The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far, either suffer from lack of accuracy and/or are limited to very small sizes of the problem, and thus have no practical usage. Here we present an advanced quantum algorithm for solving the Poisson equation with high accuracy and dynamically tunable problem size. After converting the Poisson equation to the linear systems through the finite difference method, we adopt the Harrow-Hassidim-Lloyd (HHL) algorithm as the basic framework. Particularly, in this work we present an advanced circuit that ensures the accuracy of the solution by implementing non-truncated eigenvalues through eigenvalue amplification as well as by increasing the accuracy of the controlled rotation angular coefficients, which are the critical factors in the HHL algorithm. We show that our algorithm not only increases the accuracy of the solutions, but also composes more practical and scalable circuits by dynamically controlling problem size in the NISQ devices. We present both simulated and experimental solutions, and conclude that overall results on the quantum hardware are dominated by the error in the CNOT gates.
Universal fault-tolerant quantum computers require millions of qubits with low error rates. Since this technology is years ahead, noisy intermediate-scale quantum (NISQ) computation is receiving tremendous interest. In this setup, quantum reservoir computing is a relevant machine learning algorithm. Its simplicity of training and implementation allows to perform challenging computations on today available machines. In this Letter, we provide a criterion to select optimal quantum reservoirs, requiring few and simple gates. Our findings demonstrate that they render better results than other comm…
Reducing the Number of Qubits from $n^2$ to $n\log_{2} (n)$ to Solve the Traveling Salesman Problem with Quantum Computers: A Proposal for Demonstrating Quantum Supremacy in the NISQ Era
Implementing a quantum algorithm on a NISQ device has several challenges that arise from the fact that such devices are noisy and have limited quantum resources. Thus, various factors contributing to the depth and width as well as to the noise of an implementation of an algorithm must be understood in order to assess whether an implementation will execute successfully on a given NISQ device. In this contribution, we discuss these factors and their impact on algorithm implementations. Especially, we will cover state preparation, oracle expansion, connectivity, circuit rewriting, and readout: th…
The progress in developing quantum hardware with functional quantum processors integrating tens of noisy qubits, together with the availability of near-term quantum algorithms has led to the release of the first quantum computers. These quantum computing systems already integrate different software and hardware components of the so-called "full-stack", bridging quantum applications to quantum devices. In this paper, we will provide an overview on current full-stack quantum computing systems. We will emphasize the need for tight co-design among adjacent layers as well as vertical cross-layer de…
Quantum machine learning is at the crossroads of two of the most exciting current areas of research; quantum computing and classical machine learning. It explores the interaction between quantum computing and machine learning, investigating how results and techniques from one field can be used to solve the problems of the other. Here, we investigate quantum support vector machine (QSVM) algorithm and its circuit version on present quantum computers. We propose a general encoding procedure extending QSVM algorithm, which would allow one to feed vectors with higher dimension in the training-data…
As superconducting qubits continue to advance technologically, the realization of quantum algorithms from theoretical abstraction to physical implementation requires knowledge of both quantum circuit construction as well as hardware limitations. In this study we present results from experiments run on IBM's 20-qubit `Poughkeepsie' architecture, with the goal of demonstrating various qubit qualities and challenges that arise in designing quantum algorithms. These include experimentally measuring $T_1$ and $T_2$ coherence times, gate fidelities, sequential CNOT gates, techniques for handling anc…
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…
We are in the Noisy Intermediate-Scale Quantum (NISQ) devices' era, in which quantum hardware has become available for application in real-world problems. However, demonstrating the usefulness of such NISQ devices are still rare. In this work, we consider a practical railway dispatching problem: delay and conflict management on single-track railway lines. We examine the issue of train dispatching consequences caused by the arrival of an already delayed train to the network segment being considered. This problem is computationally hard and needs to be solved almost in real-time. We introduce a …
Near-term quantum computation holds potential across multiple application domains. However, imperfect preparation and evolution of states due to algorithmic and experimental shortcomings, characteristic in the near-term implementation, would typically result in measurement outcomes deviating from the ideal setting. It is thus crucial for any near-term application to quantify and bound these output errors. We address this need by deriving robustness intervals which are guaranteed to contain the output in the ideal setting. The first type of interval is based on formulating robustness bounds as …
