Implementation Of Quantum Circuits Research Articles

Industry 4.0 Quantum Strategic Organizational Design Configurations. The Case of 3 Qubits: One Reports to Two.

In this work we explore how the relationship between one subordinate reporting to two leaders influences the alignment of the latter with the company’s strategic objectives in an Industry 4.0 environment. We do this through the implementation of quantum circuits that represent decision networks. This is done for two cases: One in which the leaders do not communicate with each other, and one in which they do. Through the quantum simulation of strategic organizational design configurations (QSOD) through 500 quantum circuit simulations, we conclude that in the first case both leaders are not simultaneously in alignment, and in the second case that both reporting nodes need to have an alignment probability higher than 90% to support the leader node.

Two-level systems in superconducting quantum devices due to trapped quasiparticles.

A major issue for the implementation of large-scale superconducting quantum circuits is the interaction with interfacial two-level system (TLS) defects that lead to qubit parameter fluctuations and relaxation. Another major challenge comes from nonequilibrium quasiparticles (QPs) that result in qubit relaxation and dephasing. Here, we reveal a previously unexplored decoherence mechanism in the form of a new type of TLS originating from trapped QPs, which can induce qubit relaxation. Using spectral, temporal, thermal, and magnetic field mapping of TLS-induced fluctuations in frequency tunable resonators, we identify a highly coherent subset of the general TLS population with a low reconfiguration temperature ∼300 mK and a nonuniform density of states. These properties can be understood if the TLS are formed by QPs trapped in shallow subgap states formed by spatial fluctutations of the superconducting order parameter. This implies that even very rare QP bursts will affect coherence over exponentially long time scales.

Digital quantum simulation framework for energy transport in an open quantum system

Quantum effects such as the environment assisted quantum transport (ENAQT) displayed in photosynthetic Fenna–Mathews–Olson (FMO) complex has been simulated on analog quantum simulators. Digital quantum simulations offer greater universality and flexibility over analog simulations. However, digital quantum simulations of open quantum systems face a theoretical challenge; one does not know the solutions of the continuous time master equation for developing quantum gate operators. We give a theoretical framework for digital quantum simulation of ENAQT by introducing new quantum evolution operators. We develop the dynamical equation for the operators and prove that it is an analytical solution of the master equation. As an example, using the dynamical equations, we simulate the FMO complex in the digital setting, reproducing theoretical and experimental evidence of the dynamics. The framework gives an optimal method for quantum circuit implementation, giving a log reduction in complexity over known methods. The generic framework can be extrapolated to study other open quantum systems.

An improved heuristic technique for nearest neighbor realization of quantum circuits in 2D architecture

Last couple of years has witnessed tremendous advancements in the field of quantum computing and even it has started providing technological footprints in the design industry. Though advancements in the physical implementation of quantum circuits has taken a giant leap but it has faced with several design challenges and one such design constraint is Nearest Neighbor (NN) criteria which demands the operating qubits of the quantum gates to be adjacent.Focusing on the design issue, here, we show a heuristic design technique for efficient transformation of quantum circuits to NN based designs in 2D configuration. Our entire strategy is based on initial qubit mapping policy, where we have introduced three different mapping techniques 1) Influence Index, 2) Adjacency Matrix and 3) Distance Ratio based strategy. After placing the qubits in appropriate positions, we also undertake a dynamic windowing based local reordering scheme to further reduce the SWAP requirement in the designs. At the end of the work, to check the effectiveness of our transformation algorithms, we have tested a wide range of benchmarks over our algorithms and a comparative study over state-of-the-art design techniques also has been undertaken.

Quantum image encryption algorithm based on generalized Arnold transform and Logistic map

In the era of big data, image security and real-time processing become more and more important and increasingly difficult to satisfy. To improve the security and processing efficiency of image encryption algorithm, an enhanced quantum scheme is proposed for generalized novel enhanced quantum image representation. The proposed quantum encryption scheme mainly consists of two-stage operation in order, i.e., twice scrambling based generalized Arnold transform and pixel encryption based on the quantum key image (which are generated and prepared based on Logistic map). In the first stage, generalized Arnold transform are employed to simultaneously disturb the coordinate information and pixel gray value of quantum plain image. Following that, the scrambled image is further encrypted into a quantum cipher image based on quantum key image, which is divided into three sub-processes in detail, i.e., CNOT operations, bit-plane scrambling and controlled perfect shuffle permutations are executed orderly. The quantum image decryption process can be easily implemented in a reverse way. The complete quantum circuit implementation for above two stages operation is constructed and analyzed in terms of quantum cost and time complexity. Compared to classical image processing algorithm, the investigated quantum encryption algorithm demonstrates an exponential speedup with computational cost of $${\rm O}\left( n \right)$$ for a $$2^{n} \times 2^{n}$$ quantum grayscale or color images. The proposed scheme is simulated and verified on a classical computer with MATLAB environments, i.e., not in a real quantum version that not considers the effects of quantum noise. Experimental results and numerical analysis indicate that the presented quantum algorithm has good visual effects and high security.

