Network-assisted collective operations for efficient distributed quantum computing

Grover’s quantum search algorithm promises a quadratic speedup for unstructured search over its classical counterpart. But this advantage is affected by noise acting on the search space. Here, we show that a quantum switch can act as a resource to mitigate the effects of noise. In this scenario, the noise is modeled by a depolarizing channel, which coherently acts on the entire quantum register. We show that a quantum switch can significantly reduce the error in Grover’s search algorithm. We consider the success probability of finding the marked item as the sole quantifier of diminishing the effect of noise in the search space in the presence of quantum switch. We propose two frameworks for the application of quantum switches. In the first framework, we apply the superposition of channel’s orders in the form of a switch and do a post-selection at every iteration of the applications of the Grover operator. In the second framework, we delay this measurement and post-selection until the very end. The number of post selections is minimal in the second scenario, and hence the noise reduction can be attributed more to the presence of quantum switch. We illustrate with an example of significant advantage in the success probability of Grover’s algorithm using quantum switch.

Quantum teleportation is one of the most basic quantum protocols, which transfers an unknown quantum state from one location to another through local operation and classical communication by using shared quantum entanglement without physical transfer of the information carrier. And it has been widely used in various quantum information protocols such as entanglement swapping, quantum repeaters, quantum gate teleportation, quantum computation based on measurement, and quantum teleportation networks, which have important application value in quantum computation and quantum information. Quantum teleportation is a naturally bipartite process, in which an unknown quantum state can only be transmitted from one node to another. With the further development of quantum information research, it is necessary to transfer quantum states or quantum information among more and more nodes. Multipartite quantum protocols are expected to form fundamental components for larger-scale quantum communication and computation. A bipartite quantum teleportation should be extended to a multipartite protocol known as a quantum teleportation network. In this paper, a multifunctional quantum teleportation network is proposed theoretically. We first propose a special method of constructing four-partite quantum resources in continuous variables (CVs), and based on this, construct two different types of CV quantum teleportation networks. One type of network contains just one quantum teleportation process consisting of a sender, a receiver and two controllers. In this type of network, the unknown quantum state can be recovered at any other node according to the requirement after the measurement in the input node, which enriches the transfer direction and transfer mode of the unknown quantum state. And meanwhile, the two controllers can control the transfer of a quantum state from the sender to the receiver by restricting the sender and receiver’s access to their information, which makes the quantum teleportation network controllable. The other type of network has two quantum teleportation processes, each containing only a sender, a receiver and no controllers, which increases the number of quantum states that can be transmitted. Then we analyze the dependence of the fidelity of each quantum teleportation network on different physical parameters, and compare the characteristics, advantages and disadvantages among different types of quantum teleportation networks. The scheme for constructing a multifunctional quantum teleportation network in this paper shows some advantages, such as the greater number of quantum nodes, diversity of types, simple operation procedure. And all these advantages provide a broader application prospect for establishing larger and more complex quantum information networks in the future and quicken the pace of the application of quantum information.

The development of programming languages for quantum computing has increased rapidly over the last few years, making it practical for a hands-on approach in teaching quantum computation. In this paper, I introduce the standard textbook example of searching for one item out of four using Grover's search algorithm and extend it by including a quantum database. In addition to explaining how to include a quantum database using a quantum circuit model, I give a complete program implementing the algorithm written in the quantum computing language Qiskit from IBM. If presented in the classroom, this extension of Grover's search algorithm alleviates some unsatisfying aspects of the standard textbook example. If given as an exercise to students, it allows them to extend the standard example and provides experience in developing quantum algorithms. I also outline searching for one (or more) items out of eight with a quantum database, which could be used for student projects.

Quantum computing introduces an efficient way for unfolding complex problems on computing systems. It uses concept of superposition and entanglement, & hence supports intrinsic parallelism for obtaining the speedup in context of time over classical computing. Quantum algorithms can be efficiently implemented over quantum computing system. Most popular quantum algorithms like Grover's and Shor's provide a great foundation to specifically design the algorithms. These algorithms work on improving the lower runtime bounds of classical algorithms. Grover's algorithm exhibits a quadratic polynomial speedup while searching an element among ‘N’ elements unstructured database. The algorithmic strategy can be applied over various computer science related applications and some important are being considered in this article i.e. pattern matching, data mining and machine learning. This article explores quantum fundamentals; history based evolution followed by Grover's search algorithm in detail with cascading advantages, limitations & applications and also finally concludes with the significance of quantum computing & quantum algorithmic domains.

