Noisy Intermediate-Scale Quantum Era Research Articles

QFaaS: A Serverless Function-as-a-Service framework for Quantum computing

Quantum computing is rapidly reaching a point in which its application design and engineering aspects must be seriously considered. However, quantum software engineering is still in its infancy, with numerous challenges, especially in dealing with the diversity of quantum programming languages and noisy intermediate-scale quantum (NISQ) systems. To alleviate these challenges, we propose QFaaS, a holistic Quantum Function-as-a-Service framework, which leverages the advantages of the serverless model, DevOps lifecycle, and the state-of-the-art software techniques to advance practical quantum computing for next-generation application development in the NISQ era. Our framework provides essential elements of a serverless quantum system to streamline service-oriented quantum application development in cloud environments, such as combining hybrid quantum–classical computation, automating the backend selection, cold start mitigation, and adapting DevOps techniques. QFaaS offers a full-stack and unified quantum serverless platform by integrating multiple well-known quantum software development kits (Qiskit, Q#, Cirq, and Braket), quantum simulators, and cloud providers (IBM Quantum and Amazon Braket). This paper proposes the concept of quantum function-as-a-service, system design, operation workflows, implementation of QFaaS, and lessons learned on the benefits and limitations of quantum serverless computing. We also present practical use cases with various quantum applications on today’s quantum computers and simulators to demonstrate our framework capability to facilitate the ongoing quantum software transition.

Applications of noisy quantum computing and quantum error mitigation to "adamantaneland": a benchmarking study for quantum chemistry.

The field of quantum computing has the potential to transform quantum chemistry. The variational quantum eigensolver (VQE) algorithm has allowed quantum computing to be applied to chemical problems in the noisy intermediate-scale quantum (NISQ) era. Applications of VQE have generally focused on predicting absolute energies instead of chemical properties that are relative energy differences and that are most interesting to chemists studying a chemical problem. We address this shortcoming by constructing a molecular benchmark data set in this work containing isomers of C10H16 and carbocationic rearrangements of C10H15+, calculated at a high-level of theory. Using the data set, we compared noiseless VQE simulations to conventionally performed density functional and wavefunction theory-based methods to understand the quality of results. We also investigated the effectiveness of a quantum state tomography-based error mitigation technique in applications of VQE under noise (simulated and real). Our findings reveal that the use of quantum error mitigation is crucial in the NISQ era and advantageous to yield almost noiseless quality results.

Quantum Walk Computing: Theory, Implementation, and Application

The classical random walk formalism plays an important role in a wide range of applications. Its quantum counterpart, the quantum walk, is proposed as an important theoretical model for quantum computing. By exploiting quantum effects such as superposition, interference, and entanglement, quantum walks and their variations have been extensively studied for achieving computing power beyond that of classical computing and have been broadly used in designing quantum algorithms for algebraic and optimization problems, graph and network analysis, and quantum Hamiltonian and biochemical process simulations. Moreover, quantum walk models have been proven capable of universal quantum computation. Unlike conventional quantum circuit models, quantum walks provide a feasible path for implementing application-specific quantum computing, particularly in the noisy intermediate-scale quantum era. Recently, remarkable progress has been achieved in implementing a wide variety of quantum walks and quantum walk applications, which demonstrates the great potential of quantum walks. In this review, we provide a thorough summary of quantum walks and quantum walk computing, including theories and characteristics, physical implementations, and applications. We also discuss the challenges facing quantum walk computing, which aims to realize a practical quantum computer in the near future.