Theory of quantum path computing with Fourier optics and future applications for quantum supremacy, neural networks and nonlinear Schr\xf6dinger equations

The scalability, error correction and practical problem solving are important challenges for quantum computing (QC) as more emphasized by quantum supremacy (QS) experiments. Quantum path computing (QPC), recently introduced for linear optic based QCs as an unconventional design, targets to obtain scalability and practical problem solving. It samples the intensity from the interference of exponentially increasing number of propagation paths obtained in multi-plane diffraction (MPD) of classical particle sources. QPC exploits MPD based quantum temporal correlations of the paths and freely entangled projections at different time instants, for the first time, with the classical light source and intensity measurement while not requiring photon interactions or single photon sources and receivers. In this article, photonic QPC is defined, theoretically modeled and numerically analyzed for arbitrary Fourier optical or quadratic phase set-ups while utilizing both Gaussian and Hermite-Gaussian source laser modes. Problem solving capabilities already including partial sum of Riemann theta functions are extended. Important future applications, implementation challenges and open issues such as universal computation and quantum circuit implementations determining the scope of QC capabilities are discussed. The applications include QS experiments reaching more than 2^{100} Feynman paths, quantum neuron implementations and solutions of nonlinear Schrödinger equation.

Hybrid Helmholtz machines: a gate-based quantum circuit implementation

Quantum machine learning has the potential to overcome problems that current classical machine learning algorithms face, such as large data requirements or long learning times. Sampling is one of the aspects of classical machine learning that might benefit from quantum machine learning, as quantum computers intrinsically excel at sampling. Current hybrid quantum-classical implementations provide ways to already use near-term quantum computers for practical applications. By expanding the horizon on hybrid quantum-classical approaches, this work proposes the first implementation of a gated quantum-classical hybrid Helmholtz machine, a gate-based quantum circuit approximation of a neural network for unsupervised tasks. Our approach focuses on parameterized shallow quantum circuits and effectively implements an approximate Bayesian network, overcoming the exponential complexity of exact networks. In addition, a new balanced cost function is introduced, preventing the need of millions of training samples. Using a bars and stripes data set, the model, implemented on the Quantum Inspire platform, is shown to outperform classical Helmholtz machines in terms of the Kullback–Leibler divergence.

Quantum algorithm for the collisionless Boltzmann equation

A novel quantum algorithm implementing a discrete-velocity method for the collisionless Boltzmann equation is introduced. The algorithm is designed for application on a quantum computer with a number of quantum bits feasible in the near future (e.g. 40−50). Following the quantum-circuit model of quantum computation, the present works shows the quantum-circuit implementations for the convection or transport part of the kinetic model, inspired by work on quantum algorithms for the Dirac equation. The present work represents the advection step as a quantum walk process, implemented as a series of multiple-input controlled-NOT gates. A detailed discussion on the background to this new method is presented, including how a rarefied-flow problem can be encoded as the quantum state of a qubit register in a quantum computer. A complexity analysis is presented showing potential benefits of the proposed algorithm. Based on the concept of quantum parallelism, the extension to multiple species is demonstrated to not increase the number of required gate operations. A key aspect of the developed algorithm is the implementation of boundary conditions. This work describes how the specular-reflection boundary conditions can be effectively imposed with a quantum circuit implementation. The developed method is then applied to the supersonic flow around a blunt body as well as the free-molecular flow escaping from a rectangular container. As validation, the flow along the stagnation streamline of the blunt-body flow is compared with exact solutions for a piston-driven flow, showing excellent agreement. Finally, directions for future work are discussed in this work.