Numerous conceptually important quantum algorithms rely on a blackbox device known as an oracle, which is typically difficult to construct without knowing the answer to the problem that the algorithm is intended to solve. A notable example is Grover's search algorithm. Here we propose a Grover search for solutions to a class of NP-complete decision problems known as subset sum problems, including the special case of number partitioning. Each problem instance is encoded in the couplings of a set of qubits to a central spin or boson, which enables a realization of the oracle without knowledge of the solution. The algorithm provides a quantum speedup across a known phase transition in the computational complexity of the partition problem, and we identify signatures of the phase transition in the simulated performance. Whereas the naive implementation of our algorithm requires a spectral resolution that scales exponentially with system size for NP-complete problems, we also present a recursive algorithm that enables scalability. We propose and analyze implementation schemes with cold atoms, including Rydberg-atom and cavity-QED platforms.

A significant amount of study is being done to review the security promises made for the various ciphers now in use as a result of the development of quantum computing technology. A general attack against symmetric key cryptography primitives that can reduce search costs to the square root is Grover's search algorithm. To implement Grover's algorithm, it is necessary that the target cipher be implemented as a quantum circuit. Despite being relatively new, this area of study has received significant attention from the research community. The authors have estimated the cost of Grover's key search attack against the stream cipher Atom, for the first time, under circuit depth restrictions defined in National Institute of Standards and Technology (NIST) PQC standardisation process. The authors implement the quantum circuit of Atom in QISKIT, (open‐source software development kit for working with quantum computers running on IBM Quantum Experience). The results are also compared with other existing literature on LFSR‐based stream ciphers, such as Grain‐v1, Grain‐128‐AEAD, and Lizard. The authors also find that, to the best of their knowledge, in the existing literature on estimating the cost of Grover's attack on symmetric ciphers, Atom is the only 128‐bit key cipher that meets the threshold of ≈2 170 set by NIST for quantum security of 128‐bit key ciphers. The authors also analyse the security of Atom against quantum TMDTO attacks.

We present a simple and general simulation technique that transforms any black-box quantum algorithm (a la Grover's database search algorithm) to a quantum communication protocol for a related problem, in a way that fully exploits the quantum parallelism. This allows us to obtain new positive and negative results. The positive results are novel quantum communication protocols that are built from nontrivial quantum algorithms via this simulation. These protocols, combined with (old and new) classical lower bounds, are shown to provide the first asymptotic separation results between the quantum and classical (probabilistic) two-party communication complexity models. In particular, we obtain a quadratic separation for the bounded-error model, and an exponential separation for the zero-error model. The negative results transform known quantum communication lower bounds to computational lower bounds in the black-box model. In particular, we show that the quadratic speed-up achieved by Grover for the OR function is impossible for the PARITY function or the MAJORITY function in the bounded-error model, nor is it possible for the OR function itself in the exact case. This dichotomy naturally suggests a study of bounded-depth predicates (i.e. those in the polynomial hierarchy) between OR and MAJORITY. We present black-box algorithms that achieve near quadratic speed up for all such predicates.

The exploration of distributed quantum computing (DQC) represents a significant frontier in quantum information science, aiming to harness the unique properties of quantum mechanics to solve complex computational problems effectively. This paper discusses the diverse architectures and models that facilitate the distribution of quantum computing tasks across multiple quantum nodes, thereby addressing the limitations inherent in single quantum devices. DQC systems exploit the principles of superposition and entanglement to enhance computational capabilities beyond what classical computing systems can achieve. We examine various DQC architectures, including both quantum-classical hybrid systems and fully quantum distributed systems, highlighting their respective benefits and challenges. Key issues such as coherence, communication overhead, and error correction are discussed in detail, and we analyze specific use cases where DQC demonstrates superior performance relative to classical computing approaches, including optimization problems in logistics and finance, as well as quantum simulations for material science. Furthermore, we identify future research directions aimed at overcoming existing barriers to the practical implementation of DQC systems. By assessing the current landscape and future possibilities of DQC, this paper underscores the transformative potential of distributed quantum computing in various fields, paving the way for realizing more complex quantum algorithms and applications.

