Experimental comparison of two quantum computing architectures

Although the concept of quantum computing has existed for decades, the technology needed to successfully implement a quantum computing system has not yet reached the level of sophistication, reliability, and scalability necessary for commercial viability until very recently. Significant progress on this front was made in the past few years, with IBM planning to create a 1000-qubit chip by the end of 2023, and Google already claiming to have achieved quantum supremacy. Other major industry players such as Intel and Microsoft have also invested significant amounts of resources into quantum computing research. Any viable computing system requires both hardware and software to work together harmoniously in order to perform useful computations. While the achievements of IBM and other companies represent a large step forward for quantum hardware, many gaps remain to be filled with respect to the corresponding software. Specifically, there is currently no clear path towards a complete process for translating quantum algorithms into physical operations that are directly executable on quantum hardware. Such a process is analogous to a compiler that translates programs written in a high-level language into executable machine instructions on a conventional digital computer, and it is necessary if quantum computers are to be harnessed to perform practically useful computations. Existing work has addressed individual components of this process, but so far no unified method for translating the whole of a quantum algorithm into executable operations has been described. I make substantial progress towards filling this gap by describing a set of high-level and low-level quantum circuit design techniques, which when taken together reduce the need of a circuit designer to be concerned with low-level details. On the high-level side, I describe an approach or strategy to designing quantum oracles for Grover's algorithm that allows it to be applied to several types of problems. This approach involves designing oracles in terms of high-level blocks such as counters, multiplexers, comparators, and arbitrary Boolean functions. The implementations of these blocks in terms of lower-level quantum gates are demonstrated in a way that makes it clear that scaled-up versions of them can be generated in a completely automated fashion. For a specific class of problems, which I call state-space path planning problems, I also introduce a paradigm for quantum oracle design that involves representing the problem in terms of individual states and moves. Problems of this sort have applications in robotics and games. Low-level techniques that I introduce

Abstract: The chapter "Advancements in Quantum Computing and Information Science" explores the fundamental principles, historical development, and modern applications of quantum computing. Quantum computing leverages the principles of quantum mechanics, utilizing qubits that can exist in multiple states simultaneously due to superposition and entanglement. Key milestones such as Shor's algorithm and Grover's algorithm have demonstrated quantum computing's potential to solve complex problems more efficiently than classical computers. The chapter discusses the evolution of quantum hardware, including superconducting qubits, trapped ions, and photonic qubits, and highlights significant experimental achievements like Google's demonstration of quantum supremacy.The chapter also delves into the transformative applications of quantum computing in various industries, such as finance, healthcare, energy, and logistics. Quantum simulations offer unprecedented insights into molecular interactions and material properties, while quantum cryptography ensures secure communication. Ethical considerations, including data privacy and equitable access, are emphasized alongside the potential economic and societal impacts. The future outlook of quantum computing envisions further advancements in quantum algorithms, hardware, and interdisciplinary integration, paving the way for a quantum-enabled era with profound implications for science, technology, and society. Keywords: Quantum Computing, Qubits, Superposition, Entanglement, Quantum Algorithms, Shor's Algorithm, Grover's Algorithm, Quantum Supremacy, Quantum Hardware, Quantum Cryptography, Quantum Simulations, Ethical Considerations, Economic Impact, Future Prospects.

