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 Variational Quantum Simulator (SVQS), Variational Fast Forwarding (VFF), fixed-state Variational Fast Forwarding (fs-VFF), and the Variational Hamiltonian Diagonalisation (VHD) algorithms. However, these algorithms require a feedback loop between the classical and quantum computers, which can be a crucial bottleneck in practical application. Here, we present the Classical Quantum Fast Forwarding (CQFF) as an alternative diagonalisation based algorithm for quantum simulation. CQFF shares some similarities with SVQS, VFF, fs-VFF and VHD but removes the need for a classical-quantum feedback loop and controlled multi-qubit unitaries. The CQFF algorithm does not suffer from the barren plateau problem and the accuracy can be systematically increased. Furthermore, if the Hamiltonian to be simulated is expressed as a linear combination of tensored-Pauli matrices, the CQFF algorithm reduces to the task of sampling some many-body quantum state in a set of Pauli-rotated bases, which is easy to do in the NISQ era. We run the CQFF algorithm on existing quantum processors and demonstrate the promise of the CQFF algorithm for current-term quantum hardware. Our work provides a $10^4$ improvement over the previous record.
Using Grover algorithm, this work investigates a technique for encoding search phrases used in wildcard searches. The technique involves creating a phase Oracle that loads data into a quantum circuit together with the search terms that have been encoded. The method entails constructing a phase Oracle programmatically using encoded input information and encoded search terms. By combining Grover diffusion operator with the phase Oracle, Hadamard gates, and zero-initialized three-qubit states, a complete quantum circuit is created. Trapped ion and superconducting qubit quantum computers, which we…
Quantum walks are an analog of classical random walks in quantum systems. Quantum walks have smaller hitting times compared to classical random walks on certain types of graphs, leading to a quantum advantage of quantum-walks-based algorithms. An important feature of quantum walks is that they are accompanied by the excitation transfer from one site to another, and a moment of hitting the destination site is characterized by the maximum probability amplitude of observing the excitation on this site. It is therefore prospective to consider such problems as candidates for quantum advantage demon…
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…
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 bee…
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…
Reconfigurable linear optical networks are a key component for the development of optical quantum information processing platforms in the NISQ era and beyond. We report the implementation of such a device based on an innovative design that uses the mode mixing of a multimode fiber in combination with the programmable wavefront shaping of a SLM. The capabilities of the platform are explored in the classical regime. For up to 8 inputs and a record number of 38 outputs, we achieve fidelities in excess of 93%, and losses below 6.5dB. The device was built inside a standard server rack to allow for …
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…
In this work, we propose IQGAN, a quantum Generative Adversarial Network (GAN) framework for multiqubit image synthesis that can be efficiently implemented on Noisy Intermediate Scale Quantum (NISQ) devices. We investigate the reasons for the inferior generative performance of current quantum GANs in our preliminary study and conclude that an adjustable input encoder is the key to ensuring high-quality data synthesis. We then propose the IQGAN architecture featuring a trainable multiqubit quantum encoder that effectively embeds classical data into quantum states. Furthermore, we propose a comp…
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…
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…
Because noisy, intermediate-scale quantum (NISQ) machines accumulate errors quickly, we need new approaches to designing NISQ-aware algorithms and assessing their performance. Algorithms with characteristics that appear less desirable under ideal circumstances, such as lower success probability, may in fact outperform their ideal counterparts on existing hardware. We propose an adaptation of Grover's algorithm, subdividing the phase flip into segments to replace a digital counter and complex phase flip decision logic. We applied this approach to obtaining the best solution of the MAX-CUT probl…
Efficient time-series prediction on NISQ devices via time-delayed quantum extreme learning machine
Tokyo University of Agriculture and Technology（东京农工大学）；Technische Universität Ilmenau（埃尔朗根-纽伦堡工业大学）；The Institute of Medical Science, The University of Tokyo（东京大学医学科学研究所）；The Graduate School of Information Science and Technology, The University of Tokyo（东京大学信息理工学系研究科）
Some of the most problematic issues that limit the implementation of applications on Noisy Intermediate Scale Quantum (NISQ) machines are the adverse impacts of both incoherent and coherent errors. We conducted an in-depth study of coherent errors on a quantum hardware platform using a transverse field Ising model Hamiltonian as a sample user application. We report here on the results from these computations using several error mitigation protocols that profile these errors and provide an indication of the hardware qubit stability. Through a detailed set of measurements we identify inter-day a…
To bridge the gap between limited hardware access and the huge demand for experiments for Noisy Intermediate-Scale Quantum (NISQ) computing system study, a simulator which can capture the modeling of both the quantum processor and its classical control system to realize early-stage evaluation and design space exploration, is naturally invoked but still missing. This paper presents SANQ, a Simulation framework for Architecting NISQ computing system. SANQ consists of two components, 1) an optimized noisy quantum computing (QC) simulator with flexible error modeling accelerated by eliminating red…
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…
Fraunhofer Institute for Industrial Mathematics ITWM（弗劳恩霍夫工业数学研究所）；University of Kaiserslautern（凯泽斯劳滕大学）
In image processing, the amount of data to be processed grows rapidly, in particular when imaging methods yield images of more than two dimensions or time series of images. Thus, efficient processing is a challenge, as data sizes may push even supercomputers to their limits. Quantum image processing promises to encode images with logarithmically less qubits than classical pixels in the image. In theory, this is a huge progress, but so far not many experiments have been conducted in practice, in particular on real backends. Often, the precise conversion of classical data to quantum states, the …
