Real Quantum Devices Research Articles

Efficient quantum state estimation with low-rank matrix completion

This paper introduces a novel and efficient technique for quantum state estimation, coined as low-rank matrix-completion quantum state tomography for characterizing pure quantum states, as it requires only non-entangling bases and 2n+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$2n + 1$\\end{document} local Pauli operators. This significantly reduces the complexity of the process and increases the accuracy of the state estimation, as it eliminates the need for the entangling bases, which are experimentally difficult to implement on quantum devices. The required minimal post-processing, improved accuracy and efficacy of this matrix-completion-based method make it an ideal benchmarking tool for investigating the properties of quantum systems, enabling researchers to verify the accuracy of quantum devices, characterize their performance, and explore the underlying physics of quantum phenomena. Our numerical results demonstrate that this method outperforms contemporary techniques in its ability to accurately reconstruct multi-qubit quantum states on real quantum devices, making it an invaluable contribution to the field of quantum state characterization and an essential step toward the reliable deployment of intermediate- and large-scale quantum devices.

Adaptive diversity-based quantum circuit architecture search

Quantum variational algorithms (VQAs) are highly promising to realize quantum advantages on near-term quantum devices. Existing VQAs based on a manually fixed quantum are computationally inefficient due to noise and the limited coupling maps of these devices. Previous work considers various quantum architecture search (QAS) algorithms to autodesign a quantum based on specific questions to improve the performance of VQAs. Compared to manual design, autodesign can more efficiently explore the large space of a possible and achieve better performance. However, two main challenges in utilizing QAS to design quantum circuits efficiently are the tremendous amount of space required for candidate quantum circuits, and the disconnection between quantum devices and autodesign in terms of qubit mapping and quantum noise. To address these issues, we propose an adaptive diversity-based quantum search algorithm to efficiently generate the optimal quantum circuit based on device qubit mapping and noise. By considering the diversity among different candidate circuits and adaptively adding circuit depths, our approach only needs to focus on a small optimization space at each iteration step. In addition, the synchronization of optimizing circuit structure and aligning qubit mapping enables us to generate quantum circuits while avoiding additional mapping overhead. We evaluate the performance of our algorithm on simulators and real quantum devices for quantum eigenvalue problems and classification tasks. Results demonstrate that quantum circuits generated by our method outperform both a fixed hardware-efficient and randomly generated quantum circuits in terms of final performance and resource-saving. Our algorithm provides a flexible way to efficiently generate excellent quantum circuits for significantly improving the performances of VQAs on near-term quantum devices. Published by the American Physical Society 2024

Efficient and practical quantum compiler towards multi-qubit systems with deep reinforcement learning ∗ ∗The authors list is in alphabetical order.

Efficient quantum compiling is essential for complex quantum algorithms realization. The Solovay–Kitaev (S–K) theorem offers a theoretical lower bound on the required operations for approaching any unitary operator. However, it is still an open question that this lower bound can be actually reached in practice. Here, we present an efficient quantum compiler which, for the first time, approaches the S–K lower bound in practical implementations, both for single-qubit and two-qubit scenarios, marking a significant milestone. Our compiler leverages deep reinforcement learning (RL) techniques to address current limitations in terms of optimality and inference time. Furthermore, we show that our compiler is versatile by demonstrating comparable performance between inverse-free basis sets, which is always the case in real quantum devices, and inverse-closed sets. Our findings also emphasize the often-neglected constant term in scaling laws, bridging the gap between theory and practice in quantum compiling. These results highlight the potential of RL-based quantum compilers, offering efficiency and practicality while contributing novel insights to quantum compiling theory.

Quantum error mitigation via quantum-noise-effect circuit groups

Near-term quantum computers have been built as intermediate-scale quantum devices and are fragile against quantum noise effects, namely, NISQ devices. Traditional quantum-error-correcting codes are not implemented on such devices and to perform quantum computation in good accuracy with these machines we need to develop alternative approaches for mitigating quantum computational errors. In this work, we propose quantum error mitigation (QEM) scheme for quantum computational errors which occur due to couplings with environments during gate operations, i.e., decoherence. To establish our QEM scheme, first we estimate the quantum noise effects on single-qubit states and represent them as groups of quantum circuits, namely, quantum-noise-effect circuit groups. Then our QEM scheme is conducted by subtracting expectation values generated by the quantum-noise-effect circuit groups from those obtained by the quantum circuits for the quantum algorithms under consideration. As a result, the quantum noise effects are reduced, and we obtain approximately the ideal expectation values via the quantum-noise-effect circuit groups and the numbers of elementary quantum circuits composing them scale polynomial with respect to the products of the depths of quantum algorithms and the numbers of register bits. To numerically demonstrate the validity of our QEM scheme, we run noisy quantum simulations of qubits under amplitude damping effects for four types of quantum algorithms. Furthermore, we implement our QEM scheme on IBM Q Experience processors and examine its efficacy. Consequently, the validity of our scheme is verified via both the quantum simulations and the quantum computations on the real quantum devices. Our QEM scheme is solely composed of quantum-computational operations (quantum gates and measurements), and thus, it can be conducted by any type of quantum device. In addition, it can be applied to error mitigation for many other types of quantum noise effects as well as noisy quantum computing of long-depth quantum algorithms.

