Swap Operation Research Articles

Fidelity of a sequence of SWAP operations on a spin chain

We consider the ``transport'' of the state of a spin across a Heisenberg-coupled spin chain via the use of repeated SWAP gates, starting with one of two states---one in which the leftmost spin is down and the others up, and one in which the leftmost two spins are in a singlet state (i.e., they are entangled), and the others are again all up. More specifically, we ``transport'' the state of the leftmost spin in the first case and the next-to-leftmost spin in the second to the other end of the chain, and then back again. We accomplish our SWAP operations here by increasing the exchange coupling between the two spins that we operate on from a base value $J$ to a larger value $J_\text{SWAP}$ for a time $t=\pi\hbar/4J_\text{SWAP}$. We determine the fidelity of this sequence of operations in a number of situations---one in which only nearest-neighbor coupling exists between spins and there is no magnetic dipole-dipole coupling or noise (the most ideal case), one in which we introduce next-nearest-neighbor coupling, but none of the other effects, and one in which all of these effects are present. In the last case, the noise is assumed to be quasistatic, i.e., the exchange couplings are each drawn from a Gaussian distribution, truncated to only nonnegative values. We plot the fidelity as a function of $J_\text{SWAP}$ to illustrate various effects, namely crosstalk due to coupling to other spins, as well as noise, that are detrimental to our ability to perform a SWAP operation. Our theory should be useful to the ongoing experimental efforts in building semiconductor-based spin quantum computer architectures.

Multi-objective traveling salesman problem: an ABC approach

Using the concept of swap operation and swap sequence on the sequence of paths of a Traveling Salesman Problem(TSP) Artificial Bee Colony (ABC) algorithm is modified to solve multi-objective TSP. The fitness of a solution is determined using a rule following the dominance property of a multi-objective optimization problem. This fitness is used for the selection process of the onlooker bee phase of the algorithm. A set of rules is used to improve the solutions in each phase of the algorithm. Rules are selected according to their performance using the roulette wheel selection process. At the end of each iteration, the parent solution set and the solution sets after each phase of the ABC algorithm are combined to select a new solution set for the next iteration. The combined solution set is divided into different non-dominated fronts and then a new solution set, having cardinality of parent solution set, is selected from the upper-level non-dominated fronts. When some solutions are required to select from a particular front then crowding distances between the solutions of the front are measured and the isolated solutions are selected for the preservation of diversity. Different standard performance metrics are used to test the performance of the proposed approach. Different sizes standard benchmark test problems from TSPLIB are used for the purpose. Test results show that the proposed approach is efficient enough to solve multi-objective TSP.

Quantum-inspired Fredkin gate based on spatial modes of light.

Insights gained from quantum physics can inspire novel classical technologies. These quantum-inspired technologies are protocols that aim at mimicking particular features of quantum algorithms. They are generally easier to implement and make use of intense beams. Here we demonstrate in a proof-of-concept experiment a quantum-inspired protocol based on the idea of quantum fingerprinting (Phys. Rev. Lett. 87, 167902, 2001).The carriers of information are optical beams with orbital angular momentum (OAM). These beams allow the implementation of a Fredkin gate or polarization-controlled SWAP operation that exchanges data encoded on beams with different OAM. We measure the degree of similarity between waveforms and strings of bits without unveiling the information content of the data.

Continuous-variable quantum repeater based on quantum scissors and mode multiplexing

Quantum repeaters are indispensable for high-rate, long-distance quantum communications. The vision of a future quantum internet strongly hinges on realizing quantum repeaters in practice. Numerous repeaters have been proposed for discrete-variable (DV) single-photon-based quantum communications. Continuous variable (CV) encodings over the quadrature degrees of freedom of the electromagnetic field mode offer an attractive alternative. For example, CV transmission systems are easier to integrate with existing optical telecom systems compared to their DV counterparts. Yet, repeaters for CV have remained elusive. We present a novel quantum repeater scheme for CV entanglement distribution over a lossy bosonic channel that beats the direct transmission exponential rate-loss tradeoff. The scheme involves repeater nodes consisting of a) two-mode squeezed vacuum (TMSV) CV entanglement sources, b) the quantum scissors operation to perform nondeterministic noiseless linear amplification of lossy TMSV states, c) a layer of switched, mode multiplexing inspired by second-generation DV repeaters, which is the key ingredient apart from probabilistic entanglement purification that makes DV repeaters work, and d) a non-Gaussian entanglement swap operation. We report our exact results on the rate-loss envelope achieved by the scheme.