Quantum Computing represents a paradigm shift in computation, leveraging the principles of quantum mechanics to solve problems intractable for classical computers. This book provides a comprehensive exploration of quantum computing, encompassing its foundational concepts, architecture, algorithms, programming techniques, and real-world applications. Beginning with an overview and historical evolution, it delves into the fundamental differences between classical and quantum computing, highlighting key quantum mechanical phenomena such as superposition, entanglement, and interference. The book further examines quantum states, qubits, and gates, elucidating their roles in quantum computation. The architecture of quantum systems, including superconducting qubits, trapped ions, and photonic qubits, is analyzed alongside quantum circuits, hardware challenges, and error correction mechanisms. Core quantum algorithms, including Shor’s algorithm for factorization and Grover’s algorithm for search, are discussed with practical examples. The book also emphasizes quantum programming, featuring tools like Qiskit, Cirq, and PyQuil, and explores challenges in quantum simulation and circuit development. Applications in cryptography, artificial intelligence, drug discovery, and optimization are detailed, underscoring quantum computing’s transformative potential. The book concludes with an examination of challenges such as scalability, noise, and ethical concerns, while providing insights into future directions, including hardware advancements, emerging algorithms, and integration with classical systems. It serves as an essential resource for students, researchers, and professionals aiming to understand and contribute to the quantum revolution. Keywords: Quantum computing, classical computing, quantum mechanics, qubits, quantum gates, superposition, entanglement, quantum algorithms, Shor’s algorithm, Grover’s algorithm, quantum programming, Qiskit, Cirq, quantum circuits, quantum hardware, error correction, cryptography, artificial intelligence, drug discovery, optimization, scalability, quantum noise, ethical implications, future directions

This chapter describes results of a recent investigation aiming to assess the potential of quantum computing and suitably designed algorithms for future computational fluid dynamics applications. For quantum computers becoming available in the near future, it can be expected that applications of quantum computing follow the quantum coprocessor model, where selected parts of the computational task for which efficient quantum algorithms exist are executed on the quantum hardware. For example, in computational fluid dynamics algorithm, this hybrid quantum/classical approach is discussed, and in particular it is shown how the approximate quantum Fourier transform (AQFT) can be used in the Poisson solvers of the considered method for the incompressible-flow Navier-Stokes equations. The analysis shows that despite the inevitable errors introduced by applying AQFT, the method produces meaningful results for three-dimensional example problems. A second example of a quantum algorithm for flow simulations is then described. This method based on kinetic modeling of the flow was developed to reduce the information transfer between quantum and classical hardware in the quantum coprocessor model. It is shown that this quantum algorithm can be executed fully on quantum hardware during a simulation. The conclusion summarizes further challenges for algorithm developments and future work.

The simulation of chemical reactions is an anticipated application of quantum computers. Using a Diels-Alder reaction as a test case, in this study we explore the potential applications of quantum algorithms and hardware in investigating chemical reactions. Our specific goal is to calculate the activation barrier of a reaction between ethylene and cyclopentadiene forming a transition state. To achieve this goal, we use quantum algorithms for near-term quantum hardware (entanglement forging and quantum subspace expansion) and classical post-processing (many-body perturbation theory) in concert. We conduct simulations on IBM quantum hardware using up to 8 qubits, and compute accurate activation barrier in the reaction between cyclopentadiene and ethylene by accounting for both static and dynamic electronic correlation. This work illustrates a hybrid quantum-classical computational workflow to study chemical reactions on near-term quantum devices, showcasing the potential for performing quantum chemistry simulations on quantum hardware to predict activation barriers in agreement with those predicted by CASCI.

Effectively manipulating quantum computing (QC) hardware in the presence of imperfect devices and control systems is a central challenge in realizing useful quantum computers. Susceptibility to noise critically limits the performance and capabilities of today’s so-called noisy intermediate-scale quantum devices, as well as any future QC technologies. Fortunately, quantum control enables efficient execution of quantum logic operations and quantum algorithms with built-in robustness to errors, and without the need for complex logical encoding. In this manuscript we introduce software tools for the application and integration of quantum control in QC research, serving the needs of hardware R&D teams, algorithm developers, and end users. We provide an overview of a set of Python-based classical software tools for creating and deploying optimized quantum control solutions at various layers of the QC software stack. We describe a software architecture leveraging both high-performance distributed cloud computation and local custom integration into hardware systems, and explain how key functionality is integrable with other software packages and quantum programming languages. Our presentation includes a detailed mathematical overview of key features including a flexible optimization toolkit, engineering-inspired filter functions for analyzing noise susceptibility in high-dimensional Hilbert spaces, and new approaches to noise and hardware characterization. Pseudocode is presented in order to elucidate common programming workflows for these tasks, and performance benchmarking is reported for numerically intensive tasks, highlighting the benefits of the selected cloud-compute architecture. Finally, we present a series of case studies demonstrating the application of quantum control solutions derived from these tools in real experimental settings using both trapped-ion and superconducting quantum computer hardware.

