Despite the advent of Grover's algorithm for the unstructured search, its successful implementation on near-term quantum devices is still limited. We apply three strategies to reduce the errors associated with implementing quantum search algorithms. Our improved search algorithms have been implemented on the IBM quantum processors. Using them, we demonstrate three- and four-qubit search algorithm with higher average success probabilities compared to previous works. We present the successful execution of the five-qubit search on the IBM quantum processor for the first time. The results have been benchmarked using degraded ratio, which is the ratio between the experimental and the theoretical success probabilities. The fast decay of the degraded ratio supports our divide-and-conquer strategy. Our proposed strategies are also useful for implementation of quantum search algorithms in the post-NISQ era.
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…
Utility of NISQ devices: optimizing experimental parameters for the fabrication of Au atomic junction using gate-based quantum computers
Tokyo University of Agriculture and Technology（东京农工大学）；The Institute of Medical Science, The University of Tokyo（东京大学医学科学研究所）；The University of Tokyo（东京大学）
Quantum computational experiments exploiting Noisy Intermediate-Scale Quantum (NISQ) devices to demonstrate violation of a Bell inequality are proposed. They consist of running specified quantum algorithms on few-qubit computers. If such a device assures entanglement and performs single-shot measurements, the detection loophole is avoided. Four concise quantum circuits determining the expectation values of the relevant observables are used for a two-qubit system. It is possible to add an ancilla qubit to these circuits and eventually only measure the ancilla to obtain the relevant information.…
Current noise levels in physical realizations of qubits and quantum operations limit the applicability of conventional methods to characterize entanglement. In this adverse scenario, we follow a quantum variational approach to estimate the geometric measure of entanglement of multiqubit pure states. The algorithm requires only single-qubit gates and measurements, so it is well suited for NISQ devices. This is demonstrated by successfully implementing the method on IBM Quantum devices for Greenberger-Horne-Zeilinger states of $3$, $4$, and $5$ qubits. Numerical simulations with random states sh…
Sequence and Image Transformations with Monarq: Quantum Implementations for NISQ Devices
National Energy Research Scientific Computing Center, Lawrence Berkeley National Laboratory（美国能源部先进科学计算研究中心，劳伦斯伯克利国家实验室）；Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory（应用数学与计算研究处，劳伦斯伯克利国家实验室）；Computer Science Department, San Francisco State University（旧金山州立大学计算机科学系）；Scientific Data Division, Lawrence Berkeley National Laboratory（科学数据处，劳伦斯伯克利国家实验室）
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…
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…
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
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…
Simulating the dynamics of many-body quantum systems is believed to be one of the first fields that quantum computers can show a quantum advantage over classical computers. Noisy intermediate-scale quantum (NISQ) algorithms aim at effectively using the currently available quantum hardware. For quantum simulation, various types of NISQ algorithms have been proposed with individual advantages as well as challenges. In this work, we propose a new algorithm, truncated Taylor quantum simulator (TTQS), that shares the advantages of existing algorithms and alleviates some of the shortcomings. Our alg…
Kernel methods are the basis of most classical machine learning algorithms such as Gaussian Process (GP) and Support Vector Machine (SVM). Computing kernels using noisy intermediate scale quantum (NISQ) devices has attracted considerable attention due to recent progress in the design of NISQ devices. However noise and errors on current NISQ devices can negatively affect the predicted kernels. In this paper we utilize two quantum kernel machine learning (ML) algorithms to predict the labels of a Breast Cancer dataset on two different NISQ devices: quantum kernel Gaussian Process (qkGP) and quan…
Cloud-based quantum computers have become a reality with a number of companies allowing for cloud-based access to their machines with tens to more than 100 qubits. With easy access to quantum computers, quantum information processing will potentially revolutionize computation, and superconducting transmon-based quantum computers are among some of the more promising devices available. Cloud service providers today host a variety of these and other prototype quantum computers with highly diverse device properties, sizes, and performances. The variation that exists in today's quantum computers, e…
This paper explores two circuit approaches for quantum walks: the first consists of generalised controlled inversions, whereas the second one effectively replaces them with rotation operations around the basis states. We show the theoretical foundation of the rotational implementation. The rotational approach nullifies the large amount of ancilla qubits required to carry out the computation when using the inverter implementation. Our results concentrate around the comparison of the two architectures in terms of structure, benefits and detriments, as well as the computational resources needed f…
