Rotation Gate Research Articles

Creation of qutrit and one-qubit gates in atom–cavity–laser systems by adiabatic passage

We derive an adiabatic technique that implements arbitrary qutrit and one-qubit rotation gates in a quantum system composed of two tripod atoms each of which interacting with two laser pulses and a cavity field. In this method, the atomic ground states playing the role of the qutrit and qubit subspace and losses due to atomic spontaneous emissions and the cavity decay are efficiently suppressed by employing adiabatic passage technique. In order to create qutrit gates, we exploit generalized quantum Householder reflection in which each Householder reflection is implemented by two-step adiabatic passage technique in a seven-state system with two dark states. With a similar method, an arbitrary rotation gate is constructed in this system. We also implement the Fourier transform in a qutrit as an example.

Subpicosecond X rotations of atomic clock states

We demonstrate subpicosecond-timescale population transfer between the pair of hyperfine ground states of atomic rubidium using a single laser-pulse. Our scheme utilizes the geometric and dynamic phases induced during Rabi oscillation through the fine-structure excited state to construct an $X$ rotation gate for the hyperfine-state qubit system. The experiment performed with a femtosecond laser and cold rubidium atoms, in a magnetooptical trap, shows over 98% maximal population transfer between the clock states.

Quantum rotation gate in quantum-inspired evolutionary algorithm: A review, analysis and comparison study

Abstract Quantum-inspired Evolutionary Algorithm (QEA) is a kind of intelligent algorithm which widely and effectively used in many fields. In QEA, the basic and common operations usually include quantum chromosome observation and quantum gate update. Quantum rotation gate (QRG) is the most commonly used operator for the operation of quantum gate update, which has a significant influence on the performance of QEA. Many kinds of QRGs have been proposed with different methods to set the only parameter of QRG, i.e., rotation angle. In this paper, a study on classification of QRG is first conducted with respect to rotation direction and magnitude of rotation angle by analyzing and summarizing various kinds of QRGs in literature, and then the corresponding definitions, descriptions and analyses are presented. Furthermore, in order to investigate and compare performances of different QRGs, we set 21 kinds of QRG schemes based on the classification of rotation direction and magnitude of rotation angle. Four typical complex function optimization problems and a 0–1 knapsack problem are selected as experiment objects to test the 21 kinds of schemes. Comprehensive processing and analyzing for the experiment data are conducted, which draws some valuable conclusions for the more reasonable and more effective applications of QEA.

Improved quantum bacterial foraging algorithm for tuning parameters of fractional-order PID controller

The quantum bacterial foraging optimization (QBFO) algorithm has the characteristics of strong robustness and global searching ability. In the classical QBFO algorithm, the rotation angle updated by the rotation gate is discrete and constant, which cannot affect the situation of the solution space and limit the diversity of bacterial population. In this paper, an improved QBFO (IQBFO) algorithm is proposed, which can adaptively make the quantum rotation angle continuously updated and enhance the global search ability. In the initialization process, the modified probability of the optimal rotation angle is introduced to avoid the existence of invariant solutions. The modified operator of probability amplitude is adopted to further increase the population diversity. The tests based on benchmark functions verify the effectiveness of the proposed algorithm. Moreover, compared with the integer-order PID controller, the fractional-order proportion integration differentiation (PID) controller increases the complexity of the system with better flexibility and robustness. Thus the fractional-order PID controller is applied to the servo system. The tuning results of PID parameters of the fractional-order servo system show that the proposed algorithm has a good performance in tuning the PID parameters of the fractional-order servo system.