Implementation of sequential game on quantum circuits

It is known that Eisert–Wilkens–Lewenstein scheme and Marinatto–Weber scheme are widely used to quantize simultaneous games. Further, distributed quantum game can be implemented in quantum networks using the schemes based on client–server model and peer-to-peer model. While most of the research works focus on simultaneous games, in this work, we propose the quantum circuit implementation of sequential game, namely cop and robber game using peer-to-peer model. Thus we have made a modest attempt to show the possibility of implementing sequential games in quantum circuits. Further, quantum version of cop and robber game is analyzed. Implications of the results are discussed from the game-theoretic point of view and quantum circuit point of view.

Circuit-Based Modular Implementation of Quantum Ghost Imaging

Efforts on enhancing the ghost imaging speed and quality are intensified when the debate around the nature of ghost imaging (quantum vs. classical) is suspended for a while. Accordingly, most of the studies these years in the field fall into the improvement regarding these two targets by utilizing the different imaging mediums. Nevertheless, back to the raging debate occurred but with different focus, to overcome the inherent difficulties in the classical imaging domain, if we are able to utilize the superiority that quantum information science offers us, the ghost imaging experiment may be implemented more practically. In this study, a quantum circuit implementation of ghost imaging experiment is proposed, where the speckle patterns and phase mask are encoded by utilizing the quantum representation of images. To do this, we formulated several quantum models, i.e. quantum accumulator, quantum multiplier, and quantum divider. We believe this study will provide a new impetus to explore the implementation of ghost imaging using quantum computing resources.

Distance-based classifier on the Quantum Inspire

With quantum computers entering a new phase of maturity and quantum algorithms covering a growing range of applications, it is important that the two meet at some point in the middle. Currently, the two meet only by toy-problem implementations for some algorithms. In this work, we extend a recently proposed distance-based classifier and give explicit quantum circuit implementations, and we give a method to overcome restrictions on the data, present in the original work.

Quantum Implementation of Powell’s Conjugate Direction Method

A quantum circuit implementation of Powell’s conjugate direction method (“Powell’s method”) is proposed based on quantum basic transformations in this study. Powell’s method intends to find the minimum of a function, including a sequence of parameters, by changing one parameter at a time. The quantum circuits that implement Powell’s method are logically built by combining quantum computing units and basic quantum gates. The main contributions of this study are the quantum realization of a quadratic equation, the proposal of a quantum one-dimensional search algorithm, the quantum implementation of updating the searching direction array (SDA), and the quantum judgment of stopping the Powell’s iteration. A simulation demonstrates the execution of Powell’s method, and future applications, such as data fitting and image registration, are discussed.

Optimal LSBs-based quantum watermarking with lower distortion

Based on the NEQR representation of quantum grayscale images and binary images, the optimal LSBs-based quantum watermarking scheme is investigated in this paper, which embeds several binary images (watermark images) into a grayscale image (cover image). The size of the cover image and secret image are both assumed to be [Formula: see text]. Compared to quantum simple LSBs substitution method generating one stego-pixel, our presented quantum optimal LSBs-based method can generate three stego-pixel simultaneously first. Then one of them with lowest visual distortion is chosen as the final stego-pixel. To this end, first of all, the quantum circuits for a few basic quantum modules (i.e. Quantum Comparator, Parallel CNOT, Parallel Swap, ADDER MOD, Subtracter (SUB.ER) MOD and Absolute Value) are predefined. Following that, based on these simple modules, two composite quantum modules (i.e. the ADDER and SUB.ER MOD [Formula: see text] module and Choose final stego-pixel module) are further constructed. With the help of the basic and composite quantum modules, the integrated quantum circuit implementation of the optimal LSBs-based quantum watermark images embedding/extracting procedures are illustrated. Then, the experiment result are simulated under the classical computer software MATLAB 2014(b), which illustrates our presented optimal LSBs-based quantum watermarking methods are superior to the simple LSBs scheme in terms of PSNR and histogram graphs on the basis of visual effect, and the circuit’s complexity analysis also demonstrates our investigated scheme with a very low computational complexity. Finally, we analyze the security of quantum cryptography system, which verifies the quantum watermarking data can be securely transmitted to other legal normal users.