Effects of quantum noise on Shor’s algorithm

Shor’s quantum factoring algorithm (Shor’s algorithm) can solve factorization problem of large integers by using a fully-operational quantum computer with the complexity of polynomial-time level, thereby cracking a series of encryption algorithms (such as Rivest-Shamir-Adleman encryption algorithm, and Diffie-Hellman key exchange protocol) whose security is guaranteed by factorizing large integers, which is a difficult problem. We are currently in a noisy intermediate-scale quantum era, which means that we can only operate on quantum computers with a limited number of qubits and we have to take care of the effects of quantum noise. Quantum states on a quantum computer are prone to quantum noise caused by low-fidelity gates or interactions between qubits and the environment, which results in inaccurate measurements. We study the influence of quantum noise on Shor’s algorithm through 3 typical quantum noise channels: the depolarizing channel, the state preparation and measurement channel, and the thermal relaxation channel. We successfully simulate the factorization of the numbers 15, 21, and 35 into their corresponding prime factors by using the quantum circuit we have constructed on a classical computer. Then we simulate a running quantum circuit of Shor’s algorithm in a noisy environment with different level of noise for a certain type of noise channel and present numerical results. We can obtain precise measurements by calculating the state vector prior to measurement, instead of simulating and measuring expending much time, which contributes to higher efficiency. Each experiment is repeated 1000 times to reduce discrepancy. Our research indicates that Shor’s algorithm is easily affected by quantum noise. Successful rate of Shor’s algorithm decreases exponentially with the increase of noise level in the depolarizing channel, where the successful rate is an indicator we propose in this research to quantify the influence of noise on Shor’s algorithm, meanwhile the noise in the state preparation and measurement channel and the thermal relaxation channel can linearly affect the successful rate of Shor’s algorithm. There are <inline-formula><tex-math id="M1">\begin{document}$O(n^4) $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231414_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231414_M1.png"/></alternatives></inline-formula> quantum gates in the circuit, each of which is disrupted by noise in depolarizing channel during running the circuit, meanwhile there are only <i>O</i>(<i>n</i>) interruptions caused by noise in state preparation and measurement channel since we repeat the measurements only <i>O</i>(<i>n</i>) times in the circuit where <i>n</i> is the number of bits of the integer about to be factored. Linear relationship in thermal relaxation channel is mainly due to the large gap between quantum gate time and relaxation time even if each gate in the circuit is disrupted by noise in thermal relaxation channel such as depolarizing channel. The present research results can be used for correcting the subsequent errors, improving Shor’s algorithm, and providing guidance for the fidelity required in engineering implementation of Shor’s algorithm.

Variational quantum eigensolver for closed-shell molecules with non-bosonic corrections.

The realization of quantum advantage with noisy-intermediate-scale quantum (NISQ) machines has become one of the major challenges in computational sciences. Maintaining coherence of a physical system with more than ten qubits is a critical challenge that motivates research on compact system representations to reduce algorithm complexity. Toward this end, the variational quantum eigensolver (VQE) used to perform quantum simulations is considered to be one of the most promising algorithms for quantum chemistry in the NISQ era. We investigate reduced mapping of one spatial orbital to a single qubit to analyze the ground state energy in a way that the Pauli operators of qubits are mapped to the creation/annihilation of singlet pairs of electrons. To include the effect of non-bosonic (or non-paired) excitations, we introduce a simple correction scheme in the electron correlation model approximated by the geometrical mean of the bosonic (or paired) terms. Employing it in a VQE algorithm, we assess ground state energies of H2O, N2, and Li2O in good agreement with full configuration interaction (FCI) models respectively, using only 6, 8, and 12 qubits with quantum gate depths proportional to the squares of the qubit counts. With the adopted seniority-zero approximation that uses only one half of the qubit counts of a conventional VQE algorithm, we find that our non-bosonic correction method reaches reliable quantum chemistry simulations at least for the tested systems.

Quantum Neural Network Inspired Hardware Adaptable Ansatz for Efficient Quantum Simulation of Chemical Systems.

The variational quantum eigensolver is a promising way to solve the Schrödinger equation on a noisy intermediate-scale quantum (NISQ) computer, while its success relies on a well-designed wave function ansatz. Inspired by the quantum neural network, we propose a new hardware heuristic ansatz where its expressibility can be improved by increasing either the depth or the width of the circuit. Such a character makes this ansatz adaptable to different hardware environments. More importantly, it provides a general framework to improve the efficiency of the quantum resource utilization. For example, on a superconducting quantum computer where circuit depth is usually the bottleneck and the qubits thus cannot be fully used, circuit depth can be significantly reduced by introducing ancilla qubits. Ancilla qubits also make the circuit less sensitive to noises in practical application. These results open a new avenue to develop practical applications of quantum computation in the NISQ era.

Basis Set Generation and Optimization in the NISQ Era with Quiqbox.jl.

In the noisy intermediate-scale quantum era, ab initio computation of electronic structure problems has become one of the major benchmarks for identifying the boundary between classical and quantum computational power. Basis sets play a key role in the electronic structure methods implemented on both classical and quantum devices. To investigate the consequences of single-particle basis sets, we propose a framework for more customizable basis set generation and optimization. This framework allows composite basis sets to go beyond typical basis set frameworks, such as atomic basis sets, by introducing the concept of mixed-contracted Gaussian-type orbitals. These basis set generations set the stage for more flexible variational optimization of basis set parameters. To realize this framework, we have developed an open-source software package named "Quiqbox" in the Julia programming language. We demonstrate various examples of using Quiqbox for basis set optimization and generation, ranging from optimizing atomic basis sets on the Hartree-Fock level, preparing the initial state for variational quantum eigensolver computation, and constructing basis sets with completely delocalized orbitals. We also include various benchmarks of Quiqbox for basis set optimization and ab initial electronic structure computation.