Quantum criticality emerges from the collective behavior of many interacting quantum particles, often at the transition between different phases of matter. It is one of the cornerstones of condensed matter physics, which we access on noisy intermediate-scale (NISQ) quantum devices by leveraging a dynamically driven phenomenon. We probe the critical properties of the one-dimensional quantum Ising model on a programmable superconducting quantum chip via a Kibble-Zurek process, obtain scaling laws, and estimate critical exponents despite inherent sources of errors on the hardware. In addition, we…
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…
Routing plays an important role in programming noisy, intermediate-scale quantum (NISQ) devices, where limited connectivity in the register is overcome by swapping quantum information between locations. However, routing a quantum state using noisy gates introduces non-trivial noise dynamics, and deciding on an optimal route to minimize accumulated error requires estimates of the expected state fidelity. Here we validate a model for state-dependent routing dynamics in a NISQ processor based on correlated binary noise. We develop a composable, state-dependent noise model for CNOT and SWAP operat…
As the advances in quantum hardware bring us into the noisy intermediate-scale quantum (NISQ) era, one possible task we can perform without quantum error correction using NISQ machines is the variational quantum eigensolver (VQE) due to its shallow depth. A specific problem that we can tackle is the strongly interacting Fermi-Hubbard model, which is classically intractable and has practical implications in areas like superconductivity. In this Article, we outline the details about the gate sequence, the measurement scheme and the relevant error mitigation techniques for the implementation of t…
We present experimental results on running 4-qubit unstructured search on IBM quantum processors. Our best attempt attained probability of success around 24.5%. We try several algorithms and use the most recent developments in quantum search to reduce the number of entangling gates that are currently considered the main source of errors in quantum computations. Comparing theoretical expectations of an algorithm performance with the actual data, we explore the hardware limits, showing sharp, phase-transition-like degradation of performance on quantum processors. We conclude that it is extremely…
The advent of Noisy Intermediate-Scale Quantum (NISQ) technology is changing rapidly the landscape and modality of research in quantum physics. NISQ devices, such as the IBM Q Experience, have very recently proven their capability as experimental platforms accessible to everyone around the globe. Until now, IBM Q Experience processors have mostly been used for quantum computation and simulation of closed systems. Here we show that these devices are also able to implement a great variety of paradigmatic open quantum systems models, hence providing a robust and flexible testbed for open quantum …
The Quantum Approximate Optimization Algorithm (QAOA), which is a variational quantum algorithm, aims to give sub-optimal solutions of combinatorial optimization problems. It is widely believed that QAOA has the potential to demonstrate application-level quantum advantages in the noisy intermediate-scale quantum(NISQ) processors with shallow circuit depth. Since the core of QAOA is the computation of expectation values of the problem Hamiltonian, an important practical question is whether we can find an efficient classical algorithm to solve quantum mean value in the case of general shallow qu…
Hybrid quantum-classical algorithms are central to much of the current research in quantum computing, particularly when considering the noisy intermediate-scale quantum (NISQ) era, with a number of experimental demonstrations having already been performed. In this perspective, we discuss in a very broad sense what it means for an algorithm to be hybrid quantum-classical. We first explore this concept very directly, by building a definition based on previous work in abstraction/representation theory, arguing that what makes an algorithm hybrid is not directly how it is run (or how many classica…
As noisy intermediate-scale quantum (NISQ) processors increase in size and complexity, their use as general purpose quantum simulators will rely on algorithms based on the Trotter-Suzuki expansion. We run quantum simulations on a small, highly accurate quantum processor, and show how one can optimize simulation accuracy by balancing algorithmic (Trotter) errors against native errors specific to the quantum hardware at hand. We further study the interplay between native errors, Trotter errors, and the emergence of chaos as seen in measurements of a time averaged fidelity-out-of-time-ordered-cor…
Variational quantum algorithms (VQAs) have shown strong evidences to gain provable computational advantages for diverse fields such as finance, machine learning, and chemistry. However, the heuristic ansatz exploited in modern VQAs is incapable of balancing the tradeoff between expressivity and trainability, which may lead to the degraded performance when executed on the noisy intermediate-scale quantum (NISQ) machines. To address this issue, here we demonstrate the first proof-of-principle experiment of applying an efficient automatic ansatz design technique, i.e., quantum architecture search…
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）
The analogy between quantum chemistry and light-front quantum field theory, first noted by Kenneth G. Wilson, serves as motivation to develop light-front quantum simulation of quantum field theory. We demonstrate how calculations of hadron structure can be performed on Noisy Intermediate-Scale Quantum devices within the Basis Light-Front Quantization framework. We calculate the light-front wave functions of pions using an effective light-front Hamiltonian in a basis representation on a current quantum processor. We use the Variational Quantum Eigensolver to find the ground state energy and wav…
Quantum Computers, one fully realized, can represent an exponential boost in computing power. However, the computational power of the current quantum computers, referred to as Noisy Internediate Scale Quantum, or NISQ, is severely limited because of environmental and intrinsic noise, as well as the very low connectivity between qubits compared to their total amount. We propose a virtual quantum processor that emulates a generic hybrid quantum machine which can serve as a logical version of quantum computing hardware. This hybrid classical quantum machine powers quantum-logical computations whi…
A Useful Metric for the NISQ Era: Qubit Error Probability and Its Role in Zero Noise Extrapolation
The Abdus Salam International Center for Theoretical Physics (ICTP)（阿卜杜斯·萨拉姆国际理论物理中心）；Mondragon Unibertsitatea（蒙德拉贡大学）；Universidad del País Vasco UPV/EHU（巴斯克大学）；University of the Basque Country (UPV/EHU)（巴斯克大学）
