FRC and Quantum Computing

Quantum computing relies fundamentally on maintaining coherence. The FRC framework provides new insights into why some quantum computations succeed and others fail.

The Decoherence Challenge

Current quantum computers struggle with decoherence:

Superconducting qubits: ~100 μs coherence times
Ion traps: ~1-10 seconds
Topological qubits: theoretically longer

FRC suggests decoherence isn't random but follows coherence attractor dynamics.

FRC Insights for Quantum Computing

Coherence Attractors

Standard view: decoherence is environmental noise FRC view: specific coherence patterns are more stable

$$ C_{\text{stable}} = \arg\max_C \left( \frac{dC}{dt} = 0 \right) $$

Implication: design quantum circuits to operate near natural attractors.

The D ≈ 1.90 Signature

FRC predicts measurement outcomes cluster at fractal dimension D ≈ 1.90 (see FRC-100-003). For quantum computing:

Qubit measurements should show this signature
Random Number Generators (QRNGs) can be characterized by D
Deviation from D ≈ 1.90 may indicate systematic errors

Coherence-Aware Gates

Standard quantum gates optimize for unitary fidelity. FRC suggests optimizing for coherence preservation:

$$ U_{\text{FRC}} = \arg\max_U \left( C(U|\psi\rangle) - C(|\psi\rangle) \right) $$

Gates that align with coherence flow may outperform conventional designs.

Practical Applications

Error Correction

Current approach: redundancy (many physical qubits → one logical qubit) FRC approach: coherence-based error detection

If the witness function W drops unexpectedly: $$ W < W_{\text{threshold}} \implies \text{error likely} $$

This could enable earlier error detection with less overhead.

Quantum Annealing

D-Wave style quantum annealers explicitly use coherence dynamics. FRC predicts:

Optimal annealing schedules follow coherence gradients
Final states concentrate at high-C attractors
The D ≈ 1.90 signature appears in solution distributions

Coherent Advantage

FRC suggests "quantum advantage" requires:

Initial coherence — Well-prepared superpositions
Coherence maintenance — Operations that preserve C
Coherent readout — Measurements aligned with attractors

Resonant Computing

FRC-841-004 explores speculative architectures:

R-bits — Resonance-based qubits with intrinsic coherence
CPUs — Coherence Processing Units
Non-Boolean logic — Computing with continuous coherence values

Current Limitations

FRC for quantum computing remains theoretical:

No FRC-designed quantum chip exists yet
Predictions need experimental validation
Integration with existing error correction is unclear

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