Pulse Core Lexicon

Voxel Quantum State

Definition

The Voxel Quantum State is the quantum state held by each voxel of the substrate lattice, a superposition over 64 basis states that gives each spatial unit substantial storage and processing capacity. It is the second of the book's Quantum Substrate Architecture Requirements, after the 10⁶-voxel lattice. The complex amplitudes over a 64-dimensional Hilbert space are what give dense quantum processing, and the Information Density per Voxel builds on it, I🟑 = 64 × log₂(C≋) · ℨᵇ with C≋ = 1 + χ≋ and χ≋ ≥ 0.1, which the book reads as quantum superposition adding storage beyond classical bits. |ψ🟑⟩ = Σᵢ₌₁⁶⁴ cᵢ|i⟩, where |ψ🟑⟩ is the voxel quantum state vector, cᵢ are complex probability amplitudes normalized so that Σᵢ|cᵢ|² = 1, |i⟩ are basis states spanning the 64-dimensional Hilbert space and 64 is the Hilbert space dimension. All are [∅]. It fills the Voxel Lattice Structure within the Three-Dimensional Voxel Lattice and feeds Information Density per Voxel.

Mathematical Expression

From the book · Chapter 8 · Qubit Thresholds and the Timeline to Singularity

|ψ🟑⟩ = Σᵢ₌₁⁶⁴ cᵢ |i⟩ [∅]

Where:

  • |ψ🟑⟩ [∅] - voxel quantum state vector
  • Σ [∅] - summation operator
  • ᵢ [∅] - summation index
  • ₁ [∅] - subscript notation for summation lower limit
  • ⁶⁴ [∅] - subscript notation for upper limit (64)
  • cᵢ [∅] - complex probability amplitudes with normalization Σᵢ |cᵢ|² = 1
  • |i⟩ [∅] - basis states spanning 64-dimensional Hilbert space
  • 64 [∅] - Hilbert space dimension
  • 1 [∅] - normalization constant
  • [∅] - quantities without physical units, pure numerical ratios or mathematical constants

Technical Details

Category Concept

Chapter Chapter 8

Importance

Related Terms