In order to understand the bounds of utilization of the Grover's search algorithm for the large unstructured data in presence of the quantum computer noise, we undertake a series of simulations by inflicting various types of noise, modelled by the IBM QISKit. We apply three forms of Grover's algorithms: (1) the standard one, with 4-10 qubits, (2) recently published modified Grover's algorithm, set to reduce the circuit depth, and (3) the algorithms in (1) and (2) with multi-control Toffoli's modified by addition of an ancilla qubit. Based on these simulations, we find the upper bound of noise for these cases, establish its dependence on the quantum depth of the circuit and provide comparison among them. By extrapolation of the fitted thresholds, we predict what would be the typical gate error bounds when apply the Grover's algorithms for the search of a data in a data set as large as thirty two thousands.

Programming a quantum computer is still a challenge for researchers. Quantum computers operate based on a fundamentally different paradigm from classical computers. Programming a quantum computer today is somewhat like programming a classical computer in the 1950s, in a manner close to assembly language. This paper presents a Grover-assisted compact genetic algorithm to solve some real-world problems on a quantum computer. This method is a combination of Grover's search algorithm initializing with the probability distribution, and a compact genetic algorithm with elite (cGA*), which keeps the current best individual. The compact genetic algorithm (cGA) is a powerful and popular method in evolutionary computation. The results of the proposed algorithm are compared with the cGA running on classical computers in terms of the solution quality and the number of function evaluations. The compared results illustrate that the proposed methodology can successfully reach 100% accuracy of the solution with a higher number of function evaluations than the cGA.

Introduction. Widespread use of unmanned aerial vehicles in the civilian and military spheres requires the development of new algorithms for identification friend or foe of targets, as used in the Armed Forces of Ukraine (AFU) devices of the "Parol" system are designed to service approximately 110 objects military equipment. AFU automation systems allow the use of additional sources of information about various objects from civil or special data transmission networks, which can be the basis for building a networked multi-level system of state recognition. Predictions of the development of quantum computers foresee the possibility of breaking modern algorithms for information security in polynomial time in the next 5-10 years, which requires the development and implementation of new encryption algorithms and revision of modern parameters. The purpose of the article is to develop a new algorithm for state recognition of objects, which can be scaled to process the required number of manned and unmanned aerial vehicles. Potential threats to classical cryptographic protection algorithms for data networks, which will result in the execution of algorithms such as Grover and Shore on quantum computers, were also discussed. Results. The article proposes a new multilevel algorithm of state recognition based on modern cryptographic methods of information protection, which allows to perform reliable automated identification of objects, scale systems using data on potential targets from other sources through secure special networks. Grover's search algorithm does not give a strong increase in key search performance for symmetric encryption algorithms, so there is no need to increase the key lengths for this type of information security algorithms. Post-quantum asymmetric encryption algorithms require additional study and comprehensive testing of information security or increasing the key lengths of cryptographic algorithms, which corresponds to the number of qubits, i.e. more than twice. The most promising is the family of asymmetric post-quantum cryptographic algorithms based on supersingular isogenic elliptic curves. Conclusions. The developed algorithm of identification friend or foe of objects is more secure compared to existing algorithms and is focused on the use of modern on-board computers and programmable radio modems. Shore's algorithm and the like will be a significant threat to modern asymmetric cryptography algorithms when the number of qubits of quantum computers exceeds the number of bits in public keys more than twice. Keywords: identification friend or foe, symmetric encryption, asymmetric cryptography, quantum computer, post-quantum cryptography.

