Quantum computing for pattern classification

It is well known that for certain tasks, quantum computing outperforms classical computing. A growing number of contributions try to use this advantage in order to improve or extend classical machine learning algorithms by methods of quantum information theory. This paper gives a brief introduction into quantum machine learning using the example of pattern classification. We introduce a quantum pattern classification algorithm that draws on Trugenberger's proposal for measuring the Hamming distance on a quantum computer (CA Trugenberger, Phys Rev Let 87, 2001) and discuss its advantages using handwritten digit recognition as from the MNIST database.Comment: 14 pages, 3 figures, presented at the 13th Pacific Rim International Conference on Artificial Intelligenc

Supervised learning with quantum enhanced feature spaces

Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern recognition, with support vector machines (SVMs) being the most well-known method for classification problems. However, there are limitations to the successful solution to such problems when the feature space becomes large, and the kernel functions become computationally expensive to estimate. A core element to computational speed-ups afforded by quantum algorithms is the exploitation of an exponentially large quantum state space through controllable entanglement and interference. Here, we propose and experimentally implement two novel methods on a superconducting processor. Both methods represent the feature space of a classification problem by a quantum state, taking advantage of the large dimensionality of quantum Hilbert space to obtain an enhanced solution. One method, the quantum variational classifier builds on [1,2] and operates through using a variational quantum circuit to classify a training set in direct analogy to conventional SVMs. In the second, a quantum kernel estimator, we estimate the kernel function and optimize the classifier directly. The two methods present a new class of tools for exploring the applications of noisy intermediate scale quantum computers [3] to machine learning.Comment: Fixed typos, added figures and discussion about quantum error mitigatio

Physical-Layer Supervised Learning Assisted by an Entangled Sensor Network

Many existing quantum supervised learning (SL) schemes consider data given a priori in a classical description. With only noisy intermediate-scale quantum (NISQ) devices available in the near future, their quantum speedup awaits the development of quantum random access memories (qRAMs) and fault-tolerant quantum computing. There, however, also exist a multitude of SL tasks whose data are acquired by sensors, e.g., pattern classification based on data produced by imaging sensors. Solving such SL tasks naturally requires an integrated approach harnessing tools from both quantum sensing and quantum computing. We introduce supervised learning assisted by an entangled sensor network (SLAEN) as a means to carry out SL tasks at the physical layer. The entanglement shared by the sensors in SLAEN boosts the performance of extracting global features of the object under investigation. We leverage SLAEN to construct an entanglement-assisted support-vector machine for data classification and entanglement-assisted principal component analyzer for data compression. In both schemes, variational circuits are employed to seek the optimum entangled probe states and measurement settings to maximize the entanglement-enabled {enhancement}. We observe that SLAEN enjoys an appreciable entanglement-enabled performance gain, even in the presence of loss, over conventional strategies in which classical data are acquired by separable sensors and subsequently processed by classical SL algorithms. SLAEN is realizable with available technology, opening a viable route toward building NISQ devices that offer unmatched performance beyond what the optimum classical device is able to afford.Comment: 9+2 pages, 9 figure