Two novel measurement-based, quantum clustering algorithms are proposed based on quantum parallelism and entanglement. The first algorithm follows a divisive approach. The second algorithm is based on unsharp measurements, where we construct an effect operator with a Gaussian probability distribution to cluster similar data points. A major advantage of both algorithms is that they are simplistic in nature, easy to implement, and well suited for noisy intermediate scale quantum computers. We have successfully applied the first algorithm on a concentric circle data set, where the classical clustering approach fails, as well as on the Churrtiz data set of $130$ cities, where we show that the algorithm succeeds with very low quantum resources. We applied the second algorithm on the labeled Wisconsin breast cancer dataset, and found that it is able to classify the dataset with high accuracy using only $O(log(D))$ qubits and polynomial measurements, where $D$ is the maximal distance within any two points in the dataset. We also show that this algorithm works better with an assumed measurement error in the quantum system, making it extremely well-suited for NISQ devices.
A practical fault-tolerant quantum computer is worth looking forward to as it provides applications that outperform their known classical counterparts. However, millions of interacting qubits with stringent criteria are required, which is intractable with current quantum technologies. As it would take decades to make it happen, exploiting the power of noisy intermediate-scale quantum(NISQ) devices, which already exist, is becoming one of current goals. Matrix exponentiation, especially hermitian matrix exponentiation, is an essential element for quantum information processing. In this article,…
Naval Surface Warfare Center, Dahlgren Division（海军水面作战中心达尔格伦分部）
In the NISQ-era of quantum computing, we should not expect to see quantum devices that provide an exponential improvement in runtime for practical problems, due to the lack of error correction and small number of qubits available. Nevertheless, these devices should be able to provide other performance improvements, particularly when combined with existing classical machines. In this article, we develop several hybrid quantum-classical clustering algorithms that can be employed as subroutines on small, NISQ-era devices. These new hybrid algorithms require a number of qubits that is at most loga…
Real-time clustering of big performance data generated by the telecommunication networks requires domain-specific high performance compute infrastructure to detect anomalies. In this paper, we evaluate noisy intermediate-scale quantum (NISQ) computers characterized by low decoherence times, for K-means clustering and propose three strategies to generate shorter-depth quantum circuits needed to overcome the limitation of NISQ computers. The strategies are based on exploiting; i) quantum interference, ii) negative rotations and iii) destructive interference. By comparing our implementations on I…
Quantum machine learning is one of the most promising applications of quantum computing in the Noisy Intermediate-Scale Quantum(NISQ) era. Here we propose a quantum convolutional neural network(QCNN) inspired by convolutional neural networks(CNN), which greatly reduces the computing complexity compared with its classical counterparts, with $O((log_{2}M)^6) $ basic gates and $O(m^2+e)$ variational parameters, where $M$ is the input data size, $m$ is the filter mask size and $e$ is the number of parameters in a Hamiltonian. Our model is robust to certain noise for image recognition tasks and the…
TensorCircuit is an open source quantum circuit simulator based on tensor network contraction, designed for speed, flexibility and code efficiency. Written purely in Python, and built on top of industry-standard machine learning frameworks, TensorCircuit supports automatic differentiation, just-in-time compilation, vectorized parallelism and hardware acceleration. These features allow TensorCircuit to simulate larger and more complex quantum circuits than existing simulators, and are especially suited to variational algorithms based on parameterized quantum circuits. TensorCircuit enables orde…
Toward quantum machine learning deployed on imperfect near-term intermediate-scale quantum (NISQ) processors, the entire physical implementation of should include as less as possible hand-designed modules with only a few ad-hoc parameters to be determined. This work presents such a hardware-friendly end-to-end quantum machine learning scheme that can be implemented with imperfect near-term intermediate-scale quantum (NISQ) processors. The proposal transforms the machine learning task to the optimization of controlled quantum dynamics, in which the learning model is parameterized by experimenta…
Non-equilibrium physics including many-body localization (MBL) has attracted increasing attentions, but theoretical approaches of reliably studying non-equilibrium properties remain quite limited. In this Letter, we propose a systematic approach to probe MBL phases via the excited-state variational quantum eigensolver (VQE) and demonstrate convincing results of MBL on a quantum hardware, which we believe paves a promising way for future simulations of non-equilibrium systems beyond the reach of classical computations in the noisy intermediate-scale quantum (NISQ) era. Moreover, the MBL probing…
