EP-PQM: Efficient Parametric Probabilistic Quantum Memory with Fewer Qubits and Gates

Machine learning (ML) classification tasks can be carried out on a quantum computer (QC) using Probabilistic Quantum Memory (PQM) and its extension, Parameteric PQM (P-PQM) by calculating the Hamming distance between an input pattern and a database of $r$ patterns containing $z$ features with $a$ distinct attributes. For accurate computations, the feature must be encoded using one-hot encoding, which is memory-intensive for multi-attribute datasets with $a>2$. We can easily represent multi-attribute data more compactly on a classical computer by replacing one-hot encoding with label encoding. However, replacing these encoding schemes on a QC is not straightforward as PQM and P-PQM operate at the quantum bit level. We present an enhanced P-PQM, called EP-PQM, that allows label encoding of data stored in a PQM data structure and reduces the circuit depth of the data storage and retrieval procedures. We show implementations for an ideal QC and a noisy intermediate-scale quantum (NISQ) device. Our complexity analysis shows that the EP-PQM approach requires $O\left(z \log_2(a)\right)$ qubits as opposed to $O(za)$ qubits for P-PQM. EP-PQM also requires fewer gates, reducing gate count from $O\left(rza\right)$ to $O\left(rz\log_2(a)\right)$. For five datasets, we demonstrate that training an ML classification model using EP-PQM requires 48% to 77% fewer qubits than P-PQM for datasets with $a>2$. EP-PQM reduces circuit depth in the range of 60% to 96%, depending on the dataset. The depth decreases further with a decomposed circuit, ranging between 94% and 99%. EP-PQM requires less space; thus, it can train on and classify larger datasets than previous PQM implementations on NISQ devices. Furthermore, reducing the number of gates speeds up the classification and reduces the noise associated with deep quantum circuits. Thus, EP-PQM brings us closer to scalable ML on a NISQ device.