Stabilized quantum-enhanced SIEM architecture and speed-up through Hoeffding tree algorithms enable quantum cybersecurity analytics in botnet detection.

For the first time, we enable the execution of hybrid quantum machine learning (HQML) methods on real quantum computers with 100 data samples and real-device-based simulations with 5000 data samples, thereby outperforming the current state of research of Suryotrisongko and Musashi from 2022 who were dealing with 1000 data samples and quantum simulators (pure software-based emulators) only. Additionally, we beat their reported accuracy of 76.8% by an average accuracy of 91.2%, all within a total execution time of 1687 s. We achieve this significant progress through two-step strategy: Firstly, we establish a stable quantum architecture that enables us to execute HQML algorithms on real quantum devices. Secondly, we introduce new hybrid quantum binary classifiers (HQBCs) based on Hoeffding decision tree algorithms. These algorithms speed up the process via batch-wise execution, reducing the number of shots required on real quantum devices compared to conventional loop-based optimizers. Their incremental nature serves the purpose of online large-scale data streaming for domain generation algorithm (DGA) botnet detection, and allows us to apply HQML to the field of cybersecurity analytics. We conduct our experiments using the Qiskit library with the Aer quantum simulator, and on three different real quantum devices from Azure Quantum: IonQ, Rigetti, and Quantinuum. This is the first time these tools are combined in this manner.

Deep Neural Network Assisted Quantum Chemistry Calculations on Quantum Computers.

The variational quantum eigensolver (VQE) is a widely employed method to solve electronic structure problems in the current noisy intermediate-scale quantum (NISQ) devices. However, due to inherent noise in the NISQ devices, VQE results on NISQ devices often deviate significantly from the results obtained on noiseless statevector simulators or traditional classical computers. The iterative nature of VQE further amplifies the errors in each loop. Recent works have explored ways to integrate deep neural networks (DNN) with VQE to mitigate iterative errors, albeit primarily limited to the noiseless statevector simulators. In this work, we trained DNN models across various quantum circuits and examined the potential of two DNN-VQE approaches, DNN1 and DNNF, for predicting the ground state energies of small molecules in the presence of device noise. We carefully examined the accuracy of the DNN1, DNNF, and VQE methods on both noisy simulators and real quantum devices by considering different ansatzes of varying qubit counts and circuit depths. Our results illustrate the advantages and limitations of both VQE and DNN-VQE approaches. Notably, both DNN1 and DNNF methods consistently outperform the standard VQE method in providing more accurate ground state energies in noisy environments. However, despite being more accurate than VQE, the energies predicted using these methods on real quantum hardware remain meaningful only at reasonable circuit depths (depth = 15, gates = 21). At higher depths (depth = 83, gates = 112), they deviate significantly from the exact results. Additionally, we find that DNNF does not offer any notable advantage over VQE in terms of speed. Consequently, our study recommends DNN1 as the preferred method for obtaining quick and accurate ground state energies of molecules on current quantum hardware, particularly for quantum circuits with lower depth and fewer qubits.

Machine Learning based Noise Characterization and Correction on Neutral Atoms NISQ Devices

AbstractNeutral atoms devices represent a promising technology using optical tweezers to geometrically arrange atoms and modulated laser pulses to control their quantum states. They are exploited as noisy intermediate‐scale quantum (NISQ) processors. Indeed, like all real quantum devices, they are affected by noise introducing errors in the computation. Therefore, it is important to understand and characterize the noise sources and possibly to correct them. Here, two machine‐learning based approaches are proposed respectively to estimate the noise parameters and to mitigate their effects using only measurements of the final quantum state. Our analysis is then tested on a real neutral atom platform, comparing our predictions with a priori estimated parameters. It turns out that increasing the number of atoms is less effective than using more measurements on a smaller scale. The agreement is not always good but this may be due to the limited amount of real data that are obtained from a still under development device. Finally, reinforcement learning is employed to design a pulse that mitigates the noise effects. Our machine learning‐based approach is espected to be very useful for the noise benchmarking of NISQ processors and, more in general, of real quantum technologies.

