Triplet Loss Based Quantum Encoding Improves Class Separability and Reduces Circuit Depth for Binary Classification

Researchers are developing new ways to represent information for quantum computers, and a team led by Marco Mordacci, Mahul Pandey, and Paolo Santini from the University of Parma, alongside Michele Amoretti, has achieved a significant advance in this area. They introduce a novel encoding method that prepares quantum states in a way that clearly distinguishes between different classes of data, such as images. This approach, inspired by techniques used in classical facial recognition, uses a ‘triplet loss’ function to train the quantum circuit, effectively creating well-defined clusters for each category. Testing on challenging image datasets, including MNIST and MedMNIST, demonstrates that this method substantially outperforms existing quantum encoding techniques while requiring fewer computational steps, paving the way for more efficient and powerful quantum machine learning algorithms.

Classification tasks benefit from well-defined input states that form distinct clusters in the quantum Hilbert space, according to their classification labels. This research introduces a novel data encoding scheme that enhances the ability of quantum classifiers to distinguish between different classes, achieving better performance than traditional amplitude encoding while utilizing a significantly lower circuit depth.

Triplet-Based Quantum Data Encoding and Training

Scientists addressed a key challenge in quantum machine learning: efficiently encoding classical data into quantum states. They developed a method for generating quantum data encodings using a triplet-based approach, inspired by techniques used in face verification, to create optimal quantum states that effectively represent input data. The algorithm iteratively builds a quantum circuit by adding gates based on a triplet loss function, guided by triplets of data points to ensure good separation in the quantum feature space. The algorithm utilizes the triplet loss function to encourage similar data points to cluster together while pushing dissimilar points apart. The encoding is built iteratively, starting with a simple initial state and adding quantum gates based on the gradient of the loss function, then used as input to a Variational Quantum Circuit (VQC) for classification. The team prioritized hardware efficiency, meaning the encoding can be implemented on near-term quantum devices with limited resources, and explored various optimization strategies for the encoding generation process.

Encoded States Enhance Quantum Classification Performance

Scientists developed a novel data encoding scheme to enhance classification performance, particularly for complex datasets like images. This work focuses on creating input states that form well-separated clusters in the quantum Hilbert space based on their classification labels, improving the ability of quantum classifiers to distinguish between different classes. Experiments demonstrate considerable improvement over traditional amplitude encoding while utilizing a significantly lower circuit depth, and researchers measured class separability using the average trace distance between encoded density matrices. The results show that this new method effectively clusters encoded state vectors into distinct regions of the Hilbert space, maximizing the distance between states belonging to different classes and minimizing the distance between states of the same class. To quantify performance, scientists defined both intra-class and inter-class pairs of encoded states, aiming to minimize the average trace distance between intra-class pairs and maximize the average distance between inter-class pairs, employing a triplet selection strategy similar to hard mining in image recognition.

Learned Quantum Encoding For Image Classification

This research presents a novel quantum encoding scheme designed to improve the performance of quantum classifiers, particularly when applied to complex datasets like images. The team developed a method that trains an encoding circuit to create well-separated clusters in the quantum state space, corresponding to different classification labels, and testing on benchmark datasets, including MNIST and MedMNIST, demonstrates the effectiveness of this approach. Importantly, the team also evaluated the method on real quantum hardware, confirming that the results closely match those obtained through simulation. Future work will focus on refining the triplet-mining strategy used to select training data, and on optimising the gate selection process to better capture feature correlations and reduce circuit depth, with plans to evaluate the encoding scheme with deeper quantum circuits and extend its application to multiclass classification problems.