Noisy Intermediate-scale Quantum Research Articles

Measurement-induced entanglement and teleportation on a noisy quantum processor

Measurement has a special role in quantum theory1: by collapsing the wavefunction, it can enable phenomena such as teleportation2 and thereby alter the ‘arrow of time’ that constrains unitary evolution. When integrated in many-body dynamics, measurements can lead to emergent patterns of quantum information in space–time3–10 that go beyond the established paradigms for characterizing phases, either in or out of equilibrium11–13. For present-day noisy intermediate-scale quantum (NISQ) processors14, the experimental realization of such physics can be problematic because of hardware limitations and the stochastic nature of quantum measurement. Here we address these experimental challenges and study measurement-induced quantum information phases on up to 70 superconducting qubits. By leveraging the interchangeability of space and time, we use a duality mapping9,15–17 to avoid mid-circuit measurement and access different manifestations of the underlying phases, from entanglement scaling3,4 to measurement-induced teleportation18. We obtain finite-sized signatures of a phase transition with a decoding protocol that correlates the experimental measurement with classical simulation data. The phases display remarkably different sensitivity to noise, and we use this disparity to turn an inherent hardware limitation into a useful diagnostic. Our work demonstrates an approach to realizing measurement-induced physics at scales that are at the limits of current NISQ processors.

Benchmarking noisy intermediate scale quantum error mitigation strategies for ground state preparation of the HCl molecule

Benchmarking noisy intermediate scale quantum error mitigation strategies for ground state preparation of the HCl molecule

Quantum generative adversarial networks based on a readout error mitigation method with fault tolerant mechanism

Readout errors caused by measurement noise are a significant source of errors in quantum circuits, which severely affect the output results and are an urgent problem to be solved in noisy-intermediate scale quantum (NISQ) computing. In this paper, we use the bit-flip averaging (BFA) method to mitigate frequent readout errors in quantum generative adversarial networks (QGAN) for image generation, which simplifies the response matrix structure by averaging the qubits for each random bit-flip in advance, successfully solving problems with high cost of measurement for traditional error mitigation methods. Our experiments were simulated in Qiskit using the handwritten digit image recognition dataset under the BFA-based method, the Kullback–Leibler (KL) divergence of the generated images converges to 0.04, 0.05, and 0.1 for readout error probabilities of p = 0.01, p = 0.05, and p = 0.1, respectively. Additionally, by evaluating the fidelity of the quantum states representing the images, we observe average fidelity values of 0.97, 0.96, and 0.95 for the three readout error probabilities, respectively. These results demonstrate the robustness of the model in mitigating readout errors and provide a highly fault tolerant mechanism for image generation models.

Erasure conversion in a high-fidelity Rydberg quantum simulator

Minimizing and understanding errors is critical for quantum science, both in noisy intermediate scale quantum (NISQ) devices1 and for the quest towards fault-tolerant quantum computation2,3. Rydberg arrays have emerged as a prominent platform in this context4 with impressive system sizes5,6 and proposals suggesting how error-correction thresholds could be significantly improved by detecting leakage errors with single-atom resolution7,8, a form of erasure error conversion9–12. However, two-qubit entanglement fidelities in Rydberg atom arrays13,14 have lagged behind competitors15,16 and this type of erasure conversion is yet to be realized for matter-based qubits in general. Here we demonstrate both erasure conversion and high-fidelity Bell state generation using a Rydberg quantum simulator5,6,17,18. When excising data with erasure errors observed via fast imaging of alkaline-earth atoms19–22, we achieve a Bell state fidelity of ge 0.997{1}_{-13}^{+10}, which improves to ge 0.998{5}_{-12}^{+7} when correcting for remaining state-preparation errors. We further apply erasure conversion in a quantum simulation experiment for quasi-adiabatic preparation of long-range order across a quantum phase transition, and reveal the otherwise hidden impact of these errors on the simulation outcome. Our work demonstrates the capability for Rydberg-based entanglement to reach fidelities in the 0.999 regime, with higher fidelities a question of technical improvements, and shows how erasure conversion can be utilized in NISQ devices. These techniques could be translated directly to quantum-error-correction codes with the addition of long-lived qubits7,22–24.

