Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 13

Search results for: qubit

13 Ground State Phases in Two-Mode Quantum Rabi Models

Authors: Suren Chilingaryan


We study two models describing a single two-level system coupled to two boson field modes in either a parallel or orthogonal setup. Both models may be feasible for experimental realization through Raman adiabatic driving in cavity QED. We study their ground state configurations; that is, we find the quantum precursors of the corresponding semi-classical phase transitions. We found that the ground state configurations of both models present the same critical coupling as the quantum Rabi model. Around this critical coupling, the ground state goes from the so-called normal configuration with no excitation, the qubit in the ground state and the fields in the quantum vacuum state, to a ground state with excitations, the qubit in a superposition of ground and excited state, while the fields are not in the vacuum anymore, for the first model. The second model shows a more complex ground state configuration landscape where we find the normal configuration mentioned above, two single-mode configurations, where just one of the fields and the qubit are excited, and a dual-mode configuration, where both fields and the qubit are excited.

Keywords: quantum optics, quantum phase transition, cavity QED, circuit QED

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12 Quantum Entanglement and Thermalization in Superconducting Two-Qubit Systems

Authors: E. Karami, M. Bohloul, P. Najmadi


The superconducting system is a suitable system for quantum computers. Quantum entanglement is a fundamental phenomenon that is key to the power of quantum computers. Quantum entanglement has been studied in different superconducting systems. In this paper, we are investigating a superconducting two-qubit system as a macroscopic system. These systems include two coupled Quantronium circuits. We calculate quantum entanglement and thermalization for system evolution and compare them. We observe, thermalization and entanglement have different behavior, and equilibrium thermal state has maximum entanglement.

Keywords: macroscopic system, quantum entanglement, thermalization, superconducting system

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11 The Role of Metal-Induced Gap States in the Superconducting Qubit Decoherence at Low-Dimension

Authors: Dominik Szczesniak, Sabre Kais


In the present communication, we analyze selected local aspects of the metal-induced gap states (MIGSs) that may be responsible for the magnetic flux noise in some of the superconducting qubit modalities at low-dimension. The presented theoretical analysis stems from the earlier bulk considerations and is aimed at further explanation of the decoherence effect by recognizing its universal character. Specifically, the analysis is carried out by using the complex band structure method for arbitrary low-dimensional junctions. This allows us to provide the most fundamental and general observations for the systems of interest. In particular, herein, we investigate in detail the MIGSs behavior in the momentum space as a function of the potential fluctuations and the electron-electron interaction magnitude at the interface. In what follows, this study is meant to provide a direct relationship between the MIGSs behavior, the discussed decoherence effect, and the intrinsic properties of the low-dimensional Josephson junctions.

Keywords: superconducting qubits, metal-induced gap states, decoherence, low-dimension

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10 Genome Sequencing, Assembly and Annotation of Gelidium Pristoides from Kenton-on-Sea, South Africa

Authors: Sandisiwe Mangali, Graeme Bradley


Genome is complete set of the organism's hereditary information encoded as either deoxyribonucleic acid or ribonucleic acid in most viruses. The three different types of genomes are nuclear, mitochondrial and the plastid genome and their sequences which are uncovered by genome sequencing are known as an archive for all genetic information and enable researchers to understand the composition of a genome, regulation of gene expression and also provide information on how the whole genome works. These sequences enable researchers to explore the population structure, genetic variations, and recent demographic events in threatened species. Particularly, genome sequencing refers to a process of figuring out the exact arrangement of the basic nucleotide bases of a genome and the process through which all the afore-mentioned genomes are sequenced is referred to as whole or complete genome sequencing. Gelidium pristoides is South African endemic Rhodophyta species which has been harvested in the Eastern Cape since the 1950s for its high economic value which is one motivation for its sequencing. Its endemism further motivates its sequencing for conservation biology as endemic species are more vulnerable to anthropogenic activities endangering a species. As sequencing, mapping and annotating the Gelidium pristoides genome is the aim of this study. To accomplish this aim, the genomic DNA was extracted and quantified using the Nucleospin Plank Kit, Qubit 2.0 and Nanodrop. Thereafter, the Ion Plus Fragment Library was used for preparation of a 600bp library which was then sequenced through the Ion S5 sequencing platform for two runs. The produced reads were then quality-controlled and assembled through the SPAdes assembler with default parameters and the genome assembly was quality assessed through the QUAST software. From this assembly, the plastid and the mitochondrial genomes were then sampled out using Gelidiales organellar genomes as search queries and ordered according to them using the Geneious software. The Qubit and the Nanodrop instruments revealed an A260/A280 and A230/A260 values of 1.81 and 1.52 respectively. A total of 30792074 reads were obtained and produced a total of 94140 contigs with resulted into a sequence length of 217.06 Mbp with N50 value of 3072 bp and GC content of 41.72%. A total length of 179281bp and 25734 bp was obtained for plastid and mitochondrial respectively. Genomic data allows a clear understanding of the genomic constituent of an organism and is valuable as foundation information for studies of individual genes and resolving the evolutionary relationships between organisms including Rhodophytes and other seaweeds.