Best practices for portfolio optimization by quantum computing, experimented on real quantum devices

In finance, portfolio optimization aims at finding optimal investments maximizing a trade-off between return and risks, given some constraints. Classical formulations of this quadratic optimization problem have exact or heuristic solutions, but the complexity scales up as the market dimension increases. Recently, researchers are evaluating the possibility of facing the complexity scaling issue by employing quantum computing. In this paper, the problem is solved using the Variational Quantum Eigensolver (VQE), which in principle is very efficient. The main outcome of this work consists of the definition of the best hyperparameters to set, in order to perform Portfolio Optimization by VQE on real quantum computers. In particular, a quite general formulation of the constrained quadratic problem is considered, which is translated into Quadratic Unconstrained Binary Optimization by the binary encoding of variables and by including constraints in the objective function. This is converted into a set of quantum operators (Ising Hamiltonian), whose minimum eigenvalue is found by VQE and corresponds to the optimal solution. In this work, different hyperparameters of the procedure are analyzed, including different ansatzes and optimization methods by means of experiments on both simulators and real quantum computers. Experiments show that there is a strong dependence of solutions quality on the sufficiently sized quantum computer and correct hyperparameters, and with the best choices, the quantum algorithm run on real quantum devices reaches solutions very close to the exact one, with a strong convergence rate towards the classical solution, even without error-mitigation techniques. Moreover, results obtained on different real quantum devices, for a small-sized example, show the relation between the quality of the solution and the dimension of the quantum processor. Evidences allow concluding which are the best ways to solve real Portfolio Optimization problems by VQE on quantum devices, and confirm the possibility to solve them with higher efficiency, with respect to existing methods, as soon as the size of quantum hardware will be sufficiently high.

Gate-based quantum computing for protein design.

Protein design is a technique to engineer proteins by permuting amino acids in the sequence to obtain novel functionalities. However, exploring all possible combinations of amino acids is generally impossible due to the exponential growth of possibilities with the number of designable sites. The present work introduces circuits implementing a pure quantum approach, Grover's algorithm, to solve protein design problems. Our algorithms can adjust to implement any custom pair-wise energy tables and protein structure models. Moreover, the algorithm's oracle is designed to consist of only adder functions. Quantum computer simulators validate the practicality of our circuits, containing up to 234 qubits. However, a smaller circuit is implemented on real quantum devices. Our results show that using [Formula: see text] iterations, the circuits find the correct results among all N possibilities, providing the expected quadratic speed up of Grover's algorithm over classical methods (i.e., [Formula: see text]).

Development of a quantum calculator on the IBM Quantum experience platform and its application for converting the decimal number system to binary

This article demonstrates a quantum calculator by experimentally simulating and performing basic arithmetic operations, namely addition, subtraction, multiplication, division on real quantum devices using the IBM Quantum Experience (IBM QE) platform. Two addition algorithms are considered, the classical version, using the Toffoli gate, and using the quantum Fourier transform (QFT). In particular summation with QFT saves memory and time. The task of the work is to build a quantum circuit that performs arithmetic operations between the binary representation of two integers. We then propose a quantum algorithm for converting decimal to binary. This method also allows for massive parallelization during its execution. The addition, subtraction, multiplication, and division functions based on QFT have been improved with some changes. The proposed operations are compared with the closest quantum arithmetic operations. Therefore, we can implement a practical quantum calculator by performing operations on a real quantum computer. The circuits are defined as a kind of quantum adder using a quantum Fourier transform, implemented in Qiskit and demonstrated on one or two copies.

Multiparameter transmission estimation at the quantum Cramér–Rao limit on a cloud quantum computer