Variational Quantum Linear Solver-based Combination Rules in Dempster–Shafer Theory

Dempster–Shafer Theory (DST), as a method of handling uncertain information, is widely used in decision-making and information fusion. But the issue of exponential computational complexity limits its real-time application. Since quantum computers with its natural parallel computing capability can theoretically achieve speedup, an HHL-based algorithm for implementing DST operations on quantum circuits has been proposed. However, the algorithm is impossible to be implemented with high accuracy due to the limited performance of quantum computers in the current noisy intermediate-scale quantum (NISQ) era. In response to that, we utilize an up-to-date scheme Variational Quantum Linear Solver (VQLS) to conduct DST operations by solving the linear system. Besides, VQLS further reveals the structural consistency of DST with quantum computation, which enables faster circuit configuration and computation. In this paper, we first realize the transformation in belief functions by VQLS and then extends it to a methods of implementing combination rules. Simulated under a realistic classification task, the feasibility and accuracy of the proposed VQLS-based method are verified. The new VQLS-based method proposed is able to achieve combination rules at a lower error level with fewer quantum resources, which is more suitable for the NISQ era.

Boosting quantum amplitude exponentially in variational quantum algorithms

We introduce a family of variational quantum algorithms, which we coin as quantum iterative power algorithms (QIPAs), and demonstrate their capabilities as applied to global-optimization numerical experiments. Specifically, we demonstrate the QIPA based on a double exponential oracle as applied to ground state optimization of the H 2 molecule, search for the transmon qubit ground-state, and biprime factorization. Our results indicate that QIPA outperforms quantum imaginary time evolution (QITE) and requires a polynomial number of queries to reach convergence even with exponentially small overlap between an initial quantum state and the final desired quantum state, under some circumstances. We analytically show that there exists an exponential amplitude amplification at every step of the variational quantum algorithm, provided the initial wavefunction has non-vanishing probability with the desired state and that the unique maximum of the oracle is given by , while all other values are given by the same value (here λ can be taken as eigenvalues of the problem Hamiltonian). The generality of the global-optimization method presented here invites further application to other problems that currently have not been explored with QITE-based near-term quantum computing algorithms. Such approaches could facilitate identification of reaction pathways and transition states in chemical physics, as well as optimization in a broad range of machine learning applications. The method also provides a general framework for adaptation of a class of classical optimization algorithms to quantum computers to further broaden the range of algorithms amenable to implementation on current noisy intermediate-scale quantum computers.

Characterizing arbitrary quantum networks in the noisy intermediate-scale quantum era

Characterizing arbitrary quantum networks in the noisy intermediate-scale quantum era

An improved QFT-based quantum comparator and extended modular arithmetic using one ancilla qubit

Quantum comparators and modular arithmetic are fundamental in many quantum algorithms. Current research mainly focuses on operations between two quantum states. However, various applications, such as integer factorization, optimization, and financial risk analysis, commonly require one of the inputs to be classical. It requires many ancillary qubits, especially when subsequent computations are involved. In this paper, we propose a quantum–classical comparator based on the quantum Fourier transform. Then we extend it to compare two quantum integers and modular arithmetic. Proposed operators only require up to one ancilla qubit, which is optimal for qubit resources. We analyze limitations in the current modular addition circuit and develop it to process arbitrary quantum states in the entire n-qubit space. The proposed algorithms reduce computing resources and make them valuable for noisy intermediate-scale quantum computers.

Federated quanvolutional neural network: a new paradigm for collaborative quantum learning

In recent years, the concept of federated machine learning has been actively driven by scientists to ease the privacy concerns of data owners. Currently, the combination of machine learning and quantum computing technologies is a hot industry topic and is positioned to be a major disruptor. It has become an effective new tool for reshaping several industries ranging from healthcare to finance. Data sharing poses a significant hurdle for large-scale machine learning in numerous industries. It is a natural goal to study the advanced quantum computing ecosystem, which will be comprised of heterogeneous federated resources. In this work, the problem of data governance and privacy is handled by developing a quantum federated learning approach, that can be efficiently executed on quantum hardware in the noisy intermediate-scale quantum era. We present the federated hybrid quantum–classical algorithm called a quanvolutional neural network with distributed training on different sites without exchanging data. The hybrid algorithm requires small quantum circuits to produce meaningful features for image classification tasks, which makes it ideal for near-term quantum computing. The primary goal of this work is to evaluate the potential benefits of hybrid quantum–classical and classical-quantum convolutional neural networks on non-independently and non-identically partitioned (Non-IID) and real-world data partitioned datasets among several healthcare institutions/clients. We investigated the performance of a collaborative quanvolutional neural network on two medical machine learning datasets, COVID-19 and MedNIST. Extensive experiments are carried out to validate the robustness and feasibility of the proposed quantum federated learning framework. Our findings demonstrate a decrease of 2%–39% times in necessary communication rounds compared to the federated stochastic gradient descent approach. The hybrid federated framework maintained a high classification testing accuracy and generalizability, even in scenarios where the medical data is unevenly distributed among clients.