Quantum entanglement patterns in the structure of atomic nuclei within the nuclear shell model

Quantum entanglement offers a unique perspective into the underlying structure of strongly-correlated systems such as atomic nuclei. In this paper, we use quantum information tools to analyze the structure of light and medium-mass berillyum, oxygen, neon and calcium isotopes within the nuclear shell model. We use different entanglement metrics, including single-orbital entanglement, mutual information, and von Neumann entropies for different equipartitions of the shell-model valence space and identify mode-entanglement patterns related to the energy, angular momentum and isospin of the nuclear single-particle orbitals. We observe that the single-orbital entanglement is directly related to the number of valence nucleons and the energy structure of the shell, while the mutual information highlights signatures of proton–proton and neutron–neutron pairing, as well as nuclear deformation. Proton and neutron orbitals are weakly entangled by all measures, and in fact have the lowest von Neumann entropies among all possible equipartitions of the valence space. In contrast, orbitals with opposite angular momentum projection have relatively large entropies, especially in spherical nuclei. This analysis provides a guide for designing more efficient quantum algorithms for the noisy intermediate-scale quantum era.

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.

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

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

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 Simulation of Topological Zero Modes on a 41-Qubit Superconducting Processor.

Quantum simulation of different exotic topological phases of quantum matter on a noisy intermediate-scale quantum (NISQ) processor is attracting growing interest. Here, we develop a one-dimensional 43-qubit superconducting quantum processor, named Chuang-tzu, to simulate and characterize emergent topological states. By engineering diagonal Aubry-André-Harper (AAH) models, we experimentally demonstrate the Hofstadter butterfly energy spectrum. Using Floquet engineering, we verify the existence of the topological zero modes in the commensurate off-diagonal AAH models, which have never been experimentally realized before. Remarkably, the qubit number over 40 in our quantum processor is large enough to capture the substantial topological features of a quantum system from its complex band structure, including Dirac points, the energy gap's closing, the difference between even and odd number of sites, and the distinction between edge and bulk states. Our results establish a versatile hybrid quantum simulation approach to exploring quantum topological systems in the NISQ era.

Classical-to-quantum convolutional neural network transfer learning

Machine learning using quantum convolutional neural networks (QCNNs) has demonstrated success in both quantum and classical data classification. In previous studies, QCNNs attained a higher classification accuracy than their classical counterparts under the same training conditions in the few-parameter regime. However, the general performance of large-scale quantum models is difficult to examine because of the limited size of quantum circuits, which can be reliably implemented in the near future. We propose transfer learning as an effective strategy for utilizing small QCNNs in the noisy intermediate-scale quantum era to the full extent. In the classical-to-quantum transfer learning framework, a QCNN can solve complex classification problems without requiring a large-scale quantum circuit by utilizing a pre-trained classical convolutional neural network (CNN). We perform numerical simulations of QCNN models with various sets of quantum convolution and pooling operations for MNIST data classification under transfer learning, in which a classical CNN is trained with Fashion-MNIST data. The results show that transfer learning from classical to quantum CNN performs considerably better than purely classical transfer learning models under similar training conditions.

Counterdiabatic driving for long-lived singlet state preparation.

The quantum adiabatic method, which maintains populations in their instantaneous eigenstates throughout the state evolution, is an established and often a preferred choice for state preparation and manipulation. Although it minimizes the driving cost significantly, its slow speed is a severe limitation in noisy intermediate-scale quantum era technologies. Since adiabatic paths are extensive in many physical processes, it is of broader interest to achieve adiabaticity at a much faster rate. Shortcuts to adiabaticity techniques, which overcome the slow adiabatic process by driving the system faster through non-adiabatic paths, have seen increased attention recently. The extraordinarily long lifetime of the long-lived singlet states (LLS) in nuclear magnetic resonance (NMR), established over the past decade, has opened several important applications ranging from spectroscopy to biomedical imaging. Various methods, including adiabatic methods, are already being used to prepare LLS. In this article, we report the use of counterdiabatic driving (CD) to speed up LLS preparation with faster drives. Using NMR experiments, we show that CD can give stronger LLS order in shorter durations than conventional adiabatic driving.

Quantum SoC and On-Chip Circuit Synthesis in the NISQ Era

In recent years, fueled by the breakthroughs in the technology in quantum computation, there has been a rising interest in the noisy intermediate-scale quantum (NISQ) era. In addition to a large number of qubits, the study of error correction and quantum algorithms has made great progress. However, as a primary goal of quantum computation, making practicable quantum computers in the NISQ era still needs further study, mainly focusing on quantum computer organization, architecture, and circuit synthesis. This paper studies the quantum circuit synthesis in a small-scale universal quantum computing device called a “quantum system-on-chip” (QSoC). We analyze the quantum compilation of the hybrid architecture for a small-scaled universal quantum computational device with a specific size (quantum chip). Two kinds of on-chip circuit synthesis algorithms are proposed and discussed.