Estimating transmission or loss is at the heart of spectroscopy. To achieve the ultimate quantum resolution limit, one must use probe states with definite photon number and detectors capable of distinguishing the number of photons impinging thereon. In practice, one can outperform classical limits using two-mode squeezed light, which can be used to herald definite-photon-number probes, but the heralding is not guaranteed to produce the desired probes when there is loss in the heralding arm or its detector is imperfect. We show that this paradigm can be used to simultaneously measure distinct loss parameters in both modes of the squeezed light, with attainable quantum advantages. We demonstrate this protocol on Xanadu’s X8 chip, accessed via the cloud, building photon-number probability distributions from 106 shots and performing maximum likelihood estimation (MLE) on these distributions 103 independent times. Because pump light may be lost before the squeezing occurs, we also simultaneously estimate the actual input power, using the theory of nuisance parameters. MLE converges to estimate the transmission amplitudes in X8’s eight modes to be 0.392 02(6), 0.307 06(8), 0.369 37(6), 0.287 30(9), 0.382 06(6), 0.304 41(8), 0.372 29(6), and 0.286 21(8) and the squeezing parameters, which are proxies for effective input coherent-state amplitudes, their losses, and their nonlinear interaction times, to be 1.3000(2), 1.3238(3), 1.2666(2), and 1.3425(3); all of these uncertainties are within a factor of two of the quantum Cramér–Rao bound. This study provides crucial insight into the intersection of quantum multiparameter estimation theory, MLE convergence, and the characterization and performance of real quantum devices.

Method for generating randomly perturbed density operators subject to different sets of constraints

This paper presents a general method for producing randomly perturbed density operators subject to different sets of constraints. The perturbed density operators are a specified “distance" away from the state described by the original density operator. This approach is applied to a bipartite system of qubits and used to examine the sensitivity of various entanglement measures on the perturbation magnitude. The constraint sets used include constant energy, constant entropy, and both constant energy and entropy. The method is then applied to produce perturbed random quantum states that correspond with those obtained experimentally for Bell states on the IBM quantum device ibmq_manila. The results show that the methodology can be used to simulate the outcome of real quantum devices where noise, which is important both in theory and simulation, is present.

Experimental Implementation of Quantum Algorithm for Association Rules Mining

Recently, a quantum algorithm for a fundamentally important task in data mining, association rules mining (ARM), called qARM for short, has been proposed. Notably, qARM achieves significant speedup over its classical counterpart for implementing the main task of ARM, i.e., finding frequent itemsets from a transaction database. In this paper, we experimentally implement qARM on both real quantum computers and a quantum computing simulator via the IBM quantum computing platform. In the first place, we design quantum circuits of qARM for a 2 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 2 transaction database (i.e., a transaction database involving two transactions and two items), and run it on four real five-qubit IBM quantum computers as well as on the simulator. For a larger 4 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times $ </tex-math></inline-formula> 4 transaction database which would lead to circuits with more qubits and a higher depth than the currently accessible IBM real quantum devices can handle, we also construct the quantum circuits of qARM and execute them on “aer_simulator” alone. Both experimental results show that all the frequent itemsets from the two transaction databases are successfully derived as desired, demonstrating the correctness and feasibility of qARM. Our work may serve as a benchmarking, and provide prototypes for implementing qARM for larger transaction databases on both noisy intermediate-scale quantum devices and universal fault-tolerant quantum computers.

Qurzon: A Prototype for a Divide and Conquer-Based Quantum Compiler for Distributed Quantum Systems

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 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 qubit placement for executing on real quantum devices. A scheduling algorithm is also introduced within the compiler that can explore the power of distributed quantum computing while paving the way for quantum parallelism for large algorithms. Several benchmark circuits have been executed using the compiler, thereby demonstrating the power of the divide and compute when working with real NISQ-era quantum devices.

Optimization and noise analysis of the quantum algorithm for solving one-dimensional Poisson equation

Solving differential equations is one of the most promising applications of quantum computing. Recently we proposed an efficient quantum algorithm for solving one-dimensional Poisson equation avoiding the need to perform quantum arithmetic or Hamiltonian simulation. In this paper, we further develop this algorithm to make it closer to the real application on the noisy intermediate-scale quantum (NISQ) devices. To this end, we first optimize the quantum 1D-Poisson solver by developing a new way of performing the sine transformation. The circuit depth for implementing the sine transform is reduced from n2 to n without increasing the total qubit cost of the whole circuit, which is achieved by neatly reusing the additional ancillary quits. Then, we analyse the effect of common noise existing in the real quantum devices on our algorithm using the IBM Qiskit toolkit. We find that the phase damping noise has little effect on our algorithm, while the bit flip noise has the greatest impact. In addition, threshold errors of the quantum gates are obtained to make the fidelity of the circuit output being greater than 90%. The results of noise analysis will provide a good guidance for the subsequent work of error mitigation and error correction for our algorithm. The noise-analysis method developed in this work can be used for other algorithms to be executed on the NISQ devices.