Quantum cooperative search algorithm for 3-SAT

Quantum computing continues to face challenges in scaling both qubit quality and quantity, motivating the shift toward Distributed Quantum Computing (DQC), where multiple interconnected Quantum Processing Units (QPUs) collaboratively solve problems too complex for monolithic systems. In a quantum data center, QPUs distributed across racks can perform remote gate operations by creating entanglement between them, enabling circuit execution through DQC. However, generating end-to-end entangled pairs in a quantum data center often causes congestion and resource contention. To mitigate this, we introduce a resource management framework with efficient schedulers that maximize fidelity-guaranteed throughput while preserving the dependency constraints of sub-circuits derived from the original quantum circuit. We benchmark the scheduling problem using a MixedInteger Linear Programming (MILP) model and then propose a set of lightweight schedulers-Least Resource First (LRF) and its extension, Group LRF (GLRF). These lightweight schedulers provide practical, though less optimal, solutions for handling the high volume of remote gates in DQC workloads. Our initial results on a DCell-based quantum data center show that such heuristics perform well under current DQC conditions, balancing runtime and performance while avoiding the heavy overhead of solvers or machine learning approaches, which often struggle to meet the strict timing demands of short-lived entanglement.

With their ability to process and transfer quantum information, large-scale entanglement-based quantum networks could be at the heart of a new age of quantum information, enabling fundamentally new applications such as distributed quantum computation, quantum communication, and quantum enhanced sensing. Due to their long spin coherence, controllable local qubit registers and optically active spins, color centers in diamond are prime candidates for nodes of such a network, and have enabled some of the most advanced quantum network demonstrations to date. These demonstrations include the distribution of a 3-node GHZ state across a quantum network, entanglement swapping, entanglement distillation, and memory-enhanced quantum communication. To move beyond current proof-of-principle networks, a further increase of entanglement generation rates is crucial. This thesis presents theoretical and experimental work on enhancing the spin-photon interface of color centers in diamond to achieve this goal, making use of the Purcell effect. The discussed work follows two main directions: embedding of color centers in open, tuneable Fabry-Perot micro-cavities, and in all-diamond photonic crystal cavities. First, we describe theoretical and experimental progress towards cavity-enhanced quantum networks based on nitrogen-vacancy (NV) centers in diamond. Due to their first order sensitivity to electric fields, we choose to embed NV centers in microns-thin diamond membranes that can be integrated into open fiber-based micro-cavities. We develop analytical methods to optimize the design of such open cavity systems for maximum Purcell enhancement of embedded color centers. We demonstrate a method to fabricate optically coherent NV centers in microns-thin diamond membranes, and use such structures to demonstrate the resonant excitation and detection of coherent, Purcell enhanced NV emission. A theoretical model in excellent agreement with our results suggests our system can improve entanglement rates between distant NV centers by two orders of magnitude with near-term improvements to the setup. Second, we describe progress towards an efficient spin-photon interface of group-IV color centers in diamond by coupling them to photonic nanostructures, allowing for large-scale integration. Due to their first-order insensitivity to electric fields, group-IV color centers can be brought in close proximity to surfaces (~ 100 nm), allowing for sub-wavelength mode volumes and thus very high Purcell factors. We numerically optimize photonic crystal cavity designs to maximize the Purcell enhancement of embedded emitters, test the robustness of our designs to real-world fabrication imperfections, and devise a method to efficiently interface nanophotonic structures. We then proceed to fabricate all-diamond photonic crystal cavities, making use of a dry etching technique that is selective to different crystallographic directions, and characterize the resulting optical quality factors. Finally, we marry the developed fabrication methods to fabricate microns-sized diamond platelets that can be transferred from a holding frame in a controlled fashion. This capability could be crucial for the realization of hybrid photonic circuits that we expect to be at the heart of future large-scale quantum networks.

We report the realization, using nuclear magnetic resonance techniques, of the first quantum computer that reliably executes a complete algorithm in the presence of strong decoherence. The computer is based on a quantum error avoidance code that protects against a class of multiple-qubit errors. The code stores two decoherence-free logical qubits in four noisy physical qubits. The computer successfully executes Grover's search algorithm in the presence of arbitrarily strong engineered decoherence. A control computer with no decoherence protection consistently fails under the same conditions.