Quantum generative adversarial learning in photonics.

Quantum generative adversarial networks (QGANs), an intersection of quantum computing and machine learning, have attracted widespread attention due to their potential advantages over classical analogs. However, in the current era of noisy intermediate-scale quantum (NISQ) computing, it is essential to investigate whether QGANs can perform learning tasks on near-term quantum devices usually affected by noise and even defects. In this Letter, using a programmable silicon quantum photonic chip, we experimentally demonstrate the QGAN model in photonics for the first time to our knowledge and investigate the effects of noise and defects on its performance. Our results show that QGANs can generate high-quality quantum data with a fidelity higher than 90%, even under conditions where up to half of the generator's phase shifters are damaged, or all of the generator and discriminator's phase shifters are subjected to phase noise up to 0.04π. Our work sheds light on the feasibility of implementing QGANs on the NISQ-era quantum hardware.

Advances in Quantum Machine Learning and Deep Learning for Image Classification: A Survey

Image classification, which is a fundamental element of Computer Vision (CV) and Artificial Intelligence (AI), has been researched intensively in numerous domains and embedded in many products. However, with the exponential increase in the number of images and the complexity of the required tasks, deep-learning classification algorithms demand more intensive resources and computational power to train the models and update the massive number of parameters. Quantum computing is a new research technology with a promising capability of exponential speed up and operational parallelization with its unique phenomena including superposition and entanglement. Researchers have already started utilizing Quantum Deep Learning (QDL) and Quantum Machine Learning (QML) in image classification. Yet, to our knowledge, there exists no comprehensive published literature review on quantum image classification. Therefore, this paper analyzes the advances in this field by dividing the studies based on a unique taxonomy, discussing the limitations, summarizing essential aspects of each research, and finally, emphasizing the gaps, challenges, and recommendations. One of the key challenges presented in the paper is that quantum computers are in the Noisy Intermediate-Scale Quantum (NISQ) era, where they contain a limited number of noisy qubits, therefore challenging complex quantum classifiers and complex images from advanced datasets. This research recommends constructing a novel quantum image encoding method that adapts to the available number of qubits and enables RGB images as a critical contribution to the existing research.

Quantum machine learning – A novel approach for hydrodynamics analysis and modeling of liquid-solid circulating fluidized bed risers

The Liquid-Solid Circulating Fluidized Bed (LSCFB) system is commonly employed in chemical and biochemical applications, serving as a reactor where solids act as catalysts or biofilm carriers. Mass and heat transfer heavily rely on the distribution of solids holdups, which are influenced by various operating conditions, including superficial liquid velocities and auxiliary liquid velocities. These operating conditions play a key role in controlling the hydrodynamics of solid distribution. Quantum machine learning (QML)-based modeling techniques are employed to investigate the solids holdup distribution in a Liquid-Solid Circulating Fluidized Bed (LSCFB) system. A novel application of quantum machine learning for the hydrodynamics analysis and modeling of the LSCFB riser. This work aims to lay the groundwork for investigating the applicability of QML for understanding and predicting the hydrodynamic behavior of CFB risers by leveraging the unique properties of quantum systems during the present Noisy Intermediate-Scale Quantum (NISQ) era. The unavailability of full-scale quantum infrastructure limits proper exploitation of different quantum computing opportunities including embedding. In this study glass beads particles with 500 µm used as the solid phase and water as liquid phase. At various axial locations (H = 1.0, 2.0, 3.0, and 3.8 m above the distributor) and with varying superficial liquid velocities, radial nonuniformity of solids holdup is observed. The derived models account for the impact of operating parameters, such as auxiliary and primary liquid velocities and superficial particulate velocity, on the radial phase distribution at various axial positions in the riser. By comparing the predicted solids holdup data with experimental data obtained from a pilot-scale LSCFB reactor, the accuracy of the models is determined. The models exhibit reasonable correlations with the experimental data and consistent phase distribution trends. The correlation coefficients between predicted outputs and experimental data for sequential and nonsequential QML models are 0.95 and 0.96, respectively.