Quantum computation: Algorithms and Applications

This issue's SIGEST paper, from the SIAM Journal on Computing (SICOMP), takes SIAM readers into the world of quantum computing, a world with its roots in physics that still probably is better known to many physicists and theoretical computer scientists than to a good portion of SIAM readers. Quantum computation is a form of computing based upon quantum mechanics, rather than the classical physics that conventional computers utilize. The distinction between conventional and quantum computers starts to become apparent at the most basic level of bits: whereas standard computers utilize binary bits that may have either the state 0 or 1, quantum computers are based upon “qubits” (quantum binary digits) that may have the state 0, 1, or a superposition of these two states with a complex number that specifies the probability for being in each state. Mathematically, the state of a quantum computer can change through a sequence of unitary transformations to the initial state. One reason for the great interest in quantum computation is that it has been shown that quantum computers can solve some important problems, such as the factorization of very large integers (which has important implications for cryptography), far more efficiently than we currently are able to solve these problems on conventional computers. The selected paper, “Adiabatic Quantum Computation Is Equivalent to Standard Quantum Computation” by Dorit Aharonov, Wim van Dam, Julia Kempe, Zeph Landau, Seth Lloyd, and Oded Regev, which was originally published in SICOMP in 2007, establishes an important theoretical result in the field of quantum computation. As the title indicates, it involves adiabatic quantum computation, a form of quantum computing that has attracted interest in recent years in part because it may offer promise in the effort to build effective quantum computers. Adiabatic quantum computation is distinctly different from standard quantum computation. In the standard model, computations are represented similarly to classical circuits, except that the circuits carry qubits instead of bits. In contrast, the adiabatic model is inspired by the adiabatic theorem in quantum mechanics which states that a system in its lowest energy or ground state will remain in that state if it is subjected to conditions that change sufficiently slowly. It already was known that standard quantum computers can efficiently simulate adiabatic quantum computers. The key contribution of this paper is to show the reverse: that adiabatic quantum computation can efficiently simulate standard quantum computation. In the words of the SICOMP editorial board in nominating this paper, “This is a surprising result that continues to be very influential.” It established that the two forms of quantum computation are theoretically equivalent, one implication of which is to bolster the potential practical importance of adiabatic quantum computation. The paper by Aharonov et al. is very nicely suited to SIGEST—it is important in its field, it is nicely and accessibly written, it offers a glimpse into an area of applied mathematics and computation that is of growing importance, and it touches on many areas of applied mathematics, including linear algebra, Markov chains, and optimization. We hope it will provide SIAM readers a glimpse of current theoretical research that may, some day, help lead to a brave new world of practical computation.

