How-Possibly Explanations in (Quantum) Computer Science

Quantum computing is an extremely promising research combining theoretical and experimental quantum physics, mathematics, quantum information theory and computer science. Classical simulation of quantum computations will cover part of the gap between the theoretical mathematical formulation of quantum mechanics and the realization of quantum computers. One of the most important problems in “quantum computer science” is the development of new symbolic languages for quantum computing and the adaptation of existing symbolic languages for classical computing to quantum algorithms. The present paper is devoted to the adaptation of the Mathematica symbolic language to known quantum algorithms and corresponding simulation on the classical computer. Concretely we shall represent in the Mathematica symbolic language Simon’s algorithm, the Deutsch-Josza algorithm, Grover’s algorithm, Shor’s algorithm and quantum error-correcting codes. We shall see that the same framework can be used for all these algorithms. This framework will contain the characteristic property of the symbolic language representation of quantum computing and it will be a straightforward matter to include this framework in future algorithms.KeywordsDeutsch-Josza algorithmGrover’s algorithmQuantum computingQuantum error-correctingShor’s algorithmSimon’s algorithmSimulation of quantum algorithms

Quantum computing is a multidisciplinary field at the intersectionof quantum physics, computer science, and mathematics, aiming to har-ness quantum mechanical phenomena for computational advantage. Thisarticle provides a comprehensive review of both the foundational princi-ples and advanced theoretical models of quantum computing. We beginwith the basic framework of quantum computation, introducing the con-cept of qubits as two-level quantum systems, the linear algebra of Hilbertspaces, Dirac’s bra–ket notation, and the postulates of quantum mechan-ics (state superposition, unitary evolution, and projective measurement).We then discuss quantum logic gates and circuits, highlighting how clas-sical reversible computation principles extend to universal quantum gatesets. Next, we survey key quantum algorithms (from Shor’s factoring toGrover’s searching and beyond) and the complexity-theoretic implicationsof quantum computers, contrasting the class BQP with classical complex-ity classes. We cover the theoretical foundations of quantum error cor-rection and fault tolerance, explaining how quantum information can beprotected from decoherence using redundancy and how fault-tolerant pro-tocols can, in principle, allow scalable quantum computation despite noisyhardware. We then explore advanced models and paradigms of quantumcomputation, including measurement-based quantum computing (one-wayquantum computing), topological quantum computation with anyons, adi-abatic quantum computing and quantum annealing, continuous-variablequantum computing, and related approaches. We also provide an overviewof quantum information theory as it relates to computation, discussingentanglement, quantum entropy, and information-theoretic limits like theHolevo bound. Finally, we review the leading physical implementations(quantum hardware models) of quantum computers—trapped ions, super-conducting circuits, photonic systems, solid-state spin qubits, and oth-ers—outlining the challenges and achievements of each approach.

Classic computing can take credit for technology ranging from mobile phones to supercomputers. But in recent years, a budding counterpart to these conventional devices has emerged: quantum computers. Whereas classic computing sometimes fails to solve complex calculations, such as factoring hundred-digit numbers, quantum computing holds the potential to easily tackle such problems. The field of quantum computing has attracted researchers, such as National Academy of Sciences member Christopher Monroe. An experimental atomic physicist at the University of Maryland and fellow of the Joint Quantum Institute and the Joint Center for Quantum Information and Computer Science in Maryland, Monroe uses lasers to exploit atomic particles to study complex computational problems. Monroe spoke to PNAS about how quantum computing might evolve. Christopher Monroe. > PNAS:Can you describe some of the basic mechanics of quantum computing? > Monroe:It all comes down to the superposition principle, in which a quantum system can exist in multiple states at the same time. Consider the fundamental unit of information: the bit. A bit is binary information that can be a 0 or a 1. A quantum bit, or qubit, can be in a superposition of both 0 and 1 as long as it’s isolated and unobserved. A single qubit is pretty trivial, but when you put many qubits together, there become exponentially many possibilities. > > Let’s consider 300 qubits. That’s an interesting number because the number of possible configurations, 2300, is more than the number of particles in the universe. You could never simulate what happens with 300 qubits on a classical machine; there’s not enough stuff in the universe to do it. The magic with quantum is the power of exponential growth: every time you add a qubit, you double the number of configurations. > > But to control these qubits and exploit this massive storage, we …

With quantum computing, we are witnessing an exciting and very promising merging of three of the deepest and most successful scientific and technological developments of modern era: quantum physics, computer science, and nanotechnology. Quantum computers have the potential to perform certain calculations billions of times faster than any silicon-based computer. A functional quantum computer will be invaluable in factoring large numbers, and therefore extremely useful for decoding and encoding secret information. In this paper we have discussed contemporary cryptographic systems and their strengths and drawbacks. Two of the most common quantum key distribution protocols have been explained. This is followed by a note on the experimental realizations of quantum key distribution and the associated technological challenges. A few novel extensions of this concept in the future have also been dealt with. This paper aims at familiarizing the reader with the field of quantum cryptography and gives an insight about the latest developments.

