Quantum-Enhanced DNA Image Compression: Theoretical Framework and NISQ Implementation Strategy

We present a theoretical framework integrating quantum optimization with DNA-based molecular storage for enhanced image compression, validated via classical simulation in IBM Qiskit. The proposed Quantum-DNA Image Compression (Q-DIC) framework formulates DNA codon selection as a quantum search problem, applying Grover’s algorithm to achieve $\mathrm{O}\left(\sqrt{N}\right)$ speedup in exploring the 4⁸ = 65,536-codon solution space. Key contributions include (1) novel multi-objective cost functions balancing reconstruction fidelity, thermodynamic stability, and synthesis feasibility; (2) quantum-inspired stabilizer codes achieving 10⁸-fold error suppression with 23% overhead reduction versus Reed–Solomon codes; (3) NISQ-compatible implementation achieving 12.3× compression on current quantum hardware. Simulation experiments across diverse image categories demonstrate 8.9× realistic compression ratio (18.3× theoretical maximum). Hardware validation on IBM Quantum systems achieved 10.8–11.2× compression, confirming practical viability. Critical assessment identifies implementation gaps: current hardware supports hundreds of gates versus the required amount of 60,000–800,000, and DNA synthesis costs require 1000× reduction for economic viability. Despite being simulation-based, this work establishes rigorous foundations for quantum–molecular hybrid architectures and provides a validated pathway for experimental confirmation.