The rapid expansion of the fintech sector has brought with it an increasing demand for robust and sophisticated fraud detection systems capable of managing large volumes of financial transactions. Conventional machine learning (ML) approaches, while effective, often encounter limitations in terms of computational efficiency and the ability to model complex, high-dimensional data structures. Recent advancements in quantum computing have given rise to a promising paradigm known as quantum machine learning (QML), which leverages quantum mechanical principles to solve problems that are computationally infeasible for classical computers. The integration of QML with data science has opened new avenues for enhancing fraud detection frameworks by improving the accuracy and speed of transaction pattern analysis, anomaly detection, and risk mitigation strategies within fintech ecosystems. This paper aims to explore the potential of quantum-enhanced data science methodologies to bolster fraud detection and prevention mechanisms, providing a comparative analysis of QML techniques against classical ML models in the context of their application to financial data analysis. Fraud detection in fintech relies heavily on data-driven models to identify suspicious activities and prevent financial crimes such as identity theft, money laundering, and fraudulent transactions. Traditional ML approaches, such as decision trees, support vector machines, and deep learning, have laid the foundation for these systems. However, these approaches often fall short when faced with the challenges posed by high-dimensional, noisy, and complex financial data. Quantum machine learning, by leveraging quantum bits or qubits, possesses the unique ability to represent and process data in an exponentially larger state space, allowing for more efficient pattern recognition and computationally intensive analysis. Quantum algorithms such as the Quantum Support Vector Machine (QSVM), Quantum Principal Component Analysis (QPCA), and Quantum Neural Networks (QNNs) have been studied for their potential to outperform classical counterparts in specific problem domains, including fraud detection. This research delves into the theoretical foundations of quantum computing, outlining how quantum superposition, entanglement, and quantum interference can be harnessed to perform operations that exponentially accelerate data processing. Quantum algorithms are presented as capable of achieving faster data transformations and more nuanced pattern recognition through their ability to process all potential combinations of data simultaneously. The implementation of QML algorithms on quantum hardware, although still in its nascent stages, is beginning to demonstrate tangible benefits in terms of the speed and complexity of computations for fraud detection tasks. For example, quantum-enhanced anomaly detection can lead to the identification of rare, complex patterns that classical ML might overlook, contributing to a more proactive approach to fraud prevention. The paper also examines the integration of data science techniques with quantum-enhanced fraud detection, considering data preprocessing, feature engineering, and the application of quantum-enhanced statistical methods. Data preprocessing, a crucial step in building effective fraud detection models, involves the transformation and normalization of financial data to ensure that models can learn from relevant features without overfitting or underfitting. Quantum data structures offer the potential to represent data with a higher degree of complexity and interrelations, which is critical for capturing the multifaceted nature of financial transactions and detecting subtle signs of fraudulent activity. Quantum data encoding schemes such as Quantum Random Access Memory (QRAM) enable efficient storage and retrieval of data, providing a scalable solution for processing large datasets in real-time. A comprehensive analysis of case studies demonstrates the real-world applicability of quantum machine learning frameworks in fintech. The research highlights projects where quantum algorithms have been tested in controlled environments to detect anomalies in simulated transaction data, showcasing improvements in the identification of complex fraud scenarios over classical ML approaches. For instance, Quantum Support Vector Machines have been utilized to perform higher-dimensional classification tasks that are essential for distinguishing between legitimate and fraudulent transactions based on transaction history and user behavior. Furthermore, quantum algorithms that operate on hybrid systems, combining quantum and classical resources, are also explored to mitigate the limitations imposed by current quantum hardware, which is still constrained by issues such as noise and qubit coherence time. The paper also addresses key challenges and limitations associated with the integration of QML into practical fraud detection systems. Quantum hardware, although advancing rapidly, still faces significant challenges, including the need for error correction, qubit stability, and hardware scalability. Quantum computers with sufficient qubits and coherence time are necessary to implement complex algorithms for fraud detection effectively. Additionally, a practical approach to harnessing QML would require the development of quantum software frameworks and quantum programming languages that can operate in tandem with existing fintech systems and data infrastructure. Another area of focus is the synergy between quantum machine learning and classical machine learning models in creating hybrid systems that leverage the strengths of both methodologies. Quantum-enhanced feature extraction and dimensionality reduction can be combined with classical algorithms for final decision-making processes. This allows for a more comprehensive approach where quantum algorithms handle the computationally intensive parts of data analysis, while classical systems can be utilized for integrating real-time data and refining output for human interpretation. The paper discusses potential pathways for integrating these hybrid models, including considerations for API development, data interoperability, and the standardization of quantum-classical workflows. The discussion extends to the practical implications of implementing quantum-based fraud detection systems, particularly in terms of security and privacy. The use of quantum encryption and quantum key distribution can complement QML by ensuring that the data fed into fraud detection models is protected from external tampering. Quantum-resistant cryptography solutions are also explored, providing a comprehensive view of how quantum technologies could enhance the overall security posture of fintech ecosystems while promoting trust and compliance.

The rapidly developing topic of quantum artificial intelligence (AI) combines machine learning with quantum computing to revolutionise data processing, boost efficiency, and address issues. However, quantum AI uses the ideas of superposition, entanglement, and quantum parallelism to execute complex computations much more quickly rather than relying on conventional binary computer systems. The promise of quantum AI in domains including materials science, healthcare, finance, and cryptography is examined critically in this study. Thus, by examining certain recent developments in quantum hardware, quantum algorithms, and hybrid quantum-classical models, this paper explores the revolutionary potential of quantum computing in artificial intelligence. Advances in quantum technology indicate a bright future for investigating the area of quantum AI in new computing challenges that conventional AI cannot address, notwithstanding the limits of noise, hardware, and error correction.

