Nano-refraction Analysis for Advanced Materials: A Theoretical Roadmap for Quantum Computers

Semi-classical theories are approximations to quantum theory that treat some degrees of freedom classically and others quantum mechanically. In the usual approach, the quantum degrees of freedom are described by a wave function which evolves according to some Schrödinger equation with a Hamiltonian that depends on the classical degrees of freedom. The classical degrees of freedom satisfy classical equations that depend on the expectation values of quantum operators. In this paper, we study an alternative approach based on Bohmian mechanics. In Bohmian mechanics the quantum system is not only described by the wave function, but also with additional variables such as particle positions or fields. By letting the classical equations of motion depend on these variables, rather than the quantum expectation values, a semi-classical approximation is obtained that is closer to the exact quantum results than the usual approach. We discuss the Bohmian semi-classical approximation in various contexts, such as nonrelativistic quantum mechanics, quantum electrodynamics and quantum gravity. The main motivation comes from quantum gravity. The quest for a quantum theory for gravity is still going on. Therefore a semi-classical approach where gravity is treated classically may be an approximation that already captures some quantum gravitational aspects. The Bohmian semi-classical theories will be derived from the full Bohmian theories. In the case there are gauge symmetries, like in quantum electrodynamics or quantum gravity, special care is required. In order to derive a consistent semi-classical theory it will be necessary to isolate gauge-independent dependent degrees of freedom from gauge degrees of freedom and consider the approximation where some of the former are considered classical.

The precise quantum control of single photons, together with the intrinsic advantage of being mobile make optical quantum system ideally suited for delegated quantum information tasks, reaching from well-established quantum cryptography to quantum clouds and quantum computer networks. Here I present that the exploit of quantum photonics allows for a variety of quantum-enhanced data security for quantum and classical computers. The latter is based on feasible hybrid classical-quantum technology, which shows promising new applications of readily available quantum photonics technology for complex data processing. As outlook I will discuss technological challenges for the scale up of photonic quantum computers, and our group’s current work for addressing some of those.

Quantum gravity aims to describe gravity in quantum mechanical terms. How exactly this needs to be done remains an open question. Various proposals have been put on the table, such as canonical quantum gravity, loop quantum gravity, string theory, etc. These proposals often encounter technical and conceptual problems. In this chapter, we focus on canonical quantum gravity and discuss how many conceptual problems, such as the measurement problem and the problem of time, can be overcome by adopting a Bohmian point of view. In a Bohmian theory (also called pilot-wave theory or de Broglie-Bohm theory, after its originators de Broglie and Bohm), a system is described by certain variables in space-time such as particles or fields or something else, whose dynamics depends on the wave function. In the context of quantum gravity, these variables are a space-time metric and suitable variable for the matter fields (e.g., particles or fields). In addition to solving the conceptual problems, the Bohmian approach yields new applications and predictions in quantum cosmology. These include space-time singularity resolution, new types of semi-classical approximations to quantum gravity, and approximations for quantum perturbations moving in a quantum background.

U(1) lattice gauge theories (LGTs) offer a way to simulate quantum electrodynamics, one of the three forces unified by the Standard Model of particles physics. Here we provide complete, quantum-gate-by-quantum-gate algorithms to simulate U(1) LGTs on a fault-tolerant quantum computer. We further perform rigorous error analysis in order to derive concrete estimates of the quantum computational resources required for an accurate simulation of U(1) LGTs using a second-order product formula. We show that U(1) LGTs in any spatial dimension can be simulated using non-Clifford T gates, where T is the simulation time, N is the number of lattice sites, Λ is the truncation parameter for the bosonic gauge fields, and ε is the simulation error. This work paves the way towards fault-tolerant quantum simulations of physical models closely related to the Standard Model of particle physics.

Since the first observation of coherent quantum behaviour in a superconducting qubit, now more than 20 years ago, there have been substantial developments in the field of superconducting quantum circuits. One such advance is the introduction of the concepts of cavity quantum electrodynamics (QED) to superconducting circuits, to yield what is now known as circuit QED. This approach realizes in a single architecture the essential requirements for quantum computation, and has already been used to run simple quantum algorithms and to operate tens of superconducting qubits simultaneously. For these reasons, circuit QED is one of the leading architectures for quantum computation. In parallel to these advances towards quantum information processing, circuit QED offers new opportunities for the exploration of the rich physics of quantum optics in novel parameter regimes in which strongly nonlinear effects are readily visible at the level of individual microwave photons. We review circuit QED in the context of quantum information processing and quantum optics, and discuss some of the challenges on the road towards scalable quantum computation. The introduction of concepts from cavity quantum electrodynamics to superconducting circuits yielded circuit quantum electrodynamics, a platform eminently suitable to quantum information processing and for the exploration of novel regimes in quantum optics.