A Dynamic Look-Ahead Heuristic for the Qubit Mapping Problem of NISQ Computers

In the past few years, several quantum computers realized by the noisy intermediate-scale quantum (NISQ) technology have been released. However, there exists a significant limitation to using such computers, i.e., the connectivity constraint between physical qubits. To perform a 2-qubit quantum operation on such NISQ computers, its two logical qubits have to be mapped to a pair of physical qubits that satisfy the connectivity constraint. This mapping procedure requires additional operations to be introduced into the original quantum circuit, reducing its fidelity. Therefore, it is of great significance to design an algorithm that is able to complete the mapping task with minimal additional operations. In this article, we propose an efficient algorithm to solve this problem. Our algorithm consists of two core components, an expansion-from-center scheme to determine the initial mapping and a SWAP-based heuristic search algorithm to update the mapping. We introduce the maximum consecutive positive effect of a SWAP operation as the heuristic cost function, allowing our search algorithm to look ahead dynamically. Our algorithm is evaluated on IBM Q 20. The experimental results show that our algorithm can complete the mapping task in a very short time even for large-scale benchmarks with hundreds of thousands of operations, and outperforms the state-of-the-art in terms of the number of additional operations for most benchmarks considered.

One-shot quantum state exchange

The quantum state exchange is a quantum communication task in which two users exchange their respective quantum information in the asymptotic setting. In this work, we consider a one-shot version of the quantum state exchange task, in which the users hold a single copy of the initial state, and they exchange their parts of the initial state by means of entanglement-assisted local operations and classical communication. We first derive lower bounds on the least amount of entanglement required for carrying out this task, and provide conditions on the initial state such that the protocol succeeds with zero entanglement cost. Based on these results, we reveal two counter-intuitive phenomena in this task, which make it different from a conventional SWAP operation. One tells how the users deal with their symmetric information in order to reduce the entanglement cost. The other shows that it is possible for the users to gain extra shared entanglement after this task.

A Hybrid PSO-GA Algorithm for Traveling Salesman Problems in Different Environments

In this study particle swarm optimization (PSO) is modified and hybridised with genetic algorithm (GA) using one’s output as the other's input to solve Traveling Salesman Problem(TSP). Here multiple velocity update rules are introduced to modify the PSO and at the time of the movement of a solution, one rule is selected depending on its performances using roulette wheel selection process. Each velocity update rule and the corresponding solution update rule are defined using swap sequence (SS) and swap operation (SO). K-Opt operation is applied in a regular interval of iterations for the movement of any stagnant solution. GA is applied on the final output swarm of the PSO to search the optimal path of the large size TSPs. Roulette wheel selection process, multi-point cyclic crossover and the K-opt operation for the mutation are used in the GA phase. The algorithm is tested in crisp environment using different size benchmark test problems available in the TSPLIB. In the crisp environment the algorithm gives approximately 100% success rate for the test problems up to considerably large sizes. Efficiency of the algorithm is tested with some other existing algorithms in the literature using Friedman test. Some approaches are incorporated with this algorithm for finding solutions of the TSPs in imprecise (fuzzy/rough) environment. Imprecise problems are generated from the crisp problems randomly, solved and obtained results are discussed. It is observed that the performance of the proposed algorithm is better compared to the some other algorithms in the existing literature with respect to the accuracy and the consistency for the symmetric TSPs as well as the Asymmetric TSPs.

HIZ DEĞİŞTİRME FAALİYETLİ TEK MAKİNELİ ÇİZELGELEME PROBLEMİ İÇİN EN KISA YOL TABANLI BİR ÇÖZÜM YÖNTEMİ

In this study, scheduling of jobs and a rate modifying activity (RMA) on a single machine system is considered. A RMA is defined as a maintenance activity applied to bring production speed of the machine back to its original state. From this point of view, when a job is planned before or after the RMA, processing times of the jobs become different. The problem addressed is determination of the job sequence and the position of the RMA in this sequence. A shortest path-based method which is based on network representation is developed for the solution. In the proposed method, a network is created in the first step according to the job sequence obtained by the Shortest Processing Time algorithm. RMA assignment that gives the shortest path on the network is then searched using linear programming and the value of the found path gives total completion time for the machine. After this, using local search procedure, swap operation (binary exchange) is applied on the job positions at each step and final solution is obtained as a result of continuous comparisons on new solutions obtained.

