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