In this work, we propose to study the resonant photonic states in a new class of photonic crystal heterostructures, which can be used to make smaller and faster optoelectronic devices. Photonic quantum well (PQW) heterostructures are made from two different photonic crystals A and B. The structure is denoted as A/B/A/B/A, where the core crystal A is sandwiched between two B crystals. If crystals A and B are chosen so that the upper band edge of A lies within the gap of B, the resulting band structure acts as a double potential barrier for photons. Here we have obtained an expression for the transmission coefficient of the PQW heterostructure using the transfer matrix method, and have found that there are resonant states within the well. We have shown that the number of resonant states can be controlled by varying parameters of crystals A and B, such as their lattice constants, indices of refraction and thicknesses. It is anticipated that the resonance states described here can be used to make new types of photonic switching devices and quantum computers.

The development of quantum computation enables exponential time complexity problems on classical computers to be solved in polynomial time on quantum computers. However, it also poses a threat to the security of classical cryptographic schemes based on integer factorization and discrete logarithms. In response to this challenge, quantum cryptographic schemes based on quantum computation and quantum communication environments have become a focal point of research. The quantum public-key cryptosystem based on the QSCDff problem stands as one of the influential schemes in the realm of quantum public-key cryptography, yet its feasibility remains unexplored in current literature. Our specific focus lies in the quantum circuit implementations and fault-tolerant construction, which serve as essential prerequisites for the physical feasibility of quantum cryptographic schemes. We provide quantum circuit implementations along with rigorous theoretical proofs for the computation of the permutation product operation and the permutation sign operation in quantum public-key cryptographic schemes. Based on the fault-tolerant quantum computation process of the aforementioned quantum circuit implementations, we propose two error-correction strategies and provide a theoretical feasibility analysis within a specified range in the ion-trap quantum computation environment, adhering to the theoretical limits of quantum computation. Rigorous proofs are presented to demonstrate the correctness and reliability of the proposed methods. Our contribution provides a theoretical foundation for the physical feasibility analysis of quantum cryptographic algorithms, offering insights into the challenges and prospects of implementing these algorithms in quantum computation environments.

Longdom conferences welcome you to join Conference on “Innovations in Quantum Optics & Quantum computing” during March 23-24, 2020, London, UK. We heartily demand every one of the members who are keen on sharing their insight in Current Trends in Quantum optics, Quantum Computing and Quantum Photonics.

Background. Quantum computing is a technology that has great potential to revolutionize various scientific disciplines with its extraordinary computing capabilities. Multiple fields, such as cryptography, optimization, and complex simulation, have begun to explore quantum computing applications. However, a deep understanding of how these technologies can be used effectively in cross-disciplinary informatics still needs to be improved. Purpose. This research aims to develop a theoretical framework that explains the role of quantum computing in advancing interdisciplinary informatics. The main focus is to identify potential applications and challenges faced in applying this technology in various fields and evaluate its impact on the development of science and technology. Method. This research uses a qualitative approach, a literature review, and theoretical analysis methods. Data were collected from various academic sources, including journals, books, and conferences relevant to quantum computing and interdisciplinary informatics. Analysis was conducted to identify patterns, themes, and relationships between quantum computing and cross-disciplinary applications. Results. The research results show that quantum computing has the potential to solve complex computational problems in various fields, including cryptography, optimization, and physical simulation. Quantum computing can provide more efficient and faster solutions than classical computing. However, the research also identified several significant challenges, such as the need for quantum-specific algorithms and sophisticated technological infrastructure. Conclusion. Quantum computing is essential in advancing interdisciplinary informatics by providing superior computing capabilities. The theoretical framework developed in this research can be used to further study and develop quantum computing applications in various fields. The identified challenges require special attention to ensure effective and efficient implementation of this technology.

The security of public-key cryptography relies on well-studied hard problems, problems for which we do not have efficient algorithms. Factorization and discrete logarithm are the two most known and used hard problems. Unfortunately, they can be easily solved on a quantum computer by Shor's algorithm. Also, the research area of cryptography demands for crypto-diversity which says that we should offer a range of hard problems for public-key cryptography. If one hard problem proves to be easy, we should be able to provide alternative solutions. Some of the candidates for post-quantum hard problems, i.e. problems which are believed to be hard even on a quantum computer, are the Learning Parity with Noise (LPN), the Learning with Errors (LWE) and the Shortest Vector Problem (SVP). A thorough study of these problems is needed in order to assess their hardness. In this thesis we focus on the algorithmic study of LPN. LPN is a hard problem that is attractive, as it is believed to be post-quantum resistant and suitable for lightweight devices. In practice, it has been employed in several encryption schemes and authentication protocols. At the beginning of this thesis, we take a look at the existing LPN solving algorithms. We provide the theoretical analysis that assesses their complexity. We compare the theoretical results with practice by implementing these algorithms. We study the efficiency of all LPN solving algorithms which allow us to provide secure parameters that can be used in practice. We push further the state of the art by improving the existing algorithms with the help of two new frameworks. In the first framework, we split an LPN solving algorithm into atomic steps. We study their complexity, how they impact the other steps and we construct an algorithm that optimises their use. Given an LPN instance that is characterized by the noise level and the secret size, our algorithm provides the steps to follow in order to solve the instance with optimal complexity. In this way, we can assess if an LPN instance provides the security we require and we show what are the secure instances for the applications that rely on LPN. The second framework handles problems that can be decomposed into steps of equal complexity. Here, we assume that we have an adversary that has access to a finite or infinite number of instances of the same problem. The goal of the adversary is to succeed in just one instance as soon as possible. Our framework provides the strategy that achieves this. We characterize an LPN solving algorithm in this framework and show that we can improve its complexity in the scenario where the adversary is restricted. We show that other problems, like password guessing, can be modeled in the same framework.

