We propose a quantum version of the well known minimum distance classification model called Nearest Mean Classifier (NMC). In this regard, we presented our first results in two previous works. First, a quantum counterpart of the NMC for two-dimensional problems was introduced, named Quantum Nearest Mean Classifier (QNMC), together with a possible generalization to any number of dimensions. Secondly, we studied the n-dimensional problem into detail and we showed a new encoding for arbitrary n-feature vectors into density operators. In the present paper, another promising encoding is considered, suggested by recent debates on quantum machine learning. Further, we observe a significant property concerning the non-invariance by feature rescaling of our quantum classifier. This fact, which represents a meaningful difference between the NMC and the respective quantum version, allows us to introduce a free parameter whose variation provides, in some cases, better classification results for the QNMC. The experimental section is devoted: (i) to compare the NMC and QNMC performance on different datasets; and (ii) to study the effects of the non-invariance under uniform rescaling for the QNMC.We propose a quantum version of the well known minimum distance classification model called Nearest Mean Classifier (NMC). In this regard, we presented our first results in two previous works. First, a quantum counterpart of the NMC for two-dimensional problems was introduced, named Quantum Nearest Mean Classifier (QNMC), together with a possible generalization to any number of dimensions. Secondly, we studied the n-dimensional problem into detail and we showed a new encoding for arbitrary n-feature vectors into density operators. In the present paper, another promising encoding is considered, suggested by recent debates on quantum machine learning. Further, we observe a significant property concerning the non-invariance by feature rescaling of our quantum classifier. This fact, which represents a meaningful difference between the NMC and the respective quantum version, allows us to introduce a free parameter whose variation provides, in some cases, better classification results for the QNMC. The experimental section is devoted: (i) to compare the NMC and QNMC performance on different datasets; and (ii) to study the effects of the non-invariance under uniform rescaling for the QNMC.

EntropyDec 1, 201710 citations

Recent advances for quantum classifiers

Weikang Li, Dong-Ling Deng

arXiv:2108.13421Science China Physics Mechanics and AstronomyDec 2, 2021103 citations

On quantum ensembles of quantum classifiers

Amira Abbas, Maria Schuld, Francesco Petruccione

Quantum Machine IntelligenceJun 1, 202034 citations

A weighted quantum ensemble of homogeneous quantum classifiers

Emiliano Tolotti, Enrico Blanzieri, Davide Pastorello

Abstract Ensemble methods in machine learning aim to improve prediction accuracy by combining multiple models. This is achieved by ensuring diversity among predictors to capture different data aspects. Homogeneous ensembles use identical models, achieving diversity through different data subsets, and weighted-average ensembles assign higher influence to more accurate models through a weight learning procedure. We propose a method to achieve a weighted homogeneous quantum ensemble using quantum classifiers with indexing registers for data encoding. This approach leverages instance-based quantum classifiers, enabling feature and training point subsampling through superposition and controlled unitaries, and allowing for a quantum-parallel execution of diverse internal classifiers with different data compositions in superposition. The method integrates a learning process involving circuit execution and classical weight optimization, for a trained ensemble execution with weights encoded in the circuit at test-time. Empirical evaluation demonstrate the effectiveness of the proposed method, offering insights into its performance.Abstract Ensemble methods in machine learning aim to improve prediction accuracy by combining multiple models. This is achieved by ensuring diversity among predictors to capture different data aspects. Homogeneous ensembles use identical models, achieving diversity through different data subsets, and weighted-average ensembles assign higher influence to more accurate models through a weight learning procedure. We propose a method to achieve a weighted homogeneous quantum ensemble using quantum classifiers with indexing registers for data encoding. This approach leverages instance-based quantum classifiers, enabling feature and training point subsampling through superposition and controlled unitaries, and allowing for a quantum-parallel execution of diverse internal classifiers with different data compositions in superposition. The method integrates a learning process involving circuit execution and classical weight optimization, for a trained ensemble execution with weights encoded in the circuit at test-time. Empirical evaluation demonstrate the effectiveness of the proposed method, offering insights into its performance.