We develop a quantum computing scheme utilizing McLachlan variational principle in a hybrid quantum-classical algorithm to accurately calculate the transition dynamics of a closed quantum system with many excited states subject to a strong time-dependent perturbation. A systematic approach for optimal construction of a general N-state ansatz with unary N-qubit encoding is refined. We also utilize qubit efficient encoding in McLachlan variational quantum algorithm to reduce the number of qubits to log2 N, simultaneously diminishing depths of the quantum circuits. The significant reduction of th…
In the early years of fault-tolerant quantum computing (FTQC), it is expected that the available code distance and the number of magic states will be restricted due to the limited scalability of quantum devices and the insufficient computational power of classical decoding units. Here, we integrate quantum error correction and quantum error mitigation into an efficient FTQC architecture that effectively increases the code distance and $T$-gate count at the cost of constant sampling overheads in a wide range of quantum computing regimes. For example, while we need $10^4$ to $10^{10}$ logical op…
Noisy Intermediate-Scale Quantum (NISQ) hardware has unavoidable noises, and crosstalk error is a significant error source. When multiple quantum operations are executed simultaneously, the quantum state can be corrupted due to the crosstalk between gates during simultaneous operations, decreasing the circuit fidelity. In this work, we first report on several protocols for characterizing crosstalk. Then, we discuss different crosstalk mitigation methods from the hardware and software perspectives. Finally, we perform crosstalk injection experiments on the IBM quantum device and demonstrate the…
Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future. Quantum computers with 50-100 qubits may be able to perform tasks which surpass the capabilities of today's classical digital computers, but noise in quantum gates will limit the size of quantum circuits that can be executed reliably. NISQ devices will be useful tools for exploring many-body quantum physics, and may have other useful applications, but the 100-qubit quantum computer will not change the world right away --- we should regard it as a significant step toward the more powerful quantum technologi…
We review the development of generative modeling techniques in machine learning for the purpose of reconstructing real, noisy, many-qubit quantum states. Motivated by its interpretability and utility, we discuss in detail the theory of the restricted Boltzmann machine. We demonstrate its practical use for state reconstruction, starting from a classical thermal distribution of Ising spins, then moving systematically through increasingly complex pure and mixed quantum states. Intended for use on experimental noisy intermediate-scale quantum (NISQ) devices, we review recent efforts in reconstruct…
A key problem in the field of quantum computing is understanding whether quantum machine learning (QML) models implemented on noisy intermediate-scale quantum (NISQ) machines can achieve quantum advantages. Recently, Huang et al. [Nat Commun 12, 2631] partially answered this question by the lens of quantum kernel learning. Namely, they exhibited that quantum kernels can learn specific datasets with lower generalization error over the optimal classical kernel methods. However, most of their results are established on the ideal setting and ignore the caveats of near-term quantum machines. To thi…
GroverFigureOfMerit: An Agnostic Figure of Merit for Quantum Backend Characterization in the NISQ Era
Universidad Nacional de La Plata, Facultad de Informática, Laboratorio de Investigación y Formación en Informática Avanzada (LIFIA)（拉普拉塔国立大学，计算机学院，先进信息研究与培训实验室）
Error mitigation is one of the key challenges in realising the full potential of quantum cryptographic protocols. Consequently, there is a lot of interest in adapting techniques from quantum error correction (QEC) to improve the robustness of quantum cryptographic protocols. In this work, we benchmark the performance of different QKD protocols on noisy quantum devices, with and without error correction. We obtain the secure key rates of BB84, B92 and BBM92 QKD protocols over a quantum channel that is subject to amplitude-damping noise. We demonstrate, theoretically and via implementations on t…
Due to little consideration in the hardware constraints, e.g., limited connections between physical qubits to enable two-qubit gates, most quantum algorithms cannot be directly executed on the Noisy Intermediate-Scale Quantum (NISQ) devices. Dynamically remapping logical qubits to physical qubits in the compiler is needed to enable the two-qubit gates in the algorithm, which introduces additional operations and inevitably reduces the fidelity of the algorithm. Previous solutions in finding such remapping suffer from high complexity, poor initial mapping quality, and limited flexibility and con…
In the era of noisy intermediate-scale quantum (NISQ), executing quantum algorithms on actual quantum devices faces unique challenges. One such challenge is that quantum devices in this era have restricted connectivity: quantum gates are allowed to act only on specific pairs of physical qubits. For this reason, a quantum circuit needs to go through a compiling process called qubit routing before it can be executed on a quantum computer. In this study, we propose a CNOT synthesis method called the token reduction method to solve this problem. The token reduction method works for all quantum com…