Improving the trainability of VQE on NISQ computers for solving portfolio optimization using convex interpolation
Origin Quantum Computing Company Limited（本源量子计算科技有限责任公司）；Laboratory of Quantum Information, University of Science and Technology of China（中国科学技术大学量子信息实验室）；Department of Electronic Information and Artificial Intelligence, West Anhui University（皖西大学电子信息与人工智能学院）；College of Physics and Optoelectronic Engineering, Ocean University of China（中国海洋大学物理与电子工程学院）；Institute of Artificial Intelligence, Hefei Comprehensive National Science Center（合肥综合性国家科学中心人工智能研究院）；Anhui Province Key Laboratory of Quantum Network, University of Science and Technology of China（中国科学技术大学安徽省量子网络重点实验室）
Due to the immense potential of quantum computers and the significant computing overhead required in machine learning applications, the variational quantum classifier (VQC) has received a lot of interest recently for image classification. The performance of VQC is jeopardized by the noise in Noisy Intermediate-Scale Quantum (NISQ) computers, which is a significant hurdle. It is crucial to remember that large error rates occur in quantum algorithms due to quantum decoherence and imprecision of quantum gates. Previous studies have looked towards using ensemble learning in conventional computing …
The imaginary-time evolution method is widely known to be efficient for obtaining the ground state in quantum many-body problems on a classical computer. A recently proposed quantum imaginary-time evolution method (QITE) faces problems of deep circuit depth and difficulty in the implementation on noisy intermediate-scale quantum (NISQ) devices. In this study, a nonlocal approximation is developed to tackle this difficulty. We found that by removing the locality condition or local approximation (LA), which was imposed when the imaginary-time evolution operator is converted to a unitary operator…
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…
Quantum computers can exploit a Hilbert space whose dimension increases exponentially with the number of qubits. In experiment, quantum supremacy has recently been achieved by the Google team by using a noisy intermediate-scale quantum (NISQ) device with over 50 qubits. However, the question of what can be implemented on NISQ devices is still not fully explored, and discovering useful tasks for such devices is a topic of considerable interest. Hybrid quantum-classical algorithms are regarded as well-suited for execution on NISQ devices by combining quantum computers with classical computers, a…
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…
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…
Quantum Simulation of Magnetic Materials: from Ab-Initio to NISQ
HQS Quantum Simulations GmbH（HQS量子模拟有限公司）；Department of High Performance Computing, Institute of Software Technology, German Aerospace Center (DLR)（德国航空航天中心软件技术研究所高性能计算部）
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,…
Simulating quantum dynamics is expected to be performed more easily on a quantum computer than on a classical computer. However, the currently available quantum devices lack the capability to implement fault-tolerant quantum algorithms for quantum simulation. Hybrid classical quantum algorithms such as the variational quantum algorithms have been proposed to effectively use current term quantum devices. One promising approach to quantum simulation in the noisy intermediate-scale quantum (NISQ) era is the diagonalisation based approach, with some of the promising examples being the subspace Var…
This paper addresses the practical aspects of quantum algorithms used in numerical integration, specifically their implementation on Noisy Intermediate-Scale Quantum (NISQ) devices. Quantum algorithms for numerical integration utilize Quantum Amplitude Estimation (QAE) (Brassard et al., 2002) in conjunction with Grovers algorithm. However, QAE is daunting to implement on NISQ devices since it typically relies on Quantum Phase Estimation (QPE), which requires many ancilla qubits and controlled operations. To mitigate these challenges, a recently published QAE algorithm (Suzuki et al., 2020), wh…
Quantum search algorithm (also known as Grover's algorithm) lays the foundation for many other quantum algorithms. Although it is very simple, its implementation is limited on noisy intermediate-scale quantum (NISQ) processors. Grover's algorithm was designed without considering the physical resources, such as depth, in the real implementations. Therefore, Grover's algorithm can be improved for NISQ devices. In this paper, we demonstrate how to implement quantum search algorithms better on NISQ devices. We present detailed benchmarks of the five-qubit quantum search algorithm on different quan…
We propose a new method for evaluating NISQ devices. This paper has three distinct parts. First, we present a new quantum algorithm that solves a two hundred year old problem of finding quadratic nonresidues (QNR) in polynomial time. We show that QNR is in Exact Quantum Polynomial time, while it is still unknown whether QNR is in P. Second, we present a challenge to create a probability distribution over the quadratic nonresidues. Due to the theoretical complexity gap, a quantum computer can achieve a higher success rate than any known method on a classical computer. A device beating the class…
Experimental Implementation of the Quantum Volunteer's Dilemma on NISQ Hardware: Noise Analysis and Digital-Twin Validation
Universidad del Cauca（考卡大学）；Massachusetts Institute of Technology（麻省理工学院）；Agency for Science, Technology and Research (A*STAR)（科学技术研究局）；Singapore Management University（新加坡管理大学）