Energy and Migration Cost-Aware Dynamic Virtual Machine Consolidation in Heterogeneous Cloud Datacenters

Energy efficiency has become one of the major concerns for today's cloud datacenters. Dynamic virtual machine (VM) consolidation is a promising approach for improving the resource utilization and energy efficiency of datacenters. However, the live migration technology that VM consolidation relies on is costly in itself, and this migration cost is usually heterogeneous as well as the datacenter. This paper investigates the following bi-objective optimization problem: how to pay limited migration costs to save as much energy as possible via dynamic VM consolidation in a heterogeneous cloud datacenter. To capture these two conflicting objectives, a consolidation score function is designed for an overall evaluation on the basis of a migration cost estimation method and an upper bound estimation method for maximal saved power. To optimize the consolidation score, a greedy heuristic and a swap operation are introduced, and an improved grouping genetic algorithm (IGGA) based on them is proposed. Lastly, empirical studies are performed, and the evaluation results show that IGGA outperforms existing VM consolidation methods.

Simulation of the early stage water flooding through an opening using boundary element method

When an underwater collision or explosion happens to a ship, the water will rush into the cabin through the broken opening. The water spike induced by hydrostatic pressure has the potential to destroy the facilities and structures inside the cabin, and the water flooding may threat the vitality of ship. Dynamic characteristics of this water spike during early flooding process is studied by a three-dimensional fast multipole boundary element method (FMBEM) based on the potential theory, in this article. The edge swap operation is elaborated and adopted, to eliminate the slender elements at the air-water interface, which helps us study the evolution of the inrush water and maintains the computational efficiency. The numerical model is validated by experimental data and the result from the finite volume method. The flooding process can be divided into the developing flow stage and the stable flow stage. The flow rate increases gradually during the former stage and reaches a constant value in the latter one. Through parametric study, we find that the water flooded through the opening earlier is subjected to the gravity for longer time and achieves larger velocity, which results in a slender water spike. When the opening gets deeper, the developing flow stage becomes shorter and the flow rate increases; whilst the increasing speed slows down with the growing depth. It is the area of the opening rather than the shape, that influences the flow rate and flooding velocity, and the maximum velocity in the horizontal direction appears at the transition time between the two stages. This study reveals that the water flooding spike has complex and non-linear dynamic behaviour, and helps lay the foundation of studying the interaction between high-speed water jet and the structures. It also shows that the FMBEM is suitable for dealing with the large scale moving boundary problems efficiently and accurately.

Implementation of SWAP test for two unknown states in photons via cross-Kerr nonlinearities under decoherence effect

We present an optical scheme for a SWAP test (controlled swap operation) that can determine whether the difference between two unknown states (photons) using cross-Kerr nonlinearities (XKNLs). The SWAP test, based on quantum fingerprinting, has been widely applied to various quantum information processing (QIP) schemes. Thus, for a reliable QIP scheme, it is important to implement a scheme for a SWAP test that is experimentally feasible. Here, we utilize linearly and nonlinearly optical (XKNLs) gates to design a scheme for a SWAP test. We also analyze the efficiency and the performance of nonlinearly optical gates in our scheme under the decoherence effect and exhibit a technique employing quantum bus beams and photon-number-resolving measurements to reduce the effect of photon loss and dephasing caused by the decoherence effect. Consequently, our scheme, which is designed using linearly optical devices and XKNLs (nonlinear optics), can feasibly operate the nearly deterministic SWAP test with high efficiency, in practice.