A Modified Quantum Bacterial Foraging Algorithm for Parameters Identification of Fractional-Order System

For many physical systems, the fractional-order system can describe the dynamics more accurately comparing with the integer-order system. However, its parameters, which include not only the identification of model coefficients but also the estimation of fractional orders, are more difficult to be identified. This paper proposes a modified quantum bacterial foraging algorithm (MQBFA) for parameters identification of the fractional-order system, and the MQBFA algorithm is a relatively new issue in recent years with strong engineering backgrounds. Not only does the proposed MQBFA algorithm apply the real number encoding of the single gene to effectively perform encoding, but it also utilizes a continuously varying rotation angle to update the rotation gate. First, a real number encoding of the single gene is designed to improve the searching efficiency of the algorithm. Second, an improved quantum rotation angle is applied to update the rotation angle continuously and adaptively. Third, the modificatory factor of probability amplitude is introduced to enrich the population diversity. In addition, to prevent the generation of invariant solutions in the early stage of quantum evolution, probability of optimal rotation angle is presented. Furthermore, the convergence of the proposed algorithm is analyzed. Based on several benchmark functions and parameters identification of the fractional-order system, simulation results and comparisons demonstrate the effectiveness of the proposed MQBFA algorithm.

A Multi-Objective Quantum-Inspired Genetic Algorithm (Mo-QIGA) for Real-Time Tasks Scheduling in Multiprocessor Environment

This paper aims at providing a multi-objective real-time scheduling algorithm suitable for scheduling of real-time tasks in multiprocessor system with multi-objective criteria. In this proposed Mo-QIGA, scheduling of multi-objective realtime tasks have been targeted for minimizing completion time and total tardiness of each real-time task simultaneously. The exploration of quantum computation in the suggested Mo-QIGA mimics the principles and basic concepts of quantum mechanics. Variable length chromosomes are used in Mo-QIGA and in order to exhibit full Hilbert hyperspace, qubits representation is preferred. In addition, Quantum rotation gate is employed to update the schedules and it obviates classical genetic operators. In order to obtain Pareto-optimal solutions, a random key distribution has been adopted to convert the qubits particles to valid schedule solutions. Moreover, permutation based trimming technique has been introduced for population diversification which leads to good quality schedules. The experiments have been carried out using number of processors varying with real-time tasks priority and processing time. It has been found that the suggested multi-objective quantum inspired genetic algorithm outperforms its classical counterpart in terms of scheduling accuracy and time in multi-objective sense.

Fuel Loading Pattern Optimization with Constraint on Fuel Assembly Inventory Using Quantum-Inspired Evolutionary Algorithm

Nuclear fuel management was done by optimizing fuel loading pattern in a reactor core. Practically, performing fuel loading pattern optimization was difficult because of its combinatorial problem complexity which needed to be solved. Therefore, Quantum-inspired Evolutionary Algorithm (QEA) which could solve the combinatorial problem faster than conventional method was used. The main purpose of this research was to obtain an optimum fuel loading pattern of KSNP-1000 reactor core without altering fuel assembly inventories. KSNP-1000 core was modeled in SRAC code package using PIJ module for fuel pins and fuel assemblies’ lattices and CITATION module for fuel assemblies’ pattern in a quarter core symmetry. Optimization problem adaptation using QEA was made by presenting 52 fuel assemblies in Q-bit individuals with the length of 8 Q-bits. Q-bits were converted to corresponding bit values and then given weight which would be used as consideration to optimize the pattern. The optimization program was coupled with the SRAC neutronic code to obtain the values of effective multiplication factor (keff) and power peaking factor (PPF). The optimization was calculated based on fitness value which was a function of keff and PPF values with the particular weight factor. Using a rotation gate angle of Δθ=0.02π and a weight factor of w=0,041, fuel loading pattern optimization was done on 360 days burnup level. The optimization resulted in keff and PPF value of 1.11233 and 1.944 respectively. By calculating keff value on various burnup levels for the chosen core loading pattern, reactor cycle length obtained was 659 days with PPF at BOC was 2.19. Compared to the standard KSNP-1000 core which had 560 days of cycle length, the optimized core configuration increased 17.67% in cycle length.

Units of rotational information

Entanglement in angular momentum degrees of freedom is a precious resource for quantum metrology and control. Here we study the conversions of this resource, focusing on Bell pairs of spin-J particles, where one particle is used to probe unknown rotations and the other particle is used as reference. When a large number of pairs are given, we show that every rotated spin-J Bell state can be reversibly converted into an equivalent number of rotated spin one-half Bell states, at a rate determined by the quantum Fisher information. This result provides the foundation for the definition of an elementary unit of information about rotations in space, which we call the Cartesian refbit. In the finite copy scenario, we design machines that approximately break down Bell states of higher spins into Cartesian refbits, as well as machines that approximately implement the inverse process. In addition, we establish a quantitative link between the conversion of Bell states and the simulation of unitary gates, showing that the fidelity of probabilistic state conversion provides upper and lower bounds on the fidelity of deterministic gate simulation. The result holds not only for rotation gates, but also to all sets of gates that form finite-dimensional representations of compact groups. For rotation gates, we show how rotations on a system of given spin can simulate rotations on a system of different spin.

