Solving the eigenproblems of Hermitian matrices is a significant problem in many fields. The quantum resonant transition (QRT) algorithm has been proposed and demonstrated to solve this problem using quantum devices. To better realize the capabilities of the QRT with recent quantum devices, we improve this algorithm and develop a new procedure to reduce the time complexity. Compared with the original algorithm, it saves one qubit and reduces the complexity with error $ϵ$ from $O(1/{ϵ}^2)$ to $O(1/ϵ)$. Thanks to these optimizations, we can obtain the energy spectrum and ground state of the effective Hamiltonian of the water molecule more accurately and in only 20 percent of the time in a four-qubit processor compared to previous work. More generally, for non-Hermitian matrices, a singular-value decomposition has essential applications in more areas, such as recommendation systems and principal component analysis. The QRT has also been used to prepare singular vectors corresponding to the largest singular values, demonstrating its potential for applications in quantum machine learning.

Eigensolvers have a wide range of applications in machine learning. Quantum eigensolvers have been developed for achieving quantum speedup. Here, we propose a parallel quantum eigensolver (PQE) for solving a set of machine learning problems, which is based on quantum multi-resonant transitions that simultaneously trigger multiple energy transitions in the systems on demand. PQE has a polylogarithmic cost in problem size under certain circumstances and is hardware efficient, such that it is implementable in near-term quantum computers. As a verification, we utilize it to construct a collaborative filtering quantum recommendation system and implement an experiment of the movie recommendation tasks on a nuclear spin quantum processor. As a result, our recommendation system accurately suggests movies to the user that he/she might be interested in. We further demonstrate the applications of PQE in classification and image completion. In the future, our work will shed light on more applications in quantum machine learning.

Simulating quantum physical processes has been one of the major motivations for quantum information science. Quantum channels, which are completely positive and trace preserving processes, are the standard mathematical language to describe quantum evolution, while in recent years quantum superchannels have emerged as the substantial extension. Superchannels capture effects of quantum memory and non-Markovianality more precisely, and have found broad applications in universal models, algorithm, metrology, discrimination tasks, as examples. Here, we report an experimental simulation of qubit superchannels in a nuclear magnetic resonance (NMR) system with high accuracy, based on a recently developed quantum algorithm for superchannel simulation. Our algorithm applies to arbitrary target superchannels, and our experiment shows the high quality of NMR simulators for near-term usage. Our approach can also be adapted to other experimental systems and demonstrates prospects for more applications of superchannels.

With the rapid development of quantum technology, the growing manipulated Hilbert space makes learning the dynamics of the quantum system a significant challenge. Machine learning technique has brought apparent advantages in some learning strategies, therefore, we introduce it to indirect learning in this paper. Based on Choi–Jamiolkowski isomorphism, we propose a protocol that learns the dynamics of an inaccessible quantum system using a quantum device at hand. For an n-qubit system, the learning task can be done iteratively, with operational complexity O ( poly ( n , L ) / ϵ 2 ) in each iteration, where L is the circuit depth and ε is the measurement error. Then we theoretically prove its noise resilience to global depolarization, state preparation and measurement noise, and unitary noise in gates implementation, where we find the learned dynamics stay invariant. Finally, we investigate the protocol experimentally on a nitrogen-vacancy center system with a natural noise source. The results show that the behavior of a relatively intractable nuclear spin can be learned through an easily accessible electron spin under different noise models, demonstrating the protocol’s feasibility.

Offshore channel clearance is an essential underwater task to protect vessels and divers effectively, but current underwater target classification relies heavily on operator identification. Machine learning provides highly accurate methods for image classification as well as detection. In this paper, a new hybrid quantum-classical classification algorithm is proposed. It uses quantum devices to reduce dimension and denoise data sets, greatly reducing the difficulty of classical computer processing data. Using abundant classical classification algorithms, the classification problem of different scenarios can be processed, improving the classification efficiency. Using two kinds of underwater object data sets as examples, the numerical simulation results show that the quantum algorithm can accurately achieve dimensionality reduction. This hybrid algorithm has polynomial acceleration in dimension reduction than classical methods, even considering the classical readout of quantum data. The results also show that the classification accuracy of the training set improves from 0.772 to 0.821 compared to the original dataset. Furthermore, different classical classifiers can be selected in the case of different objects, so this hybrid algorithm has broad application prospects in different fields.