A template-based technique for efficient Clifford+T-based quantum circuit implementation

The near-future possibility of Quantum supremacy, which aspires to establish a set of algorithms running efficiently on a Quantum computer – have significantly fuelled the interest in design and automation of Quantum circuits. Multiple technologies such as Ion-Trap, Nuclear Magnetic Resonance (NMR), have made great progress in recent years towards a practical Quantum circuit implementation. For all these technologies, in order to suppress the inherent computation noise, fault-tolerance is a desirable feature. Fault tolerance is achieved by Quantum error correction codes, such as surface code. Due to the efficient realization of surface codes using Clifford + T gate library of Quantum logic gates, it is now becoming de facto gate library for Quantum circuit implementation. In this paper, we improve two key performance metrics, T − depth and T − count, for Quantum circuit realization using Clifford + T gates. In contrast with the previous approaches, we have incorporated two techniques - 1) restructuring of the gate positions in the designs to make it amenable towards a lower T − depth 2) using Binary Decision Diagrams (BDD) as an intermediate representation for achieving scalability. To validate our proposed optimizations, we have tested a wide spectrum of benchmarks, registering an average improvement of 74% and 21% on T − depth and T − count in compared works.

Efficient implementation of quantum circuits with limited qubit interactions

The quantum circuit model allows gates between any pair of qubits yet physical instantiations allow only limited interactions. We address this problem by providing an interaction graph together with an efficient method for compiling quantum circuits so that gates are applied only locally. The graph requires each qubit to interact with 4 other qubits and yet the time-overhead for implementing any n-qubit quantum circuit is 4 log n. Building a network of quantum computing nodes according to this graph enables the network to emulate a single monolithic device with minimal overhead.

Efficient quantum circuits for Szegedy quantum walks

A major advantage in using Szegedy’s formalism over discrete-time and continuous-time quantum walks lies in its ability to define a unitary quantum walk by quantizing a Markov chain on a directed or weighted graph. In this paper, we present a general scheme to construct efficient quantum circuits for Szegedy quantum walks that correspond to classical Markov chains possessing transformational symmetry in the columns of the transition matrix. In particular, the transformational symmetry criteria do not necessarily depend on the sparsity of the transition matrix, so this scheme can be applied to non-sparse Markov chains. Two classes of Markov chains that are amenable to this construction are cyclic permutations and complete bipartite graphs, for which we provide explicit efficient quantum circuit implementations. We also prove that our scheme can be applied to Markov chains formed by a tensor product. We also briefly discuss the implementation of Markov chains based on weighted interdependent networks. In addition, we apply this scheme to construct efficient quantum circuits simulating the Szegedy walks used in the quantum Pagerank algorithm for some classes of non-trivial graphs, providing a necessary tool for experimental demonstration of the quantum Pagerank algorithm.

OptQC v1.3: An (updated) optimized parallel quantum compiler

We present a revised version of the OptQC program of Loke et al. (2014) [1]. We have removed the simulated annealing process in favour of a descending random walk. We have also introduced a new method for iteratively generating permutation matrices during the random walk process, providing a reduced total cost for implementing the quantum circuit. Lastly, we have also added a synchronization mechanism between threads, giving quicker convergence to more optimal solutions. New version program summaryProgram title: OptQC v1.3Catalogue identifier: AEUA_v1_3Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEUA_v1_3.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 240903No. of bytes in distributed program, including test data, etc.: 632395Distribution format: tar.gzProgramming language: Fortran, MPI.Computer: Any computer with Fortran compiler (not gfortran4.9 or earlier) and MPI library.Operating system: Linux.Classification: 4.15.Catalogue identifier of previous version: AEUA_v1_3Journal reference of previous version: Comput. Phys. Comm. 185(2014)3307External routines: Intel MKL LAPACK routines and MPI routines.Does the new version supersede the previous version?: YesNature of problem:It aims to minimize the number of quantum gates required to implement a given unitary operation.Solution method:It utilizes a descending random walk to select permutation matrices P and Q for a given unitary matrix U such that the number of gates in the quantum circuit of U=QTPTU′PQ is minimized, where U′ is equivalent to U up to a permutation. The decomposition of a unitary operator is performed by recursively applying the cosine–sine decomposition.Reasons for new version:Simulated annealing process was found to give suboptimal results compared to a normal descending random walk. Computation time was also bloated by the necessity of running the CS decomposition thrice (for U′,P and PT) for each iteration of the optimization process.Summary of revisions:•Simulated annealing process was replaced by a descending random walk (equivalent to setting the threshold value β to 0), due to poor convergence of the simulated annealing process, and due to the lack of pathological instances of local minima in this particular search space.•Introduced an iterative method for generating the general permutation matrix P, in which we start with P=I and build up the quantum circuit (and modify P correspondingly) by adding gates onto the existing circuit. This removes the requirement of running the CS decomposition on P and PT to find the quantum circuit implementation, since it is already known by construction.•Added a synchronization mechanism between threads (after some prescribed number of iterations) in which the current state of the top 10% processes with the fittest solutions is copied over to the remaining 90%. This works so as to discard the less fit solutions and focuses the searching algorithm in the state space with the fittest solutions.Additional comments:The program contains some Fortran2003 features and will not compile with gcc4.9 or earlier.Running time:As before, running time increases with the size of the unitary matrix, as well as the prescribed maximum number of iterations for qubit permutation selection and the descending random walk. All simulation results presented in this paper are obtained from running the program on the Fornax supercomputer managed by iVEC@UWA with Intel Xeon X5650 CPUs. A comparison of running times is also given in Table 1.