As quantum computing development advances closer toward achieving fault-tolerant error-corrected realisation, debates on applications, impacts, risks, and benefits of quantum computing are timely and due. While there is awareness of the potential power and complexity of quantum computers, there has been relatively little attention on the social impacts and ethical implications of this technology. In grappling with the social impacts of quantum computing, some stakeholders have turned to applied ethics, specifically (classical) computer and Artificial Intelligence (AI) ethics, for guidance. While computer and AI ethics are useful starting points for evaluating the ethical issues posed by quantum computing, uncritically applying existing sets of ethical principles risks overlooking how quantum computing differs from these technologies. We argue that borrowing of ethical principles and guidelines from AI and computing is inappropriate for several reasons: (1) quantum computing, classical computing, and AI are different technologies with significant material differences; (2) unlike AI and classical computers which have become established, quantum computing is an emerging technology, which has implications on the levels of accessibility and immediate impact in society; and (3) there are significant differences in the way AI and quantum computing have been developed and by whom. We also briefly summarise some of the unique risks and societ al impacts posed by quantum computing. We posit that these reasons support the argument for a new sub-field of quantum computing ethics, which would allow a relevant scholarship to develop and provide guidance as quantum computing technology continues to mature.

During recent years, quantum computers have received increasing attention, primarily due to their ability to significantly increase computational performance for specific problems. Computational performance could be improved for mathematical optimization by quantum annealers. This special type of quantum computer can solve quadratic unconstrained binary optimization problems. However, multi-energy systems optimization commonly involves integer and continuous decision variables. Due to their mixed-integer problem structure, quantum annealers cannot be directly used for multi-energy system optimization.To solve multi-energy system optimization problems, we present a hybrid Benders decomposition approach combining optimization on quantum and classical computers. In our approach, the quantum computer solves the master problem, which involves only the integer variables from the original energy system optimization problem. The subproblem includes the continuous variables and is solved by a classical computer. For better performance, we apply improvement techniques to the Benders decomposition. We test the approach on a case study to design a cost-optimal multi-energy system. While we provide a proof of concept that our Benders decomposition approach is applicable for the design of multi-energy systems, the computational time is still higher than for approaches using classical computers only. We therefore estimate the potential improvement of our approach to be expected for larger and fault-tolerant quantum computers.

In the world of computation, the invention of Computers has reduced human effort for accomplishing task. Depending on the type, size and nature of the work the computers are manufactured in different magnitudes. As the technology grows, it facilitated to manufacture high performing, high throughput, and high memory Classical computers. Classical computers store any information in the form of bits in the memory device, which can be either 1 or 0 (binary system) and all the processing will be done in the same logic i.e., high voltage/low voltage. Because of this logic the classical computers solve some problems by using more resources. Quantum computer are the next level computers which uses quantum theory principles for solving problems. The quantum computer uses Qubit as basic unit which uses principles of quantum computing such as superposition and entanglement, which gives qubit, the efficiency of exhibiting many logical states at a time. This paper shows a comparative study on classical and quantum computers and illustrates various problems in classical computers and respective solutions with use of quantum computers.

Exploring the trade-off between computational power and energy efficiency: An analysis of the evolution of quantum computing and its relation to classical computing

Recent improvements in control of quantum systems make it seem feasible to finally build a quantum computer within a decade. While it has been shown that such a quantum computer can in principle solve certain small electronic structure problems and idealized model Hamiltonians, the highly relevant problem of directly solving a complex correlated material appears to require a prohibitive amount of resources. Here, we show that by using a hybrid quantum-classical algorithm that incorporates the power of a small quantum computer into a framework of classical embedding algorithms, the electronic structure of complex correlated materials can be efficiently tackled using a quantum computer. In our approach, the quantum computer solves a small effective quantum impurity problem that is self-consistently determined via a feedback loop between the quantum and classical computation. Use of a quantum computer enables much larger and more accurate simulations than with any known classical algorithm, and will allow many open questions in quantum materials to be resolved once a small quantum computer with around one hundred logical qubits becomes available.