Quantum circuits are an abstract framework to represent quantum dynamics. They are used to formally describe and reason about processes within quantum information technology. They are primarily used in quantum computation, quantum communication, and quantum cryptography—for which they provide a machine code–level description of quantum algorithms and protocols. The quantum circuit model is an abstract representation of these technologies based on the use of quantum circuits, with which algorithms and protocols can be concretely developed and studied. Quantum circuits are typically based on the concept of qubits: two-level quantum systems that serve as a fundamental unit of quantum hardware. In their simplest form, circuits take a set of qubits initialized in a simple known state, apply a set of discrete single- and two-qubit evolutions known as “gates,” and then finally measure all qubits. Any quantum computation can be expressed in this form through a suitable choice of gates, in a quantum analogy of the Boolean circuit model of conventional digital computation. More complex versions of quantum circuits can include features such as qudits, which are higher level quantum systems, as well as the ability to reset and measure qubits or qudits throughout the circuit. However, even the simplest form of the model can be used to emulate such behavior, making it fully sufficient to describe quantum information technology. It is possible to use the quantum circuit model to emulate other models of quantum computing, such as the adiabatic and measurement-based models, which formalize quantum algorithms in a very different way. As well as being a theoretical model to reason about quantum information technology, quantum circuits can also provide a blueprint for quantum hardware development. Corresponding hardware is based on the concept of building physical systems that can be controlled in the way required for qubits or qudits, including applying gates on them in sequence and performing measurements.

Quantum computing is a novel kind of computation that solves very complicated problems rapidly by applying concepts from basic physics. Concepts like quantum mechanical computing and quantum algorithms are included in the field of quantum computing study. Researchers have imagined quantum computing as a revolutionary idea among emerging technologies in terms of concepts, methods, and techniques. These are cross-pollinated. Hence, quantum computing becomes more and more multidisciplinary. Quantum computing leverages quantum mechanical phenomena like superposition and quantum interference to deal with some kinds of problems more precisely than conventional computing. Because of its unique characteristics, which set it apart from conventional computers in terms of functionality and operation, quantum computing has grown in popularity. There are possibilities of creating hybrid models, namely approaches for large-scale mixed-integer programming issues, that effectively combine the strengths of quality control techniques with deterministic algorithms to handle combinatorial challenges.