Thermodynamics of Quantum Trajectories on a Quantum Computer.

Quantum computers have recently become available as noisy intermediate-scale quantum devices. Already these machines yield a useful environment for research on quantum systems and dynamics. Building on this opportunity, we investigate open-system dynamics that are simulated on a quantum computer by coupling a system of interest to an ancilla. After each interaction the ancilla is measured, and the sequence of measurements defines a quantum trajectory. Using a thermodynamic analogy, which identifies trajectories as microstates, we show how to bias the dynamics of the open system in order to enhance the probability of quantum trajectories with desired properties, e.g., particular measurement patterns or temporal correlations. We discuss how such a biased-generally non-Markovian-dynamics can be implemented on a unitary, gate-based quantum computer and show proof-of-principle results on the publicly accessible ibmq_jakarta machine. While our analysis is solely conducted on small systems, it highlights the challenges in controlling complex aspects of open-system dynamics on digital quantum computers.

Modular Cluster Circuits for the Variational Quantum Eigensolver.

The variational quantum eigensolver algorithm recently became a popular method to compute the quantum chemical properties of molecules on noisy intermediate scale quantum (NISQ) devices. In order to avoid noise accumulation from the NISQ device in the quantum circuit, it is important to keep the so-called quantum depth of the circuit at a minimum, defined as the minimum number of quantum gates that must be operated sequentially. In the present work, we introduce a modular 2-qubit cluster circuit that allows for the design of a shallow-depth quantum circuit compared to previously proposed architectures without loss of chemical accuracy. Moreover, by virtue of the simplicity of the cluster circuit, it is possible to assign a valence bond chemical interpretation to the cluster circuit. The design was tested on the H2, (H2)2, and LiH molecules, as well as the finite-size transverse-field Ising model, as the latter provides additional insights into the construction of the circuit in a resonating valence bond picture.

Adaptive variational quantum minimally entangled typical thermal states for finite temperature simulations

Scalable quantum algorithms for the simulation of quantum many-body systems in thermal equilibrium are important for predicting properties of quantum matter at finite temperatures. Here we describe and benchmark a quantum computing version of the minimally entangled typical thermal states (METTS) algorithm for which we adopt an adaptive variational approach to perform the required quantum imaginary time evolution. The algorithm, which we name AVQMETTS, dynamically generates compact and problem-specific quantum circuits, which are suitable for noisy intermediate-scale quantum (NISQ) hardware. We benchmark AVQMETTS on statevector simulators and perform thermal energy calculations of integrable and nonintegrable quantum spin models in one and two dimensions and demonstrate an approximately linear system-size scaling of the circuit complexity. We further map out the finite-temperature phase transition line of the two-dimensional transverse field Ising model. Finally, we study the impact of noise on AVQMETTS calculations using a phenomenological noise model.

Quantum approximate optimization algorithm in non-Markovian quantum systems

Although quantum approximate optimization algorithm (QAOA) has demonstrated its quantum supremacy, its performance on Noisy Intermediate-Scale Quantum (NISQ) devices would be influenced by complicated noises, e.g. quantum colored noises. To evaluate the performance of QAOA under these noises, this paper presents a framework for running QAOA on non-Markovian quantum systems which are represented by an augmented system model. In this model, a non-Markovian environment carrying quantum colored noises is modelled as an ancillary system driven by quantum white noises which is directly coupled to the corresponding principal system; i.e. the computational unit for the algorithm. With this model, we mathematically formulate QAOA as piecewise Hamiltonian control of the augmented system, where we also optimize the control depth to fit into the circuit depth of current quantum devices. For efficient simulation of QAOA in non-Markovian quantum systems, a boosted algorithm using quantum trajectory is further presented. Finally, we show that non-Markovianity can be utilized as a quantum resource to achieve a relatively good performance of QAOA, which is characterized by our proposed exploration rate.