Generation, guiding and splitting of triggered single photons from a resonantly excited quantum dot in a photonic circuit.

We demonstrate resonance fluorescence from single In-GaAs/GaAs quantum dots embedded in a rib waveguide beamsplitter structure operated under pulsed laser excitation. A systematic study on the excitation laser pulse duration depicts that a sufficiently small laser linewidth enables a substantial improved single-photon-to-laser-background ratio inside a waveguide chip. This manifests in the observation of clear Rabi oscillations over two periods of the quantum dot emission as a function of laser excitation power. A photon cross-correlation measurement between the two output arms of an on-chip beamsplitter results in a g(2)(0)=0.18, demonstrating the generation, guiding and splitting of triggered single photons under resonant excitation in an on-chip device. The present results open new perspectives for the implementation of photonic quantum circuits with integrated quantum dots as resonantly-pumped deterministic single-photon sources.

Negative Differential Conductivity in an Interacting Quantum Gas.

We report on the observation of negative differential conductivity (NDC) in a quantum transport device for neutral atoms employing a multimode tunneling junction. The system is realized with a Bose-Einstein condensate loaded in a one-dimensional optical lattice with high site occupancy. We induce an initial difference in chemical potential at one site by local atom removal. The ensuing transport dynamics are governed by the interplay between the tunneling coupling, the interaction energy, and intrinsic collisions, which turn the coherent coupling into a hopping process. The resulting current-voltage characteristics exhibit NDC, for which we identify atom number-dependent tunneling as a new microscopic mechanism. Our study opens new ways for the future implementation and control of complex neutral atom quantum circuits.

OptQC: An optimized parallel quantum compiler

The software package Qcompiler (Chen and Wang 2013) provides a general quantum compilation framework, which maps any given unitary operation into a quantum circuit consisting of a sequential set of elementary quantum gates. In this paper, we present an extended software OptQC, which finds permutation matrices P and Q for a given unitary matrix U such that the number of gates in the quantum circuit of U=QTPTU′PQ is significantly reduced, where U′ is equivalent to U up to a permutation and the quantum circuit implementation of each matrix component is considered separately. We extend further this software package to make use of high-performance computers with a multiprocessor architecture using MPI. We demonstrate its effectiveness in reducing the total number of quantum gates required for various unitary operators. Program summaryProgram title: OptQCCatalogue identifier: AEUA_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEUA_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 178435No. of bytes in distributed program, including test data, etc.: 491574Distribution format: tar.gzProgramming language: Fortran, MPI.Computer: Any computer with Fortran compiler and MPI library.Operating system: Linux.Classification: 4.15.Nature of problem: It aims to minimize the number of quantum gates required to implement a given unitary operation.Solution method: It utilizes a threshold-based acceptance strategy for simulated annealing to select permutation matrices P and Q for a given unitary matrix U such that the number of gates in the quantum circuit of U=QTPTU′PQ is minimized, where U′ is equivalent to U up to a permutation. The decomposition of a unitary operator is performed by recursively applying the cosine–sine decomposition.Running time: Running time increases with the size of the unitary matrix, as well as the prescribed maximum number of iterations for qubit permutation selection and the subsequent simulated annealing algorithm. Running time estimates are provided for each example in Section 4. All simulation results presented in this paper are obtained from running the program on the Fornax supercomputer managed by iVEC@UWA with Intel Xeon X5650 CPUs.