Quantum computing has emerged as a transformative approach for tackling complex problems in quantum chemistry, particularly in simulating multielectron systems and electron-phonon interactions. However, the current noisy intermediate-scale quantum (NISQ) devices face significant challenges in implementing practical quantum algorithms due to error accumulation caused by increased circuit depth, qubit counts, and gate operations. To address these challenges, we present TenCirChem, an open-source Python package specifically designed for implementing variational quantum algorithms in quantum computational chemistry. TenCirChem demonstrates exceptional performance in simulating unitary coupled-cluster circuits through its innovative use of compact representations for quantum states and excitation operators. This package supports noisy circuit simulation and provides advanced algorithms for variational quantum dynamics, enabling researchers to explore complex chemical phenomena. Its capabilities are exemplified in various applications, including the calculation of potential energy curves and the investigation of quantum gate error impacts on molecular systems. Moreover, TenCirChem’s seamless integration with real quantum hardware makes it a versatile tool for both simulation and experimentation. A key innovation developed within the TenCirChem framework is the Clifford-based Hamiltonian engineering approach for molecules (CHEM). This algorithm addresses the critical challenge of achieving chemical accuracy with shallow quantum circuits, a fundamental requirement for practical applications on NISQ devices. CHEM employs a sophisticated Clifford-based Hamiltonian transformation that operates within the variational quantum eigensolver (VQE) framework using hardware-efficient ansatz. The method ensures four crucial advantages: (1) generation of initial circuit parameters corresponding to Hartree-Fock energy, (2) maximization of initial energy gradients with respect to circuit parameters, (3) minimal classical processing overhead without additional quantum resource requirements, and (4) compatibility with any circuit topology. Through quantum hardware emulator demonstrations, CHEM has achieved chemical accuracy for systems up to 12 qubits with fewer than 30 two-qubit gates, representing a significant advancement in practical quantum computational chemistry. To enhance the efficiency of variational quantum algorithms, we developed the sequential optimization with approximate parabola (SOAP) method, specifically designed for parameter optimization in unitary coupled-cluster ansatz. SOAP addresses the critical bottleneck of measurement requirements in VQE by implementing an innovative optimization strategy that approximates the energy landscape as quadratic functions. This approach minimizes the number of energy evaluations while incorporating parameter correlations through the integration of average directions from previous iterations. Benchmark studies demonstrate SOAP’s superior performance, showing faster convergence and enhanced noise robustness compared to traditional optimization methods. The method’s scalability has been validated through numerical simulations of up to 20 qubits, and its practical efficacy has been confirmed through experiments on superconducting quantum computers. For simulating electron-phonon systems, we introduce a variational basis state encoding algorithm that significantly reduces resource requirements compared to conventional unary and binary encoding schemes. Our approach achieves smaller scaling than traditional methods for qubits and gates for systems obeying the area law of entanglement entropy, this remarkable reduction in resource requirements comes at the cost of a constant amount of additional measurements. The algorithm’s effectiveness has been validated through both numerical simulations and quantum hardware experiments, demonstrating that using just one or two qubits per phonon mode can produce quantitatively accurate results across various coupling regimes. The integration of these innovations within the TenCirChem library represents a significant advancement in quantum computational chemistry. The software package provides researchers with a comprehensive toolkit for developing, testing, and implementing quantum algorithms, while the novel methods address fundamental challenges in circuit depth, parameter optimization, and resource efficiency. These developments collectively enhance the practicality of quantum computing for addressing real-world chemical problems in the NISQ era, offering improved accuracy, efficiency, and noise robustness.

Running general quantum algorithms on quantum computers is hard, especially in the early stage of development of the quantum computer that we are in today. Many resources are required to transform a general problem to be run on a quantum computer, for instance to satisfy the topology constraints of the quantum hardware. Furthermore, quantum computers need to operate at temperatures close to absolute zero, and hence resources are required to keep the quantum hardware at that level. Therefore, simulating small instances of a quantum algorithm is often preferred over running it on actual quantum hardware. This is both cheaper and gives debugging capabilities which are unavailable on actual quantum hardware, such as the evaluation of the full quantum state, at intermediate points in the algorithm as well as at the end of the algorithm. By simulating small instances of quantum algorithms, the quantum algorithm can be checked for errors and be debugged before implementing and running it on actual quantum hardware for larger instances. There are multiple initiatives to create quantum simulators and while looking alike, there are difference among them. In this work we compare seven often used quantum simulators offered by various parties by implementing the Shor-code, an error-correcting technique. The Shor-code can detect and correct all single qubit errors in a quantum circuit. For most multi-qubit errors, correct detection and correction is not possible. We compare the seven quantum simulators on different aspects, such as how easy it is to implement the Shor-code, what its capabilities are regarding translation to actual quantum hardware and what the possibilities of simulating noise are. We also discuss aspects such as topology restrictions and the programming interface.

In the last couple of decades, the world has seen several stunning instances of quantum algorithms that provably outperform the best classical algorithms. For most problems, however, it is currently unknown whether quantum algorithms can provide an advantage, and if so by how much, or how to design quantum algorithms that realize such advantages. Many of the most challenging computational problems arising in the practical world are tackled today by heuristic algorithms that have not been mathematically proven to outperform other approaches but have been shown to be effective empirically. While quantum heuristic algorithms have been proposed, empirical testing becomes possible only as quantum computation hardware is built. The next few years will be exciting as empirical testing of quantum heuristic algorithms becomes more and more feasible. While large-scale universal quantum computers are likely decades away, special-purpose quantum computational hardware has begun to emerge that will become more powerful over time, as well as some small-scale universal quantum computers.