QBitwave

Python class to model quantum-like dynamics as the deterministic evolution of compressibility in finite bitstrings.

Install

pip install qbitwave

https://pypi.org/project/qbitwave/

Description

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 — the most compressible configurations dominate.

A finite bitstring encodes a discretized wavefunction, which can be reconstructed as normalized complex amplitudes. Conceptually, the bitstring is like a “measurement” of the wavefunction: many wavefunctions may correspond to the same bitstring, but each wavefunction carries richer structure in amplitude and phase.

Through Fourier-domain transformations and entropy measures, QBitwave unifies bitstrings, complex amplitudes, and probabilistic behavior into a single information-centric framework.

Fundamental Principles

• Compression → quantum probability amplitude → predictability (smooth, emergent laws of physics)
• Smooth, regular data compresses well → high amplitude in few Fourier components (low entropy)
• Random/noisy data is incompressible → low amplitude concentration
• Wavefunction = minimal spectral description reproducing the bitstring
• Phase structure contributes to wavefunction complexity; rapid phase variation increases informational cost

Features

• Forward mapping: wavefunction → bitstring
• Reverse mapping: bitstring → minimal complex wavefunction
• Phase-aware spectral complexity measure (wave_complexity())
• Block-size selection via entropy maximization
• Shannon entropy computation
• Fourier-based compressibility measure reflecting structure
• Deterministic evolution driven by minimal spectral complexity

QBitwaveMDL

This is new rewritten version of QBitwave, with refined spectral complexity measure and old experimental and legacy code stripped.

QBitSpinor

QBitSpinor extends the spectral informational framework to two-component spinor fields, enabling representation of internal degrees of freedom (analogous to spin-½ systems) within the same MDL-based formalism.

While QBitwaveMDL models a scalar complex field ψ(x), QBitSpinor models a vector-valued wavefunction:

ψ(x) = (ψₐ(x), ψᵦ(x))

Each component is encoded spectrally, and structural complexity is computed over the combined power of both components.

Interpretation

• A spinor is not treated as a physical object, but as a more expressive compression scheme
• Two components allow encoding of relational or identity-preserving structure
• The additional degrees of freedom enable:
  • Representation of distinguishability under compression
  • Emergence of exclusion-like behavior (via structural constraints)
  • Mapping to Bloch sphere representation

In this framework:

• Scalar fields compress geometry
• Spinors compress identity

Structural Complexity

The spectral complexity generalizes to:

C_Q = Σ k_eff² (|Aₐ(k)|² + |Aᵦ(k)|²)

This reflects the total informational cost of encoding both components.

Bloch Representation

The internal structure can be mapped to a Bloch vector:

• Ex = 2 Re(ψₐ* ψᵦ)
• Ey = 2 Im(ψₐ* ψᵦ)
• Ez = |ψₐ|² − |ψᵦ|²

This provides a geometric interpretation of the internal state.

Features

• Two-component spectral encoding (α, β)
• FFT-based mode extraction
• Joint spectral complexity measure
• Wavefunction reconstruction ψ(x) ∈ ℂ²
• Bloch vector computation
• MDL-based description length estimation
• Typicality weighting via exp(-λ C_Q)

Example Usage

import numpy as np
from qbitwave.qbitspinor import QBitSpinor

N = 32
spinor = QBitSpinor(N)

# Define spinor components
alpha = np.exp(1j * np.linspace(0, 2*np.pi, N))
beta  = np.exp(-1j * np.linspace(0, 2*np.pi, N))

# Encode into spectral modes
spinor.encode(alpha, beta)

# Evaluate wavefunction
psi = spinor.evaluate()  # shape (N, 2)

# Compute Bloch vectors
bloch = spinor.get_bloch_vectors()

# Complexity and typicality
C = spinor.spectral_complexity()
w = spinor.typicality_weight()

QBitwaveND

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

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
• 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)

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