qbitwave 0.2.6

Information-theoretic reconstruction of quantum wavefunctions from discrete bitstrings

QBitwave: Emergent Information-Theoretic Wavefunctions

QBitwave models quantum-like dynamics as the deterministic evolution of compressibility in finite bitstrings. The wavefunction ψ is interpreted not as a physical field but as the minimal compression algorithm that reproduces a given informational state. Existence corresponds to compressibility — most compressible configurations dominate. Through Fourier-domain transformations and entropy measures, QBitwave unifies bitstrings, complex amplitudes, and probabilistic behavior into a single information-centric framework.

Core Concept

QBitwave

QBitwave treats the wavefunction as an emergent, information-theoretic object.
A finite bitstring encodes a discretized wavefunction, which can be reconstructed as normalized complex amplitudes — the minimal program reproducing the bitstring (Kolmogorov complexity perspective).

Fundamental principles:

• Compression = quantum probability amplitude = predictability
• Smooth, regular data compresses well → high amplitude in few Fourier components (low entropy)
• Random/noisy data is incompressible → low amplitude concentration
• Wavefunction = minimal program reproducing the bitstring

Features:

• Forward mapping: wavefunction → bitstring
• Reverse mapping: bitstring → minimal wavefunction
• Block-size selection via entropy maximization
• Shannon entropy computation
• Fourier-based compressibility measure reflecting structure

QBitwaveND

QBitwaveND generalizes QBitwave to N-dimensional continuous fields and allows dynamical evolution in time.

Conceptual Relation
QBitwave → Emergence: bitstring → ψ(x)
QBitwaveND → Evolution: ψ(x) → ψ(x, t)

QBitwaveND applies unitary, physically motivated evolution consistent with the Schrödinger free-particle dispersion relation, but framed entirely informationally:

1. Take N-dimensional complex amplitude array ψ(x₁, x₂, …, xₙ)
2. Compute Fourier transform:
   ψ̃(k) = FFT[ψ(x)] / ∏ shape
3. Apply time evolution in frequency space:
   ψ̃(k, t) = ψ̃(k) · exp(-i·ω(k)·t), where ω(k) = (ħ |k|²) / 2m
4. Inverse transform to get ψ(x, t)

Interpretation:

• Time is an informational parameter — the phase evolution of encoded structure
• Bridges algorithmic information (Kolmogorov domain) and spacetime dynamics (Fourier domain)
• Provides unitary time evolution over emergent informational geometry, extending static ψ(x) of QBitwave to ψ(x, t)

Attributes:

• amplitudes : N-dimensional complex array ψ(x) at t=0
• shape : spatial dimensions of the array
• ndim : number of spatial dimensions
• fft_coeffs : normalized Fourier coefficients ψ̃(k)
• freqs : per-axis frequency arrays
• mass : effective mass parameter (ħk² / 2m)
• c : speed of light (for optional relativistic corrections)
• hbar : reduced Planck constant

Key Methods:

• from_array(data_array) : construct from existing N-D array
• from_qbitwave(qb: QBitwave) : create N-D field from a 1D informational wavefunction
• time_evolve_coeffs(t) : return Fourier coefficients after time evolution
• evaluate(*coords, t=0.0) : compute ψ(x, t) at arbitrary coordinates
• probability(*coords, t=0.0) : return |ψ(x, t)|² (Born-rule analog)

Why It Matters

• Information as primary ontology: All physical phenomena are encoded by minimal informational descriptions; spacetime, fields, and quantum dynamics are derived, not assumed.
• Compressibility replaces renormalization: High-frequency modes that contribute divergences in conventional QFT are interpreted as incompressible configurations with vanishing physical measure, providing a natural regularization.
• Singularities as structureless limits: Zero execution-trace entropy indicates collapse of all distinguishable geometric degrees of freedom, eliminating the need to treat singularities as breakdowns of physics.

Source code

• https://github.com/juhakm/qbitwave

Example Usage

from qbitwave import QBitwave, QBitwaveND

# Create a 1D informational wavefunction
qb = QBitwave("010110110001")

# Lift it to N-dimensional dynamic field
qn = QBitwaveND.from_qbitwave(qb)

# Evaluate amplitude at x=0.2, t=0.5
psi_t = qn.evaluate(0.2, t=0.5)

# Compute probability (Born rule analog)
P = qn.probability(0.2, t=0.5)

Images