Comparative analysis of projector‐based compression and quantum autoencoders

Quantum compression is a cornerstone of quantum information science, promising efficient encoding of large quantum states into fewer qubits while retaining high fidelity. In this work, we compare two pivotal strategies for compressing an i.i.d. quantum source under small-scale (few-qubit) regimes. The first strategy relies on a projector-based compression method that discards low-probability components in the state’s spectral decomposition, achieving near-optimal asymptotic compression in principle. The second strategy employs a quantum autoencoder (QAE), a variational circuit that learns to embed essential information into fewer qubits. We implement both approaches in simulation, gauge their performance, and explore how many qubits can be ”saved” in practice. Our results highlight how projector-based compression provides a near-optimal yet analytically prescriptive solution, whereas autoencoders offer a machine-learning–style route that can adapt to varied input states.