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Inflation is Not Magic

S. Shajidul Haque, Ghadir Jafari, Bret Underwood

TL;DR

The paper investigates whether inflationary cosmology exploits quantum resources beyond stabilizer functionality. By extending the stabilizer formalism to continuous variables, it shows that quadratic inflationary perturbations form Gaussian, stabilizer states with vanishing Wigner negativity, allowing efficient classical simulation. Non-Gaussian corrections from cubic interactions contribute exponentially suppressed magic, so even with primordial non-Gaussianities the quantum resources required for universal quantum computation remain negligible. Interestingly, while circuit complexity grows linearly with squeezing, quantum magic remains essentially zero, suggesting the early universe operates in a regime of high complexity but limited non-Clifford resources, with implications for decoherence and the quantum-to-classical transition. This framework links information-theoretic measures to cosmological observational signatures and provides a perspective on how classical structure emerges from quantum origins.

Abstract

Cosmological perturbations generated during inflation exhibit striking quantum features, including entanglement and high circuit complexity. Yet their observational signatures remain effectively indistinguishable from classical stochastic variables. We quantify this tension by showing that quantum inflationary perturbations are continuous variable stabilizer states with vanishing quantum magic, a necessary resource for universal quantum computation as measured by Wigner negativity. Consequently, despite their quantum origins and description, these states can be efficiently simulated using classical algorithms. We further show that the Wigner negativity arising from primordial non-Gaussianity is suppressed not only by the non-linearity parameter $f_{NL}$, but also by the exponential squeezing of the perturbations. Viewing the early universe as a "high complexity, low magic" regime provides another perspective of what it means for the origin of structure in the universe to be "quantum."

Inflation is Not Magic

TL;DR

The paper investigates whether inflationary cosmology exploits quantum resources beyond stabilizer functionality. By extending the stabilizer formalism to continuous variables, it shows that quadratic inflationary perturbations form Gaussian, stabilizer states with vanishing Wigner negativity, allowing efficient classical simulation. Non-Gaussian corrections from cubic interactions contribute exponentially suppressed magic, so even with primordial non-Gaussianities the quantum resources required for universal quantum computation remain negligible. Interestingly, while circuit complexity grows linearly with squeezing, quantum magic remains essentially zero, suggesting the early universe operates in a regime of high complexity but limited non-Clifford resources, with implications for decoherence and the quantum-to-classical transition. This framework links information-theoretic measures to cosmological observational signatures and provides a perspective on how classical structure emerges from quantum origins.

Abstract

Cosmological perturbations generated during inflation exhibit striking quantum features, including entanglement and high circuit complexity. Yet their observational signatures remain effectively indistinguishable from classical stochastic variables. We quantify this tension by showing that quantum inflationary perturbations are continuous variable stabilizer states with vanishing quantum magic, a necessary resource for universal quantum computation as measured by Wigner negativity. Consequently, despite their quantum origins and description, these states can be efficiently simulated using classical algorithms. We further show that the Wigner negativity arising from primordial non-Gaussianity is suppressed not only by the non-linearity parameter , but also by the exponential squeezing of the perturbations. Viewing the early universe as a "high complexity, low magic" regime provides another perspective of what it means for the origin of structure in the universe to be "quantum."

Paper Structure

This paper contains 9 sections, 87 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Stabilizers, Wigner Functions, and Cumulants
  3. Stabilizers for Qubits
  4. Stabilizers in Continuous Variable Systems
  5. Cumulant Expansion and Negativity
  6. Inflationary Perturbations and Magic
  7. Non-Gaussianity and Magic
  8. Discussion
  9. Cumulant Expansion Details

Figures (1)

  • Figure 1: (LEFT) The corrected Wigner function \ref{['eq:WignerInflationCorrected2']} is negative far out on the tail of the Gaussian (dashed). The negativity \ref{['eq:Negativity']} involves the integral over the absolute value of the Wigner function (solid), and can be approximated as the integral of the Gaussian part of the distribution (CENTER) plus the tail (RIGHT).