Fundamental transformations in the basic logic of computing are few and far between. Since the invention of digital computers in the early 1940s, the logic underlying computation has remained the same, even as computing hardware evolved from vacuum tubes to silicon transistors. With the advent of quantum computation, a fundamental transformation is near. Quantum computation is based on a different type of logic: rather than being in one of the two states of a classical bit, a quantum bit or qubit can be in a superposition of two states simultaneously. Operations and measurements on these qubits obey the constraints of quantum mechanics. It is now understood that quantum computers have great power in principle to go beyond classical computers, but that not every application is well suited to implementation on quantum computers. For reasons explained in more detail in the Introduction, scientific problems in chemical and materials sciences are uniquely suited to take advantage of quantum computing in the relatively near future. Indeed, quantum computing offers the best hope to solve many of the most important and difficult problems in this field. For example, quantum materials, such as superconductors and complex magnetic materials, show novel kinds of ordered phases that are natural from the point of view of quantum mechanics but difficult to access via computation on classical computers. Quantum sensors based on solid materials are already widely used but could be greatly improved with insight from quantum computations, as could materials for information technologies. Quantum chemical dynamics is another example of a problem that is intrinsically well suited to studies on quantum computers. Applications of quantum chemical dynamics include catalysis, artificial photosynthesis, and other industrially important processes. Quantum computers exist in the laboratory and are beginning to exceed 50 qubits, which is roughly the size beyond which their behavior cannot be predicted or emulated on present-day classical supercomputers. While a quantum computer of 50 qubits is almost certainly not powerful enough to tackle the major scientific challenges in chemical and materials sciences, some of these major challenges start to become accessible with a few hundred qubits if error rates can be kept small. This roundtable was convened to ask how emerging quantum computers can be applied to major scientific problems in chemical and materials sciences, in light of Basic Energy Sciences’s leading role in these fields and the Department of Energy’s leading role in high-performance scientific computation more generally. The main outcome of the roundtable was a consensus that there are scientific problems of great importance on which emerging quantum computers have the potential for disruptive impact, and where comparable progress is unlikely to occur by other means.

This Research to Practice Full Paper discusses an approach to motivating graduate computer science and electrical engineering students in the study of quantum computing. The U.S. Congress and other governmental and industrial organizations have recognized that teaching Quantum Computing in university-level Computer Science and Electrical Engineering programs is strategically important for workforce development along with technology development. Success in this endeavor requires generating genuine interest in the topic and motivating potential students. Quantum Computing requires an understanding of relatively difficult related subjects including physics, math and computer science. Many computer science and electrical engineering students shy away from quantum computing because of its complexity. This paper discusses our success with generating interest in quantum computing among graduate students and motivating them through exploring, in related courses, some aspects of quantum computing that have the potential to generate discontinuities. The approach is also examined in terms of the Scientific Learning Cycle as discussed by Wankat & Oreovicz. Opportunities and challenges of adding Quantum Computing to Computer Science and Electrical Engineering programs were studied through a student small group project in a cybersecurity course. The work built on extensive research into the effectiveness of small group projects and the role of “play” in learning. Our small group project on quantum computing was introduced three years ago into a cybersecurity course which is required for all students in our university's Masters in Computer Science and Masters in Electrical Engineering programs. The basic goals of the project are to teach students some basics of quantum computing by allowing them to “play with it” and to alert students to the fact that quantum computing is a rapidly developing new field that they need to follow during at least the next decade. The small group project helped students to explore the potential of quantum computing to substantially undermine current Public Key Cryptography and, at the same time provide a new approach to encryption that is even more secure than Public Key Cryptography. A qualitative analysis of discussions and assigned tasks suggests that this strategy succeeded in generating significant interest in quantum computing among students. They became motivated and immersed in a difficult subject despite the requirement for investment of significant time and effort to understand a complex combination of physics, math and computer science.

Quantum machine learning recently gained prominence due to the computational ability of quantum computers in solving machine learning problems that are intractable on a classical computer. However, achieving a quantum advantage on present-day quantum computers remains an open challenge. In this work, we primarily focus on solving machine learning problems using a hybrid model based on both quantum and classical computers together for the classification task. We propose the quantum multi-class classifier (QMCC) as a variational circuit with a hybrid classical-quantum approach using quantum mechanical properties such as superposition and entanglement. A unitary operation on a single qubit for the state preparation is designed and also demonstrated using a real quantum computer on the IBMQX platform. The entire variational circuit for the classification task is implemented on a quantum simulator. We performed our quantum simulations on three benchmark datasets: Iris dataset, Banknote Authentication (BNA) dataset, and Wireless Indoor Localization (WIL) dataset for machine learning algorithms. Our simulation results show that the proposed QMCC model classified Iris dataset with an accuracy of 92.10%, BNA dataset with an accuracy of 89.50%, and WIL dataset with an accuracy of 91.73%. The proposed model can also be extended to multiple class classifiers.