Due to several physical limitations in the realisation of quantum hardware, today's quantum computers are qualified as Noisy Intermediate-Scale Quantum (NISQ) hardware. NISQ hardware is characterized by a small number of qubits (50 to a few hundred) and noisy operations. Moreover, current realisations of superconducting quantum chips do not have the ideal all-to-all connectivity between qubits but rather at most a nearest-neighbour connectivity. All these hardware restrictions add supplementary low-level requirements. They need to be addressed before submitting the quantum circuit to an actual…
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…
It is hard to achieve a theoretical quantum advantage on NISQ devices. Besides the attempts to reduce error using error mitigation and dynamical decoupling, small quantum error correction and fault-tolerant schemes that reduce the high overhead of traditional schemes have also been proposed. According to the recent advancements in fault tolerance, it is possible to minimize the number of ancillary qubits using flags. While implementing those schemes is still impossible, it is worthwhile to bridge the gap between the NISQ era and the FTQC era. Here, we introduce a benchmarking method to test fa…
When working with algorithms on quantum devices, quantum memory becomes a crucial bottleneck due to low qubit count in NISQ-era devices. In this context, the concept of `divide and compute', wherein a quantum circuit is broken into several subcircuits and executed separately, while stitching the results of the circuits via classical post-processing, becomes a viable option, especially in NISQ-era devices. This paper introduces \textbf{Qurzon}, a proposed novel quantum compiler that incorporates the marriage of techniques of divide and compute with the state-of-the-art algorithms of optimal qub…
NISQ devices have several physical limitations and unavoidable noisy quantum operations, and only small circuits can be executed on a quantum machine to get reliable results. This leads to the quantum hardware under-utilization issue. Here, we address this problem and improve the quantum hardware throughput by proposing a Quantum Multi-programming Compiler (QuMC) to execute multiple quantum circuits on quantum hardware simultaneously. This approach can also reduce the total runtime of circuits. We first introduce a parallelism manager to select an appropriate number of circuits to be executed …
First quantum computers very recently have demonstrated "quantum supremacy" or "quantum advantage": Executing a computation that would have been impossible on a classical machine. Today's quantum computers follow the NISQ paradigm: They exhibit error rates that are much higher than in conventional electronics and have insufficient quantum resources to support powerful error correction protocols. This raises questions which relevant computations are within the reach of NISQ architectures. Several "NISQ-era algorithms" are assumed to match the specifics of such computers; for instance, variation…
Recently, IBM, Google, and Intel showcased quantum computers ranging from 49 to 72 qubits. While these systems represent a significant milestone in the advancement of quantum computing, existing and near-term quantum computers are not yet large enough to fully support quantum error-correction. Such systems with few tens to few hundreds of qubits are termed as Noisy Intermediate Scale Quantum computers (NISQ), and these systems can provide benefits for a class of quantum algorithms. In this paper, we study the problems of Qubit-Allocation (mapping of program qubits to machine qubits) and Qubit-…
We explore the use of symmetry-adapted perturbation theory (SAPT) as a simple and efficient means to compute interaction energies between large molecular systems with a hybrid method combing NISQ-era quantum and classical computers. From the one- and two-particle reduced density matrices of the monomer wavefunctions obtained by the variational quantum eigensolver (VQE), we compute SAPT contributions to the interaction energy [SAPT(VQE)]. At first order, this energy yields the electrostatic and exchange contributions for non-covalently bound systems. We empirically find from ideal statevector s…
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…
We execute the quantum eraser, the Elitzur-Vaidman bomb, and the Hardy's paradox experiment using high-level programming language on a generic, gate-based superconducting quantum processor made publicly available by IBM. The quantum circuits for these experiments use a mixture of one-qubit and multi-qubit gates and require high entanglement gate accuracy. The results aligned with theoretical predictions of quantum mechanics to high confidence on circuits using up to 3 qubits. The power of quantum computers and high-level language as a platform for experimenting and studying quantum phenomena i…
Trustworthy Quantum Machine Learning: A Roadmap for Reliability, Robustness, and Security in the NISQ Era
Department of Electrical Engineering and Computer Science, University of Stavanger, Norway（斯瓦尔巴大学电气工程与计算机科学系）；School of Physics, Engineering and Technology, University of York, UK（约克大学物理、工程与技术学院）
Fraunhofer Institute for Industrial Mathematics ITWM（弗劳恩霍夫工业数学研究所ITWM）；University of Kaiserslautern（凯泽斯劳滕大学）
Edges are image locations where the gray value intensity changes suddenly. They are among the most important features to understand and segment an image. Edge detection is a standard task in digital image processing, solved for example using filtering techniques. However, the amount of data to be processed grows rapidly and pushes even supercomputers to their limits. Quantum computing promises exponentially lower memory usage in terms of the number of qubits compared to the number of classical bits. In this paper, we propose a hybrid method for quantum edge detection based on the idea of a qua…