Centre for Quantum Technologies（量子技术中心）；Institute for Quantum Computing and Quantum Technologies, NCSR Demokritos（德谟克利特国家科学研究中心量子计算与量子技术研究所）；School of Electronics and Computer Science, University of Southampton（南安普顿大学电子与计算机科学学院）；AngelQ Quantum Computing（AngelQ量子计算）
As quantum computers mature, quantum error correcting codes (QECs) will be adopted in order to suppress errors to any desired level $E$ at a cost in qubit-count $n$ that is merely poly-logarithmic in $1/E$. However in the NISQ era, the complexity and scale required to adopt even the smallest QEC is prohibitive. Instead, error mitigation techniques have been employed; typically these do not require an increase in qubit-count but cannot provide exponential error suppression. Here we show that, for the crucial case of estimating expectation values of observables (key to almost all NISQ algorithms…
Demonstration of subspace-search variational quantum eigensolver using photonic orbital angular momentum qudits
Korea Institute of Science and Technology (KIST)（韩国科学技术院）；Korea University of Science and Technology（韩国科学技术院）；Kyung Hee University（庆熙大学）；Gwangju Institute of Science and Technology（光州科学技术院）
Implementation of variational Quantum Machine Learning (QML) algorithms on Noisy Intermediate-Scale Quantum (NISQ) devices is known to have issues related to the high number of qubits needed and the noise associated with multi-qubit gates. In this paper, we propose a variational QML algorithm using a dressed quantum network to address these issues. Using the "super compressed encoding" scheme that we follow here, the classical encoding layer in our dressed network drastically scales down the input-dimension, before feeding the input to the variational quantum circuit. Hence, the number of qubi…
Ground-state preparation for a given Hamiltonian is a common quantum-computing task of great importance and has relevant applications in quantum chemistry, computational material modeling, and combinatorial optimization. We consider an approach to simulate dissipative non-Hermitian Hamiltonian quantum dynamics using Hamiltonian simulation techniques to efficiently recover the ground state of a target Hamiltonian. The proposed method facilitates the energy transfer by repeatedly projecting ancilla qubits to the desired state, rendering the effective non-Hermitian Hamiltonian evolution on the sy…
Energy Landscape Structure of Small Graph Isomorphism Under Variational Optimization
Calcutta Institute of Engineering and Management, Maulana Abul Kalam Azad University of Technology（加尔各答工程与管理学院，穆拉纳·阿布尔·卡拉姆·阿扎德技术大学）；University of Dhaka（达卡大学）；Institute of Theoretical and Applied Informatics, Polish Academy of Sciences（波兰科学院理论与应用信息研究所）；Silesian University of Technology（西里西亚理工大学）
Validating a Koopman-Quantum Hybrid Paradigm for Diagnostic Denoising of Fusion Devices
School of Physical Science and Technology, Beijing University of Posts and Telecommunications（北京邮电大学物理科学与技术学院）；China Mobile (Suzhou) Software Technology Company Limited（中国移动（苏州）软件技术有限公司）；Institute of Plasma Physics, Chinese Academy of Sciences（中国科学院等离子体物理研究所）；College of Physics and Optoelectronic Engineering, Shenzhen University（深圳大学物理与光电工程学院）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心（广东））
In the Noisy Intermediate-Scale Quantum (NISQ) era, solving the electronic structure problem from chemistry is considered as the "killer application" for near-term quantum devices. In spite of the success of variational hybrid quantum/classical algorithms in providing accurate energy profiles for small molecules, careful considerations are still required for the description of complicated features of potential energy surfaces. Because the current quantum resources are very limited, it is common to focus on a restricted part of the Hilbert space (determined by the set of active orbitals). While…
Variational quantum algorithms (VQAs) are considered as one of the most promising candidates for achieving quantum advantages on quantum devices in the noisy intermediate-scale quantum (NISQ) era. They have been developed for numerous applications such as image processing and solving linear systems of equations. The application of VQAs can be greatly enlarged if users with limited quantum capabilities can run them on remote powerful quantum computers. But the private data of clients may be leaked to quantum servers in such a quantum cloud model. To solve the problem, a novel quantum homomorphi…
Quantum enhanced stratification of Breast Cancer: exploring quantum expressivity for real omics data
National Research Council of Italy (CNR), Institute of Informatics（意大利国家研究理事会（CNR）信息学院）；Computational Biomedicine Unit, Department of Medical Sciences, University of Turin（都灵大学医学科学系计算生物医学单元）；University of Siena（锡耶纳大学）；Institute for High Performance Computing（高性能计算研究所）；Networking (ICAR), National Research Council of Italy (CNR)（网络（ICAR），意大利国家研究理事会（CNR））