Investigating the effect of circuit cutting in QAOA for the MaxCut problem on NISQ devices

Noisy intermediate-scale quantum (NISQ) devices are restricted by their limited number of qubits and their short decoherence times. An approach addressing these problems is quantum circuit cutting. It decomposes the execution of a large quantum circuit into the execution of multiple smaller quantum circuits with additional classical postprocessing. Since these smaller quantum circuits require fewer qubits and gates, they are more suitable for NISQ devices. To investigate the effect of quantum circuit cutting in a quantum algorithm targeting NISQ devices, we design two experiments using the quantum approximate optimization algorithm (QAOA) for the Maximum Cut (MaxCut) problem and conduct them on state-of-the-art superconducting devices. Our first experiment studies the influence of circuit cutting on the objective function of QAOA, and the second evaluates the quality of results obtained by the whole algorithm with circuit cutting. The results show that circuit cutting can reduce the effects of noise in QAOA, and therefore, the algorithm yields better solutions on NISQ devices.

A hybrid quantum–classical neural network for learning transferable visual representation

State-of-the-art quantum machine learning (QML) algorithms fail to offer practical advantages over their notoriously powerful classical counterparts, due to the limited learning capabilities of QML algorithms, the constrained computational resources available on today’s noisy intermediate-scale quantum (NISQ) devices, and the empirically designed circuit ansatz for QML models. In this work, we address these challenges by proposing a hybrid quantum–classical neural network (CaNN), which we call QCLIP, for Quantum Contrastive Language-Image Pre-Training. Rather than training a supervised QML model to predict human annotations, QCLIP focuses on more practical transferable visual representation learning, where the developed model can be generalized to work on unseen downstream datasets. QCLIP is implemented by using CaNNs to generate low-dimensional data feature embeddings followed by quantum neural networks to adapt and generalize the learned representation in the quantum Hilbert space. Experimental results show that the hybrid QCLIP model can be efficiently trained for representation learning. We evaluate the representation transfer capability of QCLIP against the classical Contrastive Language-Image Pre-Training model on various datasets. Simulation results and real-device results on NISQ IBM_Auckland quantum computer both show that the proposed QCLIP model outperforms the classical CLIP model in all test cases. As the field of QML on NISQ devices is continually evolving, we anticipate that this work will serve as a valuable foundation for future research and advancements in this promising area.

Classical Surrogates for Quantum Learning Models.

The advent of noisy intermediate-scale quantum computers has put the search for possible applications to the forefront of quantum information science. One area where hopes for an advantage through near-term quantum computers are high is quantum machine learning, where variational quantum learning models based on parametrized quantum circuits are discussed. In this work, we introduce the concept of a classical surrogate, a classical model which can be efficiently obtained from a trained quantum learning model and reproduces its input-output relations. As inference can be performed classically, the existence of a classical surrogate greatly enhances the applicability of a quantum learning strategy. However, the classical surrogate also challenges possible advantages of quantum schemes. As it is possible to directly optimize the Ansatz of the classical surrogate, they create a natural benchmark the quantum model has to outperform. We show that large classes of well-analyzed reuploading models have a classical surrogate. We conducted numerical experiments and found that these quantum models show no advantage in performance or trainability in the problems we analyze. This leaves only generalization capability as a possible point of quantum advantage and emphasizes the dire need for a better understanding of inductive biases of quantum learning models.

MPS-VQE: A variational quantum computational chemistry simulator with matrix product states

Quantum computing is attracting more and more attention in material and biological science. In the noisy intermediate-scale quantum (NISQ) computing era, the variational quantum eigensolver (VQE) is expected as an effective method to solve quantum chemistry problems which has potential quantum advantage. Classically simulating quantum algorithms plays a critical role in algorithmic development and the validation of noisy quantum devices before large-scale, fully fault-tolerant quantum computers are developed. However, most existing simulators are based on the state vector or density matrix representation of the quantum state which is faced with the memory bottleneck due to the exponential growth of memory requirement as the number of qubits increases. In this work, we present a VQE simulator based on the matrix product states (MPS) method from quantum many-body physics, and a detailed study of our MPS-VQE simulator in quantum chemistry applications. The memory requirement of MPS-VQE grows only polynomially and we demonstrate that accurate results can be obtained despite the truncation of the smallest singular values during the algorithm. A distributed parallelization scheme is also presented for massively parallel computer systems, and different implementations of the parallelization scheme based on the Julia language are benchmarked which demonstrate the efficiency and scalability of our method. Our method could open a new avenue towards large-scale classical simulation of quantum computational chemistry.