Optimization of University Course Scheduling Problem using Particle Swarm Optimization with Selective Search

The University Course Scheduling Problem (UCSP) is a highly constrained real-world combinatorial optimization task. Solving UCSP means creating an optimal course schedule by assigning courses to specific rooms, instructors, students, and timeslots by taking into account the given constraints. Several studies have reported different metaheuristic approaches for solving UCSP including Genetic Algorithm (GA) and Harmony Search (HS) algorithm. Various Swarm Intelligence (SI) optimization methods have also been investigated for UCSP in recent times and a few Particle Swarm Optimization (PSO) based methods among them with different adaptations are shown to be effective. In this study, a novel PSO-based method is investigated for solving highly constrained UCSP in which basic PSO operations are transformed to tackle combinatorial optimization task of UCSP and a few new operations are introduced to PSO to solve UCSP efficiently. In the proposed method, swap sequence-based velocity computation and its application are developed to transform individual particles in order to improve them. Selective search and forceful swap operation with repair mechanism are the additional new operations in the proposed method for updating particles with calculated swap sequences as velocities. The proposed PSO with selective search (PSOSS) method has been tested on an instance of UCSP for the Computer Science and Engineering Department of Khulna University of Engineering & Technology which has many hard and soft constraints. Experimental results revealed the effectiveness and the superiority of the proposed method compared to other prominent metaheuristic methods (e.g., GA, HS).

Extended quantum Maxwell demon acting over macroscopic distances

A quantum Maxwell demon is a device that can lower the entropy of a quantum system by providing it with purity. The functionality of such a quantum demon is rooted in a quantum mechanical SWAP operation exchanging mixed and pure states. We describe the setup and performance of a quantum Maxwell demon that purifies an energy-isolated system from a distance. Our cQED-based design involves two transmon qubits, where the mixed-state target qubit is purified by a pure-state demon qubit connected via an off-resonant transmission line; this configuration naturally generates an iSWAP gate. Although less powerful than a full SWAP gate, we show that assuming present-day performance characteristics of a cQED implementation, such an extended quantum Maxwell demon can purify the target qubit over macroscopic distances on the order of meters and tolerates elevated temperatures of the order of a few Kelvin in the transmission line.

A passive photon–atom qubit swap operation

Deterministic quantum interactions between single photons and single quantum emitters are a vital building block towards the distribution of quantum information between remote systems1–4. Deterministic photon–atom state transfer has previously been demonstrated with protocols that include active feedback or synchronized control pulses5–10. Here we demonstrate a passive swap operation between the states of a single photon and a single atom. The underlying mechanism is single-photon Raman interaction11–15—an interference-based scheme that leads to deterministic interaction between two photonic modes and the two ground states of a Λ-system. Using a nanofibre-coupled microsphere resonator coupled to single Rb atoms, we swap a photonic qubit into the atom and back, demonstrating fidelities exceeding the classical threshold of 2/3 in both directions. In this simultaneous write and read process, the returning photon, which carries the readout of the atomic qubit, also heralds the successful arrival of the write photon. Requiring no control fields, this single-step gate takes place automatically at the timescale of the atom’s cavity-enhanced spontaneous emission. Applicable to any waveguide-coupled Λ-system, this mechanism, which can also be harnessed to construct universal gates16,17, provides a versatile building block for the modular scaling up of quantum information systems. Demonstration of a passive swap gate between the states of a fibre-guided photonic qubit and a single atom.

A Pareto firefly algorithm for multi-objective disassembly line balancing problems with hazard evaluation

The safety hazards existing in the process of disassembling waste products pose potential harms to the physical and mental health of the workers. In this article, these hazards involved in the disassembly operations are evaluated and taken into consideration in a disassembly line balancing problem. A multi-objective mathematical model is constructed to minimise the number of workstations, maximise the smoothing rate and minimise the average maximum hazard involved in the disassembly line. Subsequently, a Pareto firefly algorithm is proposed to solve the problem. The random key encoding method based on the smallest position rule is used to adapt the firefly algorithm to tackle the discrete optimisation problem of the disassembly line balancing. To avoid the search being trapped in a local optimum, a random perturbation strategy based on a swap operation is performed on the non-inferior solutions. The validity of the proposed algorithm is tested by comparing with two other algorithms in the existing literature using a 25-task phone disassembly case. Finally, the proposed algorithm is applied to solve a refrigerator disassembly line problem based on the field investigation and a comparison of the proposed Pareto firefly algorithm with another multi-objective firefly algorithm in the existing literature is performed to further identify the superior performance of the proposed Pareto firefly algorithm, and eight Pareto optimal solutions are obtained for decision makers to make a decision.

Experimental realization of SWAP operation on hyper-encoded qubits.