A universal fault-tolerant quantum computer holds the promise to speed up computational problems that are otherwise intractable on classical computers; however, for the next decade or so, our access is restricted to noisy intermediate-scale quantum (NISQ) computers and, perhaps, early fault tolerant (EFT) quantum computers. This motivates the development of many near-term quantum algorithms including robust amplitude estimation (RAE), which is a quantum-enhanced algorithm for estimating expectation values. One obstacle to using RAE has been a paucity of ways of getting realistic error models i…
Noisy Intermediate-Scale Quantum computers are expected to be available this year. It is proposed to exploit such a device for decision making under uncertainty. The probabilistic character of quantum mechanics reflects this uncertainty. Concomitantly, the noise may add to it. The approach is standard in the sense that Bayes decision rule is used to decide on the basis of maximum expected reward. The novelty is to model the various action profiles and the development of `nature' as unitary transformations on a set of qubits. Measurement eventually yields samples of classical binary random vari…
Quantum computers are on the verge of becoming a commercially available reality. They represent a paradigm shift in computing, with a steep learning gradient. The creation of games is a way to ease the transition for beginners. We present a game similar to the Poker variant Texas hold 'em with the intention to serve as an engaging pedagogical tool to learn the basics rules of quantum computing. The concepts of quantum states, quantum operations and measurement can be learned in a playful manner. The difference to the classical variant is that the community cards are replaced by a quantum regis…
We present an architecture to investigate wave-particle duality in $N$-path interferometers on a universal quantum computer involving as low as $2\log N$ qubits and develop a measurement scheme which allows the efficient extraction of quantifiers of interference visibility and which-path information. We implement our algorithms for interferometers with up to $N=16$ paths in proof-of-principle experiments on a noisy intermediate-scale quantum (NISQ) device using down to $\mathcal{O}(\log N)$ gates and despite increasing noise consistently observe a complementary behavior between interference vi…
Variational quantum algorithms (VQAs) have been considered to be useful applications of noisy intermediate-scale quantum (NISQ) devices. Typically, in the VQAs, a parametrized ansatz circuit is used to generate a trial wave function, and the parameters are optimized to minimize a cost function. On the other hand, blind quantum computing (BQC) has been studied in order to provide the quantum algorithm with security by using cloud networks. A client with a limited ability to perform quantum operations hopes to have access to a quantum computer of a server, and BQC allows the client to use the se…
Qubit mapping is essential to quantum computing's fidelity and quantum computers' resource utilization. Yet, the existing qubit mapping schemes meet some challenges (e.g., crosstalk, SWAP overheads, diverse device topologies, etc.), leading to qubit resource under-utilization, high error rate, and low fidelity in computing results. This paper presents QuCloud+, a new qubit mapping scheme capable of handling these challenges. QuCloud+ has several new designs. (1) QuCloud+ enables multi-programming quantum computing on quantum chips with 2D/3D topology. (2) It partitions physical qubits for conc…
Quantum field theory (QFT) simulations are a potentially important application for noisy intermediate scale quantum (NISQ) computers. The ability of a quantum computer to emulate a QFT, therefore, constitutes a natural application-centric benchmark. Foundational quantum algorithms to simulate QFT processes rely on fault-tolerant computational resources, but to be useful on NISQ machines, error-resilient algorithms are required. Here we outline and implement a hybrid algorithm to calculate the lowest energy levels of the paradigmatic 1+1--dimensional interacting scalar QFT. We calculate energy …
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…
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…
As quantum technologies mature, the development of tools for benchmarking their ability to prepare and manipulate complex quantum states becomes increasingly necessary. A key concept, the state overlap between two quantum states, offers a natural tool to verify and cross-validate quantum simulators and quantum computers. Recent progress in controlling and measuring large quantum systems has motivated the development of state overlap estimators of varying efficiency and experimental complexity. Here, we demonstrate a practical approach for measuring the overlap between quantum states based on a…
In this article, we propose an interactive protocol for one party (the verifier) holding a quantum computer to verify the quantum computation power of another party's (the prover) device via a one-way quantum channel. This protocol is referred to as the dihedral coset problem (DCP) challenge. The verifier needs to prepare quantum states encoding secrets (DCP samples) and send them to the prover. The prover is then tasked with recovering those secrets with a certain accuracy. Numerical simulation demonstrates that this accuracy is sensitive to errors in quantum hardware. Additionally, the DCP c…