DECODING M-ARY LINEAR CODES WITH THE QUANTUM APPROXIMATE OPTIMIZATION ALGORITHM

Abstract The NP-hardness of the Minimum Distance Decoding Problem (MDDP) is the core of the McEliece cryptosystem. The difficulty of decoding a received word to the closest codeword in a given arbitrary code is key to its security. Related to the MDDP is the Coset Leader Problem (CLP), which consists in finding a word of a given syndrome and minimum Hamming weight. Both can be modelled as optimization problems, and solved using the Quantum Approximate Optimization Algorithm (QAOA), a well-known hybrid quantum- classical algorithm. In this paper, we model both the MDDP and CLP for linear codes over arbitrary m−ary alphabets, we make the theoretical analysis of the first level for the binary CLP problem, and introduce some experiments to test its performance. The experiments were carried out on both quantum computer simulators and real quantum devices, and use codes of different lengths and different depths of the QAOA.

Enhancing the Quantum Linear Systems Algorithm Using Richardson Extrapolation

We present a quantum algorithm to solve systems of linear equations of the form Ax = b , where A is a tridiagonal Toeplitz matrix and b results from discretizing an analytic function, with a circuit complexity of O (1/√ε, poly (log κ, log N )), where N denotes the number of equations, ε is the accuracy, and κ the condition number. The repeat-until-success algorithm has to be run O (κ/(1-ε)) times to succeed, leveraging amplitude amplification, and needs to be sampled O (1/ε 2 ) times. Thus, the algorithm achieves an exponential improvement with respect to N over classical methods. In particular, we present efficient oracles for state preparation, Hamiltonian simulation, and a set of observables together with the corresponding error and complexity analyses. As the main result of this work, we show how to use Richardson extrapolation to enhance Hamiltonian simulation, resulting in an implementation of Quantum Phase Estimation (QPE) within the algorithm with 1/√ε circuits that can be run in parallel each with circuit complexity 1/√ ε instead of 1/ε. Furthermore, we analyze necessary conditions for the overall algorithm to achieve an exponential speedup compared to classical methods. Our approach is not limited to the considered setting and can be applied to more general problems where Hamiltonian simulation is approximated via product formulae, although our theoretical results would need to be extended accordingly. All the procedures presented are implemented with Qiskit and tested for small systems using classical simulation as well as using real quantum devices available through the IBM Quantum Experience.

On the resource consumption of Software quantum computing simulators

Recently, several real quantum devices have become available through the cloud. Nevertheless, they are expected to be very limited, in the near term, in the number and quality of the fundamental storage element, the qubit. Therefore, software quantum simulators are the only widely available tools to design and test quantum algorithms. However, the representation of quantum computing components in classical computers consumes a big amount of resources. This work describes how to model the main elements of quantum computing in a classical computer and depicts resource consumption using two popular quantum simulators. In the end, we discuss different approaches to overcome this problem.

Determining the proton content with a quantum computer

We present a first attempt to design a quantum circuit for the determination of the parton content of the proton through the estimation of parton distribution functions (PDFs), in the context of high energy physics (HEP). The growing interest in quantum computing and the recent developments of new algorithms and quantum hardware devices motivates the study of methodologies applied to HEP. In this work we identify architectures of variational quantum circuits suitable for PDFs representation (qPDFs). We show experiments about the deployment of qPDFs on real quantum devices, taking into consideration current experimental limitations. Finally, we perform a global qPDF determination from collider data using quantum computer simulation on classical hardware and we compare the obtained partons and related phenomenological predictions involving hadronic processes to modern PDFs.

Efficient Discrete Feature Encoding for Variational Quantum Classifier

Recent days have witnessed significant interests in applying quantum-enhanced techniques for solving a variety of machine learning tasks. Variational methods that use quantum resources of imperfect quantum devices with the help of classical computing techniques are popular for supervised learning. Variational quantum classification (VQC) is one of such methods with possible quantum advantage in using quantum-enhanced features that are hard to compute by classical methods. Its performance depends on the mapping of classical features into a quantum-enhanced feature space. Although there have been many quantum-mapping functions proposed so far, there is little discussion on efficient mapping of discrete features, such as age group, zip code, and others, which are often significant for classifying datasets of interest. We first introduce the use of quantum random-access coding (QRAC) to map such discrete features efficiently into limited number of qubits for VQC. In numerical simulations, we present a range of encoding strategies and demonstrate their limitations and capabilities. We experimentally show that QRAC can help speeding up the training of VQC by reducing its parameters via saving on the number of qubits for the mapping. We confirm the effectiveness of the QRAC in VQC by experimenting on classification of real-world datasets with both simulators and real quantum devices.