Improved Shuffled Frog Leaping Algorithm Based on Quantum Rotation Gates

Aiming at the search speed and accuracy of the shuffled frog leaping algorithm not high, the idea of variation was integrated into the shuffled frog leaping algorithm. A new improved shuffled frog leaping algorithm was proposed which was called quantum frog leaping algorithm. The positions of frog are encoded by the probability amplitudes of quantum bits, the movements of frog are performed by quantum rotation gates, which achieve particles searching. Through the experiments on six standard functions, simulation results show the proposed algorithm has high searching efficiency and precision, Moreover, QSFLA as a promising optimization algorithm has strong convergence and high stability.

Convergence properties of quantum evolutionary algorithms on high dimension problems

Abstract We propose and investigate new rotation gates for two modified Quantum Inspired Evolutionary methods for solving high dimension optimisation problems. The Quantum Inspired Evolutionary Algorithms (QIEA) were originally used for solving binary encoded problems and their signature features follow superposition of multiple states on a quantum bit and a rotation gate. In order to apply this paradigm to high dimension problems, we propose two quantum methods Half Significant Bit (HSB) and Stepwise Real QEA (SRQEA), developed using binary and real encoding, respectively, while keeping close to the original quantum computing metaphor. We introduce five performance metrics and use them to evaluate the proposed approaches against sets of multimodal mathematical test functions and real world problems of high dimensionality. We report issues found while implementing some of the published real QIEA techniques which were the motivation for developing our real algorithm modifications. Our methods focus on introducing and implementing new rotation gate operators used for evolution, including a novel mechanism for preventing premature convergence in the binary algorithm. The applied performance metrics show superior results for our quantum methods on most of the test problems (particularly with high dimension problems), demonstrating faster convergence and accuracy.

Meta-heuristic framework: Quantum inspired binary grey wolf optimizer for unit commitment problem

This paper proposes a quantum inspired binary grey wolf optimizer (QI-BGWO) to solve unit commitment (UC) problem. The QI-BGWO integrates quantum computing concepts with BGWO to improve the hunting process of the wolf pack. The inherent properties of Q-bit and Q-gate concepts in quantum computing help in achieving better balance between exploration and exploitation properties of the search process. The position update processes of wolves at different hierarchy levels are replaced by Q-bit's individual probabilistic representation along with dynamic rotation angle and coordinate rotation gate. Therefore, solution approaches exploit the search properties of GWO and quantum computing using quantum bits, gates, superposition principle etc., to solve the unit commitment schedule efficiently. The results and statistical analysis demonstrates the effectiveness of proposed approaches in solving the UC problem and establishes the significance of proposed approaches among existing binary and quantum computing based heuristic approaches.

A Terahertz Controlled‐NOT Gate Based on Asymmetric Rotation of Polarization in Chiral Metamaterials

Logical operation based on polarization encoding of light is important for future data transmission and information processing. However, in the terahertz (THz) region, chiral materials with large optical activity are not available in nature, and the effective manipulation of polarization states remains challenging. Here, the authors demonstrate a double‐layer bi‐anisotropic metamaterial that consists of planar spiral and cut‐wire layers separated by a polyimide film. Strong asymmetric polarization rotation of two orthogonal linear polarizations can be observed around 0.53 THz. By investigating the correlation between two linear polarization states before and after the spiral‐wire metamaterial at this frequency, a controlled‐NOT (CNOT) gate operating on two linear‐polarization‐based qubits is further exploited. The processing mechanism of the asymmetric rotation and CNOT gate is attributed to the scattering of dipole momentum based on classical multipole theory. This polarization processor's architecture is promising for robust and energy‐efficient THz polarization control, and also provides an effective path for the development of future optical supercomputing technology.

