Compressing DNA to its Quantum Entropy Limit

Quantum Machine Learning Hackathon 2026 project
Applying Schumacher quantum compression to DNA sequences to reduce qubit requirements for quantum genomic algorithms.

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Overview

Current quantum computers are severely limited by the number of available qubits. While a classical DNA base requires only two bits, storing genomic data as quantum information quickly becomes infeasible at genome scale.

This project explores whether Schumacher quantum data compression can reduce the number of qubits required to represent DNA while preserving quantum fidelity.

Instead of treating DNA bases as perfectly distinguishable quantum states, we encode them as non-orthogonal quantum states, allowing compression toward the von Neumann entropy limit.

The result is a proof-of-concept implementation demonstrating that quantum compression can significantly reduce qubit requirements while maintaining high recovery fidelity.

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Motivation

A human genome contains roughly:

• 3.2 billion DNA bases
• Naïve quantum encoding:
  • 2 qubits per base
  • 6.4 billion qubits

Today's gate-model quantum computers typically contain only 10²–10³ qubits.

Every qubit matters.

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Key Idea

Schumacher's theorem is the quantum analogue of Shannon's source coding theorem.

For a quantum source with density matrix ρ, the optimal asymptotic compression rate is

[ S(\rho)=-\mathrm{Tr}(\rho\log_2\rho) ]

where S(ρ) is the von Neumann entropy.

Instead of storing every basis state independently, we:

1. Encode DNA bases as quantum states
2. Construct the density matrix
3. Project onto the typical subspace
4. Store only the compressed quantum state
5. Recover the original state with fidelity approaching 1

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Pipeline

DNA sequence
      │
      ▼
Quantum Encoding
      │
      ▼
Density Matrix
      │
      ▼
Typical Subspace Projection
      │
      ▼
Compressed Quantum Register
      │
      ▼
Quantum Reconstruction

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Encoding Strategies

Classical (Orthogonal)

A
C
G
T

Each base is perfectly distinguishable.

Compression is minimal.

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Quantum (Non-Orthogonal)

Bases are represented by overlapping Bloch sphere states.

Advantages:

• lower von Neumann entropy
• fewer qubits required
• tunable overlap angle

Tradeoff:

• bases become harder to disting