Hyper-encoding enables storing several qubits in a single photon using its different degrees of freedom like polarization and spatial ones. This approach enables feasible implementation of multi-qubit operations. One of the basic manipulations of two or more qubits is to swap their quantum state. Here we report on feasible and stable experimental implementation of a deterministic single photon two-qubit SWAP gate that interchanges path and polarization qubits. We discuss the principle of its operation and give detailed information about experimental demonstration employing two Mach-Zehnder interferometers with one common arm. The gate characterization is done by full quantum process tomography using photons produced by heralded single-photon source. The achieved quantum process fidelity reached more than 0.94 with an effective phase uncertainty of the whole setup, evaluated by means of Allan deviation, below 2.5 deg for 2.5 h without any active stabilization. Our design provides a contribution to the hyper-encoded linear quantum optics toolbox.

Conditional quantum entropy power inequality for d-level quantum systems

We propose an extension of the quantum entropy power inequality for finite dimensional quantum systems, and prove a conditional quantum entropy power inequality by using the majorization relation as well as the concavity of entropic functions also given by Audenaert et al (2016 J. Math. Phys. 57 052202). Here, we make particular use of the fact that a specific local measurement after a partial swap operation (or partial swap quantum channel) acting only on finite dimensional bipartite subsystems does not affect the majorization relation for the conditional output states when a separable ancillary subsystem is involved. We expect our conditional quantum entropy power inequality to be useful, and applicable in bounding and analyzing several capacity problems for quantum channels.

Empirical Analysis of a Quantum Classifier Implemented on IBM’s 5Q Quantum Computer

The development of artificial intelligence today is marked with increased computational power, new algorithms, and big data. One such milestone impressive achievement in this area is Google’s AlphaGo. However, this advancement is beginning to face increasing challenges and the major bottleneck of AI today is the lack of adequate computing power in the processing of big data. Quantum computing offers a new and viable solution to deal with these challenges. A recent work designed a quantum classifier that runs on IBM’s five qubit quantum computer and tested its performance on the Iris data set as well as a circles data set. As quantum machine learning is still an emerging discipline, it may be enlightening to conduct an empirical analysis of this quantum classifier on some artificial datasets to help learn its unique features and potentials. Our work on the quantum classifier can be summarized in three parts. The first is to run its original version as a binary classifier on some artificial datasets using visualization to reveal the quantum nature of this algorithm, and the second is to analyze the swap operation utilized in its original circuit due to the hardware constraint and investigate its impact on the performance of the classifier. The last part is to extend the original circuit for binary classification to a circuit for multiclass classification and test its performance. Our findings shed new light on how this quantum classifier works.

Quantum Watermarking Scheme Based on INEQR

Quantum watermarking technology protects copyright by embedding invisible quantum signal in quantum multimedia data. In this paper, a watermarking scheme based on INEQR was presented. Firstly, the watermark image is extended to achieve the requirement of embedding carrier image. Secondly, the swap and XOR operation is used on the processed pixels. Since there is only one bit per pixel, XOR operation can achieve the effect of simple encryption. Thirdly, both the watermark image extraction and embedding operations are described, where the key image, swap operation and LSB algorithm are used. When the embedding is made, the binary image key is changed. It means that the watermark has been embedded. Of course, if the watermark image is extracted, the key’s state need detected. When key’s state is |1〉, this extraction operation is carried out. Finally, for validation of the proposed scheme, both the Signal-to-noise ratio (PSNR) and the security of the scheme are analyzed.

Quantum interface between a transmon qubit and spins of nitrogen-vacancy centers

Hybrid quantum circuits combining advantages of each individual system have provided a promising platform for quantum information processing. Here we propose an experimental scheme to directly couple a transmon qubit to an individual spin in the nitrogen-vacancy (NV) center, with a coupling strength three orders of magnitude larger than that for a single spin coupled to a microwave cavity. This direct coupling between the transmon and the NV center could be utilized to make a transmon bus, leading to a coherently virtual exchange among different single spins. Furthermore, we demonstrate that, by coupling a transmon to a low-density NV ensemble, a SWAP operation between the transmon and NV ensemble is feasible and a quantum non-demolition measurement on the state of NV ensemble can be realized on the cavity-transmon-NV-ensemble hybrid system. Moreover, on this system, a virtual coupling can be achieved between the cavity and NV ensemble, which is much larger in magnitude than the direct coupling between the cavity and the NV ensemble. The photon state in cavity can be thus stored into NV spins more efficiently through this virtual coupling.