An improved quantum watermarking scheme using small-scale quantum circuits and color scrambling

In order to solve the problem of embedding the watermark into the quantum color image, in this paper, an improved scheme of using small-scale quantum circuits and color scrambling is proposed. Both color carrier image and color watermark image are represented using novel enhanced quantum representation. The image sizes for carrier and watermark are assumed to be $$2^{n+1}\times 2^{n+2}$$2n+1×2n+2 and $$2^{n}\times 2^{n}$$2n×2n, respectively. At first, the color of pixels in watermark image is scrambled using the controlled rotation gates, and then, the scrambled watermark with $$2^n\times 2^n$$2n×2n image size and 24-qubit gray scale is expanded to an image with $$2^{n+1}\times 2^{n+2}$$2n+1×2n+2 image size and 3-qubit gray scale. Finally, the expanded watermark image is embedded into the carrier image by the controlled-NOT gates. The extraction of watermark is the reverse process of embedding it into carrier image, which is achieved by applying operations in the reverse order. Simulation-based experimental results show that the proposed scheme is superior to other similar algorithms in terms of three items, visual quality, scrambling effect of watermark image, and noise resistibility.

Optimal length of decomposition sequences composed of imperfect gates

Quantum error correcting circuitry is both a resource for correcting errors and a source for generating errors. A balance has to be struck between these two aspects. Perfect quantum gates do not exist in nature. Therefore, it is important to investigate how flaws in the quantum hardware affect quantum computing performance. We do this in two steps. First, in the presence of realistic, faulty quantum hardware, we establish how quantum error correction circuitry achieves reduction in the extent of quantum information corruption. Then, we investigate fault-tolerant gate sequence techniques that result in an approximate phase rotation gate, and establish the existence of an optimal length $$L_{\text {opt}}$$Lopt of the length L of the decomposition sequence. The existence of $$L_{\text {opt}}$$Lopt is due to the competition between the increase in gate accuracy with increasing L, but the decrease in gate performance due to the diffusive proliferation of gate errors due to faulty basis gates. We present an analytical formula for the gate fidelity as a function of L that is in satisfactory agreement with the results of our simulations and allows the determination of $$L_{\text {opt}}$$Lopt via the solution of a transcendental equation. Our result is universally applicable since gate sequence approximations also play an important role, e.g., in atomic and molecular physics and in nuclear magnetic resonance.

A Simple Encryption Algorithm for Quantum Color Image

In this paper, a simple encryption scheme for quantum color image is proposed. Firstly, a color image is transformed into a quantum superposition state by employing NEQR (novel enhanced quantum representation), where the R,G,B values of every pixel in a 24-bit RGB true color image are represented by 24 single-qubit basic states, and each value has 8 qubits. Then, these 24 qubits are respectively transformed from a basic state into a balanced superposition state by employed the controlled rotation gates. At this time, the gray-scale values of R, G, B of every pixel are in a balanced superposition of 224 multi-qubits basic states. After measuring, the whole image is an uniform white noise, which does not provide any information. Decryption is the reverse process of encryption. The experimental results on the classical computer show that the proposed encryption scheme has better security.

Quantum-Inspired Immune Clonal Algorithm for solving large-scale capacitated arc routing problems

In this paper, we present an approach to Large-Scale CARP called Quantum-Inspired Immune Clonal Algorithm (QICA-CARP). This algorithm combines the feature of artificial immune system and quantum computation ground on the qubit and the quantum superposition. We call an antibody of population quantum bit encoding, in QICA-CARP. For this encoding, to control the population with a high probability evolution towards a good schema we use the information on the current optimal antibody. The mutation strategy of quantum rotation gate accelerates the convergence of the original clone operator. Moreover, quantum crossover operator enhances the exchange of information and increases the diversity of the population. Furthermore, it avoids falling into local optimum. We also use the repair operator to amend the infeasible solutions to ensure the diversity of solutions. This makes QICA-CARP approximating the optimal solution. We demonstrate the effectiveness of our approach by a set of experiments and by Comparing the results of our approach with ones obtained with the RDG-MAENS and RAM using different test sets. Experimental results show that QICA-CARP outperforms other algorithms in terms of convergence rate and the quality of the obtained solutions. Especially, QICA-CARP converges to a better lower bound at a faster rate illustrating that it is suitable for solving large-scale CARP.