Experimental quantum natural gradient optimization in photonics.

Variational quantum algorithms (VQAs) combining the advantages of parameterized quantum circuits and classical optimizers, promise practical quantum applications in the noisy intermediate-scale quantum era. The performance of VQAs heavily depends on the optimization method. Compared with gradient-free and ordinary gradient descent methods, the quantum natural gradient (QNG), which mirrors the geometric structure of the parameter space, can achieve faster convergence and avoid local minima more easily, thereby reducing the cost of circuit executions. We utilized a fully programmable photonic chip to experimentally estimate the QNG in photonics for the first time, to the best of our knowledge. We obtained the dissociation curve of the He-H+ cation and achieved chemical accuracy, verifying the outperformance of QNG optimization on a photonic device. Our work opens up a vista of utilizing QNG in photonics to implement practical near-term quantum applications.

Development of a compact Ansatz via operator commutativity screening: Digital quantum simulation of molecular systems.

Recent advancements in quantum information and quantum technology have stimulated a good deal of interest in the development of quantum algorithms toward the determination of the energetics and properties of many-fermionic systems. While the variational quantum eigensolver is the most optimal algorithm in the noisy intermediate scale quantum era, it is imperative to develop compact Ansätze with low-depth quantum circuits that are physically realizable in quantum devices. Within the unitary coupled cluster framework, we develop a disentangled Ansatz construction protocol that can dynamically tailor an optimal Ansatz using the one- and two-body cluster operators and a selection of rank-two scatterers. The construction of the Ansatz may potentially be performed in parallel over multiple quantum processors through energy sorting and operator commutativity prescreening. With a significant reduction in the circuit depth toward the simulation of molecular strong correlation, our dynamic Ansatz construction protocol is shown to be highly accurate and resilient to the noisy circumstances of the near-term quantum hardware.

Implementation of Quantum Key Distribution Algorithm in Real Time IBM Quantum Computers

Abstract: We are Currently in the NISQ(noisy intermediate scale quantum) era. Current Quantum computers have a high noise error rate. With the increasing number of qubits every year we can develop fault tolerant quantum systems which have immense power to change our current computing power. Current quantum systems have shown to have the potential to break the classical RSA algorithm using shors algorithm. With more development and increase in number of qubits available it could easily break the current security systems of our computing. In future we could transmit data safely using the same quantum principles in the post quantum cryptography era. Quantum key distribution could be the future protocol used to transfer our secure information without getting hacked even by using quantum computing and break other quantum principles like shors algorithm which can break current encryption techniques like the RSA algorithms. We need to develop Quantum network infrastructure so we can implement the quantum key distribution algorithm in the future to enable secure transmission of data.

Solving DC power flow problems using quantum and hybrid algorithms

Power flow calculation plays an important role in planning, operation, and control of the power system. The quantum HHL algorithm can achieve theoretical exponential speedup over classical algorithms on DC power flow calculation. Since the qubit resources in the Noisy Intermediate-scale Quantum (NISQ) era are limited, it is important to discuss the performance considering this limitation. The phase estimation of DC power flow problems is imperfect. This work is carried out under the assumption of imperfect phase estimation. The performance of the HHL algorithm is systematically investigated with different accuracy and redundant qubits. In order to further reduce the required qubit resources, a hybrid quantum–classical algorithm is proposed. By comparing errors of the HHL and hybrid algorithms in the DC power flow calculation of the PJM 5-bus system, it is found that the hybrid algorithm can achieve comparable precision with fewer qubits than HHL by increasing the number of phase estimation modules, which may make the hybrid algorithm a feasible route in the NISQ era.

A Survey of Recent Advances in Quantum Generative Adversarial Networks

Quantum mechanics studies nature and its behavior at the scale of atoms and subatomic particles. By applying quantum mechanics, a lot of problems can be solved in a more convenient way thanks to its special quantum properties, such as superposition and entanglement. In the current noisy intermediate-scale quantum era, quantum mechanics finds its use in various fields of life. Following this trend, researchers seek to augment machine learning in a quantum way. The generative adversarial network (GAN), an important machine learning invention that excellently solves generative tasks, has also been extended with quantum versions. Since the first publication of a quantum GAN (QuGAN) in 2018, many QuGAN proposals have been suggested. A QuGAN may have a fully quantum or a hybrid quantum–classical architecture, which may need additional data processing in the quantum–classical interface. Similarly to classical GANs, QuGANs are trained using a loss function in the form of max likelihood, Wasserstein distance, or total variation. The gradients of the loss function can be calculated by applying the parameter-shift method or a linear combination of unitaries in order to update the parameters of the networks. In this paper, we review recent advances in quantum GANs. We discuss the structures, optimization, and network evaluation strategies of QuGANs. Different variants of quantum GANs are presented in detail.