All papers have been peer reviewed. This was the 4th conference arranged by ICMM on probabilistic foundations of classical and quantum physics. The first three conferences took place in 2000, 2002, and 2004. Some closely related conferences are Bohmian Mechanics 2000 and Quantum Theory: Reconsideration of Foundations 2001, 2003, and 2005. The main aim of these conferences is to understand the role that probability plays in the foundations of physics, theoretical as well as experimental, classical as well as quantum. In this conference, as well as during our previous conferences, we are glad to welcome a fruitful assembly of theoretical physicists, experimenters, mathematicians, and even philosophers interested in the foundations of probability and physics. Among important topics discussed during the conference were the probabilistic foundations of quantum mechanics, as well as the foundations of probability itself, the formation theory, quantum computing, quantum cryptography, quantum teleportation, quantum fluctuations in relation with stochastic electrodynamics, Bohmian mechanics, measurement theory, completeness and incompleteness of quantum mechanics, macroscopic quantum systems, experiments on quantum nonlocality and locality, Bell's inequality, entanglement; philosophical problems raised by quantum mechanics, and mathematical formalism. A special session devoted to the Bayesain approach to classical and quantum probability was organized.

Solid-state quantum devices use quantum entanglement for various quantum technologies, such as quantum computation, encryption, communication and sensing. Solid-state platforms for quantum photonics include single molecules, individual defects in crystals and semiconductor quantum dots, which have enabled coherent quantum control and readout of single spins (stationary quantum bits) and generation of indistinguishable single photons (flying quantum bits) and their entanglement. In the past 6 years, new opportunities have arisen with the emergence of 2D layered van der Waals materials. These materials offer a highly attractive quantum photonic platform that provides maximum versatility, ultrahigh light–matter interaction efficiency and novel opportunities to engineer quantum states. In this Review, we discuss the recent progress in the field of 2D layered materials towards coherent quantum photonic devices. We focus on the current state of the art and summarize the fundamental properties and current challenges. Finally, we provide an outlook for future prospects in this rapidly advancing field.

Usually, the hyperparallel quantum computation can speed up quantum computing, reduce the quantum resource consumed largely, resist to noise, and simplify the storage of quantum information. Here, we present the first scheme for the self-error-corrected hyperparallel photonic quantum computation working with both the polarization and the spatial-mode degrees of freedom of photon systems simultaneously. It can prevent bit-flip errors from happening with an imperfect nonlinear interaction in the nearly realistic condition. We give the way to design the universal hyperparallel photonic quantum controlled-NOT (CNOT) gate on a two-photon system, resorting to the nonlinear interaction between the circularly polarized photon and the electron spin in the quantum dot in a double-sided microcavity system, by taking the imperfect interaction in the nearly realistic condition into account. Its self-error-corrected pattern prevents the bit-flip errors from happening in the hyperparallel quantum CNOT gate, guarantees the robust fidelity, and relaxes the requirement for its experiment. Meanwhile, this scheme works in a failure-heralded way. Also, we generalize this approach to achieve the self-error-corrected hyperparallel quantum CNOTN gate working on a multiple-photon system. These good features make this scheme more useful in the photonic quantum computation and quantum communication in the future.

Although the origin of quantum optics can be traced back to the beginning of the 20th century, when the fundamental ideas about the quantum nature of the interaction between light and matter were put forward, the splendid blossoming of this part of physics began half a century later, after the invention of masers and lasers. It is remarkable that after another half a century the tree of quantum optics is not only very strong and spreading, but all its branches continue to grow, showing new beautiful blossoms and giving very useful fruits.

The miracle of quantum error correction Correcting errors might sound like a dreary practical problem, of little aesthetic or conceptual interest. But aside from being of crucial importance for the feasibility of quantum computation, it is also one of the most beautiful and surprising parts of the subject. The surprise is that error correction is possible at all, since the only way to detect errors is to make measurements, but measurement gates disruptively alter the states of the measured Qbits, apparently making things even worse. “Quantum error correction” would seem to be an oxymoron. The beauty lies in the ingenious ways that people have found to get around this apparently insuperable obstacle. The discovery in 1995 of quantum error correction by Peter Shor and, independently, Andrew Steane had an enormous impact on the prospects for actual quantum computation. It changed the dream of building a quantum computer capable of useful computation from a clearly unattainable vision to a program that poses an enormous but not necessarily insuperable technological challenge. Error correction is not a major issue for classical computation. In a classical computer the physical systems that embody individual bits – the Cbits – are immense on the atomic scale. The two states of a Cbit representing 0 and 1 are so grossly different that the probability is infinitesimal for flipping from one to the other as a result of thermal fluctuations, mechanical vibrations, or other irrelevant extraneous interactions.