined by the mean number of quanta and its rate of change.<n>Results have direct relevance for quantum field theory in curved backgrounds.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 position and momentum operators. Using a harmonic oscillator with time-dependent mass and frequency as a toy model, we show that both circuit and spread complexity at any instant is determined by the mean number of quanta and its rate of change. Furthermore, both complexity and its growth are directly linked to the variances of the position and momentum operators, providing a clear physical interpretation of complexity in terms of the state's excitation and phase-space fluctuation. Although the analysis is carried out for a single time-dependent oscillator, the results have direct relevance for quantum field theory in curved backgrounds, where individual field modes effectively behave as time-dependent oscillators. This offers new insights into how quantum complexity encodes particle production and phase space fluctuations in non-holographic systems. Finally, we establish a precise and potentially universal relation between spread and circuit complexity for the time evolved state suggesting deeper connections between different complexity measures in the context of field theories on curved backgrounds.

Related papers

• Phase-space complexity of discrete-variable quantum states and operations [0.0]
  We introduce a quantifier of phase-space complexity for discrete-variable quantum systems.<n>The complexity is normalized such that coherent states have unit complexity, while the completely mixed state has zero complexity.<n>We extend the framework to quantum channels, defining measures for both the generation and breaking of complexity.
  arXiv  Detail & Related papers  (2026-03-03T19:00:02Z)
• Quantum fields from real-time ensemble dynamics [6.0523316051636025]
  We formulate quantum fields in a real-time Schrdinger-picture framework.<n>Within this formulation, the wave $[,t]$ encodes a first-order, causal ensemble dynamics on configuration space.<n> Entanglement, scattering, and conformal field amplitudes emerge as distinct projections of the same underlying ensemble theory.
  arXiv  Detail & Related papers  (2026-02-04T05:40:38Z)
• Direct probing of the simulation complexity of open quantum many-body dynamics [42.085941481155295]
  We study the role of dissipation in simulating open-system dynamics using both quantum and classical methods.<n>Our results show that dissipation affects correlation length and mixing time in distinct ways at intermediate and long timescales.
  arXiv  Detail & Related papers  (2025-08-27T15:14:36Z)
• Spacetime Quantum Circuit Complexity via Measurements [1.7972674269108895]
  Quantum circuit complexity is a fundamental concept whose importance permeates quantum information, computation, many-body physics and high-energy physics.<n>We introduce the notion of embedded complexity that characterizes the complexity of projected states and measurement operators.<n>For random circuits and certain strongly interacting time-independent Hamiltonian dynamics, we show that the embedded complexity is lower-bounded by the circuit volume.
  arXiv  Detail & Related papers  (2024-08-29T15:12:33Z)
• Trapped-Ion Quantum Simulation of Collective Neutrino Oscillations [55.41644538483948]
  We study strategies to simulate the coherent collective oscillations of a system of N neutrinos in the two-flavor approximation using quantum computation. We find that the gate complexity using second order Trotter- Suzuki formulae scales better with system size than with other decomposition methods such as Quantum Signal Processing.
  arXiv  Detail & Related papers  (2022-07-07T09:39:40Z)
• Out-of-time-order correlator in the quantum Rabi model [62.997667081978825]
  We show that out-of-time-order correlator derived from the Loschmidt echo signal quickly saturates in the normal phase. We show that the effective time-averaged dimension of the quantum Rabi system can be large compared to the spin system size.
  arXiv  Detail & Related papers  (2022-01-17T10:56:57Z)
• Operator Complexity for Quantum Scalar Fields and Cosmological Perturbations [0.0]
  We study the complexity of the unitary evolution of quantum cosmological perturbations in de Sitter space. The complexity of cosmological perturbations scales as the square root of the (exponentially) growing volume of de Sitter space.
  arXiv  Detail & Related papers  (2021-10-15T20:37:36Z)
• Time and Evolution in Quantum and Classical Cosmology [68.8204255655161]
  We show that it is neither necessary nor sufficient for the Poisson bracket between the time variable and the super-Hamiltonian to be equal to unity in all of the phase space. We also discuss the question of switching between different internal times as well as the Montevideo interpretation of quantum theory.
  arXiv  Detail & Related papers  (2021-07-02T09:17:55Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)
• Complexity and Floquet dynamics: non-equilibrium Ising phase transitions [0.0]
  We study the time-dependent circuit complexity of the periodically driven transverse field Ising model. In the high-frequency driving limit the system is known to exhibit non-equilibrium phase transitions governed by the amplitude of the driving field.
  arXiv  Detail & Related papers  (2020-08-31T19:13:03Z)
• Synchronisation phase as an indicator of persistent quantum correlations between subsystems [68.8204255655161]
  Spontaneous synchronisation is a collective phenomenon that can occur in both dynamical classical and quantum systems. We show that our analysis applies to a variety of spontaneously synchronising open quantum systems.
  arXiv  Detail & Related papers  (2020-06-29T17:21:32Z)
• Aspects of The First Law of Complexity [0.0]
  We investigate the first law of complexity proposed in arXiv:1903.04511, i.e., the variation of complexity when the target state is perturbed. Based on Nielsen's geometric approach to quantum circuit complexity, we find the variation only depends on the end of the optimal circuit.
  arXiv  Detail & Related papers  (2020-02-13T21:15:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.