SR Quantum Machine Learning

Quantum Autoencoder

This note describes the quantum autoencoder workflow implemented in qml.autoencoder.

The current implementation is intentionally compact and package-oriented:

  • structured four-qubit input state families
  • a trainable encoder/decoder ansatz
  • latent and trash subsystem separation
  • compression and reconstruction fidelity reporting

Overview

A quantum autoencoder learns a unitary compression map that preserves the informative degrees of freedom of a quantum state in a smaller latent subspace.

Rather than predicting labels directly, it learns a transformation that moves discardable information into a trash subsystem.

Model structure

Let the input state be

\[ |\psi(x)\rangle. \]

The encoder applies a trainable unitary

\[ |\phi(x,\theta)\rangle = U(\theta)|\psi(x)\rangle. \]

If compression succeeds, the state factorizes approximately as

\[ |\phi(x,\theta)\rangle \approx |\tilde{\psi}(x)\rangle_{\mathrm{latent}} \otimes |0\rangle_{\mathrm{trash}}. \]

The implementation retains a configurable number of latent qubits and measures how often the trash subsystem lands in the all-zero basis state.

Training objective

The training signal is the probability of measuring the trash subsystem in \(|0\rangle^{\otimes k}\).

If

\[ p_{\mathrm{trash}}(0 \cdots 0 \mid x,\theta) \]

denotes that probability, the loss is

\[ \mathcal{L}(\theta) = 1 - \mathbb{E}_x \left[p_{\mathrm{trash}}(0 \cdots 0 \mid x,\theta)\right]. \]

Minimizing this loss encourages the encoder to compress the structured state family into the latent subsystem.

Reconstruction fidelity

To assess whether useful information is preserved, the workflow also computes a reconstruction fidelity by applying the decoder

\[ U(\theta)^\dagger \]

after the encoder and comparing the resulting state to the original state.

This yields two complementary metrics:

  • compression fidelity on the trash subsystem
  • reconstruction fidelity on the full state

Example usage

from qml.autoencoder import run_quantum_autoencoder

result = run_quantum_autoencoder(
    family="correlated",
    n_samples=200,
    n_layers=2,
    latent_qubits=2,
    steps=50,
)

Outputs include:

  • train/test compression fidelity
  • train/test reconstruction fidelity
  • learned ansatz parameters
  • loss history

When save=True, the workflow writes JSON results and generated figures to:

  • results/autoencoder/
  • images/autoencoder/

State families

The current implementation provides several synthetic state families:

  • correlated
  • entangled
  • hybrid

These are designed to provide structured low-dimensional families that are meaningful compression targets for a small autoencoder.