arXiv:2506.07810Quantum Machine IntelligenceOct 31, 20250 citations

Implementation of a Hamming distance–like genomic quantum classifier using inner products on ibmqx2 and ibmq_16_melbourne

Kunal Kathuria, Aakrosh Ratan, Michael J. McConnell +1 more

Abstract Motivated by the problem of classifying individuals with a disease versus controls using a functional genomic attribute as input, we present relatively efficient general purpose inner product–based kernel classifiers to classify the test as a normal or disease sample. We encode each training sample as a string of 1 s (presence) and 0 s (absence) representing the attribute’s existence across ordered physical blocks of the subdivided genome. Having binary-valued features allows for highly efficient data encoding in the computational basis for classifiers relying on binary operations. Given that a natural distance between binary strings is Hamming distance, which shares properties with bit-string inner products, our two classifiers apply different inner product measures for classification. The active inner product (AIP) is a direct dot product–based classifier whereas the symmetric inner product (SIP) classifies upon scoring correspondingly matching genomic attributes. SIP is a strongly Hamming distance–based classifier generally applicable to binary attribute-matching problems whereas AIP has general applications as a simple dot product–based classifier. The classifiers implement an inner product betweenN= 2ndimension test and train vectors usingnFredkin gates while the training sets are respectively entangled with the class-label qubit, without use of an ancilla. Moreover, each training class can be composed of an arbitrary numbermof samples that can be classically summed into one input string to effectively execute all test–train inner products simultaneously. Thus, our circuits require the same number of qubits for any number of training samples and are $O(\log {N})$ O(logN) in gate complexity after the states are prepared. Our classifiers were implemented on ibmqx2 (IBM-Q-team 2019b) and ibmq_16_melbourne (IBM-Q-team 2019a). The latter allowed encoding of 64 training features across the genome.Abstract Motivated by the problem of classifying individuals with a disease versus controls using a functional genomic attribute as input, we present relatively efficient general purpose inner product–based kernel classifiers to classify the test as a normal or disease sample. We encode each training sample as a string of 1 s (presence) and 0 s (absence) representing the attribute’s existence across ordered physical blocks of the subdivided genome. Having binary-valued features allows for highly efficient data encoding in the computational basis for classifiers relying on binary operations. Given that a natural distance between binary strings is Hamming distance, which shares properties with bit-string inner products, our two classifiers apply different inner product measures for classification. The active inner product (AIP) is a direct dot product–based classifier whereas the symmetric inner product (SIP) classifies upon scoring correspondingly matching genomic attributes. SIP is a strongly Hamming distance–based classifier generally applicable to binary attribute-matching problems whereas AIP has general applications as a simple dot product–based classifier. The classifiers implement an inner product betweenN= 2ndimension test and train vectors usingnFredkin gates while the training sets are respectively entangled with the class-label qubit, without use of an ancilla. Moreover, each training class can be composed of an arbitrary numbermof samples that can be classically summed into one input string to effectively execute all test–train inner products simultaneously. Thus, our circuits require the same number of qubits for any number of training samples and are $O(\log {N})$ O(logN) in gate complexity after the states are prepared. Our classifiers were implemented on ibmqx2 (IBM-Q-team 2019b) and ibmq_16_melbourne (IBM-Q-team 2019a). The latter allowed encoding of 64 training features across the genome.

Quantum Machine IntelligenceJun 1, 202024 citations

Understanding the Generalization of Adversarially Trained Quantum Classifiers

Petros Georgiou, Sharu Theresa Jose

Quantum science and technologyJan 1, 20260 citations

O(\log {N})

O(logN) in gate complexity after the states are prepared. Our classifiers were implemented on ibmqx2 (IBM-Q-team 2019b) and ibmq_16_melbourne (IBM-Q-team 2019a). The latter allowed encoding of 64 training features across the genome.