An improved Hybrid Quantum-Inspired Genetic Algorithm (HQIGA) for scheduling of real-time task in multiprocessor system

This article concerns an efficient real-time task scheduling assisted by Hybrid Quantum-Inspired Genetic Algorithm (HQIGA) in multiprocessor environment. Relying on concepts and the principles of quantum mechanics, HQIGA explores the computing power of quantum computation. To drive schedule toward better convergence, HQIGA operates using rotation gate for exploration of variable chromosomes described by qubits in Hilbert hyperspace. A fitness function associated with popularly known heuristic earliest deadline first (EDF) is employed and random key distribution is adopted to convert the qubits chromosomes to valid schedule solutions. In addition to this, permutation based trimming technique is applied to diversify the population which yields good quality schedules. To establish the effectiveness of the suggested HQIGA, it demonstrates using various number of real-time tasks and processors along with arbitrary processing time. Simulation result shows that HQIGA outperforms the classical genetic algorithm (CGA) and Hybrid Particle Swarm Optimization (HPSO) in terms of fitness values obtained using less number of generations and also it improves the scheduling time significantly. HQIGA is also tested separately with the heuristic Shortest Computation Time First (SCTF) technique to show the superiority of EDF over SCTF.

A quantum encoding bat algorithm for uninhabited combat aerial vehicle path planning

Uninhabited combat aerial vehicle (UCAV) path planning aims to obtain an optimal or near-optimal flight path considering the different kinds of threats and constraints in the combat field. This paper proposes a novel quantum encoding bat algorithm (QBA) for solving the path planning of UCAV. Using quantum rotation and quantum NOT gate are implemented to change the basic qubit states and to enhance global search capability. The QBA can find a feasible and global path for the UCAV to avoid the threats and constraints. The experimental results show that the proposed QBA algorithm is an effective and feasible method in solving UCAV path planning problem than some well-known algorithms.

Quantum-inspired glowworm swarm optimisation and its application

In order to solve discrete optimisation problem, a novel intelligence algorithm called as quantum-inspired glowworm swarm optimisation (QGSO) is proposed. By hybridising the glowworm swarm optimisation, quantum coding and quantum evolutionary theory, the quantum state and binary state of the quantum glowworms can be well evolved by simulated quantum rotation gate. The classical benchmark functions are used to test effectiveness of QGSO. The proposed QGSO algorithm is an effective discrete optimisation algorithm which has better convergent accuracy and speed. Then QGSO is used to resolve thinned array optimisation difficulties. Simulation results are provided to show that the proposed thinned array method based on QGSO is superior to the thinned array methods based on previous classical intelligence algorithms. The proposed thinned array method based on QGSO can search the global optimal solution of thinned array.

Rotation-Based Design and Synthesis of Quantum Circuits

In this paper, a new synthesis method for Boolean irreversible functions has been proposed which is based on rotation quantum operators. The primary motivation is that the implementation of these operators is commonly available in quantum technologies. We introduce an approach for synthesizing Boolean irreversible functions in quantum logic which is based on quantum rotation and CNOT operators and uses a prespecified fixed design where by changing the rotation angles a new functionality can be achieved. So this design can be viewed as a programmable array of rotation gates. If reduction in quantum cost is desired, after this step the optimization approach may be applied to reduce the number of gates by using some rules, which leads to a reduction of up to 48% in the quantum cost after optimization compared to the original nonoptimized design obtained from the synthesis method. The paper also introduces efficient designs with rotation operators for some important gates in the quantum circuit libraries. Our main contribution is introducing a novel and low complexity approach for synthesizing irreversible functions using elementary rotation operators with a regular fixed design. Also having as many functions as desired with the same inputs, the execution time just increases by one for each additional function and the circuit width is increased by one for each additional function. It is proved that our approach can always be applied to each Boolean function. We show the correctness of our approach and make an upper bound of the quantum cost of the circuit.