QML on Near-Term Devices

Why do we need Quantum Methods?

The computational capacity requirement keeps growing as a business and academic challenges become more challenging. Applications involving the simulation of massive quantum systems, such as molecules, or the solution of massive linear systems, can be exceedingly costly in computation. This has grown to be one of the driving forces behind the creation of quantum computing. This computational technique uses the properties and theories of quantum systems to process data. For these kinds of issues, quantum computers promise exponential speedups.

Even though research into quantum computers has accelerated recently, the theoretical and technical obstacles still prevent the development of a large-scale quantum computer. Due to process noise, quantum computers as we know them now are severely constrained in terms of qubits and gate operations. The development of Variational Quantum Algorithms (VQA) has emerged as one of the most promising solutions to these constraints. Applications for quantum machine learning have been proposed in a variety of domains that use this method, including picture categorization.

This research proposed a modification scheme of the VQA-based Data Reuploading Classifier (DRC) for MNIST classification. A binary, four-class, and eight-class classification task reached $99.7\%$, $96.5\%$, and $86.25\%$ of testing accuracy, respectively, using the Principal Component Analysis (PCA) for dimensionality reduction and Data Re-uploading Classifier with binary representation (DRC-BR) for classification. An improvement in accuracy compared to the previous related VQA works. This research also proposed a DRC-based quantum convolution scheme. Without using PCA, quantum convolution with DRC-BR classifier for binary and four-class classification tasks achieved $98.9\%$ and $89.5\%$ of testing accuracy, …

Over the last few years, quantum machine learning research has provided a lot of insights on how we can understand and train quantum circuits as machine learning models. While many connections to neural networks have been made, it becomes increasingly clear that their mathematical foundation is intimately related to so-called kernel methods, the most famous of which is the support vector machine (SVM) (see for example Schuld and Killoran (2018), Havlicek et al. (2018), Liu et al. (2020), Huang et al. (2020), and, for a systematic summary which we will follow here, Schuld (2021)).

A primordial state of matter consisting of free quarks and gluons that existed in the early universe a few microseconds after the Big Bang is also expected to form in high-energy heavy-ion collisions. Determining the equation of state (EoS) of such a primordial matter is the ultimate goal of high-energy heavy-ion experiments. Here we use supervised learning with a deep convolutional neural network to identify the EoS employed in the relativistic hydrodynamic simulations of heavy ion collisions. High-level correlations of particle spectra in transverse momentum and azimuthal angle learned by the network act as an effective EoS-meter in deciphering the nature of the phase transition in quantum chromodynamics. Suc…

The conjectured phase diagram in quantum chromodynamics. In the region with high temperature and small baryon chemical potential, the phase transition between hadronic matter and quark–gluon plasma is a cross over according to lattice QCD calculations (blue dashed line in the small insert). In the region with low temperature and moderately high baryon chemical potential, the phase transition is first order (red line in the small insert). At low temperature and high baryon chemical potential, there might exist other phases, such as color superconductor

The best classifier (linear SVC) that generalizes well on two testing data sets achieves on average ~80% prediction accuracy. The important features from different classifiers differ from each other, however, those with good generalization capability have similar importance regions as given by the deep CNN. The deep CNN with on average ~95% prediction accuracy works much better to answer the core questions—is there a traceable encoder of the dynamical information from phase structure (EoS) that survives the evolution and exists in the final snapshot? If yes, then how to exclusively and effectively decode these information from the highly complex final output? These questions are crucial but unclear for decades …

Developing galaxy detection technique from the telescope image via QML.

Demonstrated the detection of the galaxy with an accuracy of 94% via a quantum machine learning model from a NASA image. We divided the galaxy image from NASA into a small 16x16 image as input data. Then we encoded and train the data with a quantum circuit using the parameterized quantum circuit from the paper Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms, arXiv:1905. 10876. With the circuit with high expressibility, we trained and test our model with Cross-Entropy as our loss function and L-BFGS algorithm for optimization. This algorithm is realized in PyTorch and qiskit machine-learning module. This work s…