Quantum computers have the potential to create important new opportunities for ongoing essential research on gauge theories. They can provide simulations that are unattainable on classical computers such as sign-problem afflicted models or time evolutions. In this work, we variationally prepare the low-lying eigenstates of a non-Abelian gauge theory with dynamically coupled matter on a quantum computer. This enables the observation of hadrons and the calculation of their associated masses. The SU(2) gauge group considered here represents an important first step towards ultimately studying quantum chromodynamics, the theory that describes the properties of protons, neutrons and other hadrons. Our calculations on an IBM superconducting platform utilize a variational quantum eigensolver to study both meson and baryon states, hadrons which have never been seen in a non-Abelian simulation on a quantum computer. We develop a hybrid resource-efficient approach by combining classical and quantum computing, that not only allows the study of an SU(2) gauge theory with dynamical matter fields on present-day quantum hardware, but further lays out the premises for future quantum simulations that will address currently unanswered questions in particle and nuclear physics.

Quantum computing has quickly become at the vanguard of many computer science fields today. This is motivated by quantum computers ability to perform computational tasks with efficiencies that are not possible with classical computers. Quantum computing technology has a lasting potential impact on society and a broad implications on many aspects of our lives. Communications Industry Researchers (CIR) estimates that the global quantum-computing market is expected to reach $1.9 billion in 2023, increasing to $8 billion by 2027, in spending on associated software and services. Although quantum computing has several advantages, it threatens the current cryptographic techniques, which are necessary for today’s Internet standards like the Transport Layer Security (TLS). This is due to its ability to perform infinite complex computations in parallel. Therefore, it is expected that quantum computers will be able to solve the key distribution problem and break every single cryptography and authentication algorithm based on Asymmetric cryptography, such as: RSA, ECC, and Diffie-Hellman. New emerging technologies such as the Internet of Things (IoT), blockchain, autonomous vehicles, 5G, Artificial Intelligence (AI) and robotics all rely on cryptography for their secure operation. Although quantum computing supports technological evolution and growth, it will pose a threat to the current progress and future development of these technologies. Therefore, cryptography and authentication techniques need improvements as introducing quantum computing would put today’s cybersecurity in serious risk. NSA and NIST proposed solutions to tackle these challenges. However, these solutions are still immature as they need major upgrade of hardware implementation. Instead, the recommendations focus on what is called post-quantum, quantum-proof, quantum-safe or quantum-resistant cryptosystems. This talk outlines how the impact of quantum technologies on authentication, data exchange, and data storage, as well as areas where cryptography plays an essential role, such as: blockchain, 5G, IoT, and AI technologies. It investigate the possible impact of quantum technologies on these emerging technologies. Finally, it discusses some of the current quantum security solution that are devoted to protect the devices and systems in the quantum era, and mitigate quantum attacks.

In recent years, quantum computers and algorithms have made significant progress indicating the prospective importance of quantum computing (QC). Especially combinatorial optimization has gained a lot of attention as an application field for near-term quantum computers, both by using gate-based QC via the Quantum Approximate Optimization Algorithm and by quantum annealing using the Ising model. However, demonstrating an advantage over classical methods in real-world applications remains an active area of research. In this work, we investigate the robustness verification of ReLU networks, which involves solving many-variable mixed-integer programs (MIPs), as a practical application. Classically, complete verification techniques struggle with large networks as the combinatorial space grows exponentially, implying that realistic networks are difficult to be verified by classical methods. To alleviate this issue, we propose to use QC for neural network verification and introduce a hybrid quantum procedure to compute provable certificates. By applying Benders decomposition, we split the MIP into a quadratic unconstrained binary optimization and a linear program which are solved by quantum and classical computers, respectively. We further improve existing hybrid methods based on the Benders decomposition by reducing the overall number of iterations and placing a limit on the maximum number of qubits required. We show that, in a simulated environment, our certificate is sound, and provides bounds on the minimum number of qubits necessary to approximate the problem. Finally, we evaluate our method within simulations and on quantum hardware.