Keywords: Gelidium pristoides, genome, genome sequencing and assembly, Ion S5 sequencing platform

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9 Mapping Tunnelling Parameters for Global Optimization in Big Data via Dye Laser Simulation

Authors: Sahil Imtiyaz


One of the biggest challenges has emerged from the ever-expanding, dynamic, and instantaneously changing space-Big Data; and to find a data point and inherit wisdom to this space is a hard task. In this paper, we reduce the space of big data in Hamiltonian formalism that is in concordance with Ising Model. For this formulation, we simulate the system using dye laser in FORTRAN and analyse the dynamics of the data point in energy well of rhodium atom. After mapping the photon intensity and pulse width with energy and potential we concluded that as we increase the energy there is also increase in probability of tunnelling up to some point and then it starts decreasing and then shows a randomizing behaviour. It is due to decoherence with the environment and hence there is a loss of ‘quantumness’. This interprets the efficiency parameter and the extent of quantum evolution. The results are strongly encouraging in favour of the use of ‘Topological Property’ as a source of information instead of the qubit.

Keywords: big data, optimization, quantum evolution, hamiltonian, dye laser, fermionic computations

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8 Evaluating the Diagnostic Accuracy of the ctDNA Methylation for Liver Cancer

Authors: Maomao Cao


Objective: To test the performance of ctDNA methylation for the detection of liver cancer. Methods: A total of 1233 individuals have been recruited in 2017. 15 male and 15 female samples (including 10 cases of liver cancer) were randomly selected in the present study. CfDNA was extracted by MagPure Circulating DNA Maxi Kit. The concentration of cfDNA was obtained by Qubit™ dsDNA HS Assay Kit. A pre-constructed predictive model was used to analyze methylation data and to give a predictive score for each cfDNA sample. Individuals with a predictive score greater than or equal to 80 were classified as having liver cancer. CT tests were considered the gold standard. Sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) for the diagnosis of liver cancer were calculated. Results: 9 patients were diagnosed with liver cancer according to the prediction model (with high sensitivity and threshold of 80 points), with scores of 99.2, 91.9, 96.6, 92.4, 91.3, 92.5, 96.8, 91.1, and 92.2, respectively. The sensitivity, specificity, positive predictive value, and negative predictive value of ctDNA methylation for the diagnosis of liver cancer were 0.70, 0.90, 0.78, and 0.86, respectively. Conclusions: ctDNA methylation could be an acceptable diagnostic modality for the detection of liver cancer.

Keywords: liver cancer, ctDNA methylation, detection, diagnostic performance

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7 Quantifying Parallelism of Vectors Is the Quantification of Distributed N-Party Entanglement

Authors: Shreya Banerjee, Prasanta K. Panigrahi


The three-way distributive entanglement is shown to be related to the parallelism of vectors. Using a measurement-based approach a set of 2−dimensional vectors is formed, representing the post-measurement states of one of the parties. These vectors originate at the same point and have an angular distance between them. The area spanned by a pair of such vectors is a measure of the entanglement of formation. This leads to a geometrical manifestation of the 3−tangle in 2−dimensions, from inequality in the area which generalizes for n− qubits to reveal that the n− tangle also has a planar structure. Quantifying the genuine n−party entanglement in every 1|(n − 1) bi-partition it is shown that the genuine n−way entanglement does not manifest in n− tangle. A new quantity geometrically similar to 3−tangle is then introduced that represents the genuine n− way entanglement. Extending the formalism to 3− qutrits, the nonlocality without entanglement can be seen to arise from a condition under which the post-measurement state vectors of a separable state show parallelism. A connection to nontrivial sum uncertainty relation analogous to Maccone and Pati uncertainty relation is then presented using decomposition of post-measurement state vectors along parallel and perpendicular direction of the pre-measurement state vectors. This study opens a novel way to understand multiparty entanglement in qubit and qudit systems.

Keywords: Geometry of quantum entanglement, Multipartite and distributive entanglement, Parallelism of vectors , Tangle

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6 A Novel Way to Create Qudit Quantum Error Correction Codes

Authors: Arun Moorthy


Quantum computing promises to provide algorithmic speedups for a number of tasks; however, similar to classical computing, effective error-correcting codes are needed. Current quantum computers require costly equipment to control each particle, so having fewer particles to control is ideal. Although traditional quantum computers are built using qubits (2-level systems), qudits (more than 2-levels) are appealing since they can have an equivalent computational space using fewer particles, meaning fewer particles need to be controlled. Currently, qudit quantum error-correction codes are available for different level qudit systems; however, these codes have sometimes overly specific constraints. When building a qudit system, it is important for researchers to have access to many codes to satisfy their requirements. This project addresses two methods to increase the number of quantum error correcting codes available to researchers. The first method is generating new codes for a given set of parameters. The second method is generating new error-correction codes by using existing codes as a starting point to generate codes for another level (i.e., a 5-level system code on a 2-level system). So, this project builds a website that researchers can use to generate new error-correction codes or codes based on existing codes.

Keywords: qudit, error correction, quantum, qubit

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5 Characterizing and Developing the Clinical Grade Microbiome Assay with a Robust Bioinformatics Pipeline for Supporting Precision Medicine Driven Clinical Development

Authors: Danyi Wang, Andrew Schriefer, Dennis O'Rourke, Brajendra Kumar, Yang Liu, Fei Zhong, Juergen Scheuenpflug, Zheng Feng


Purpose: It has been recognized that the microbiome plays critical roles in disease pathogenesis, including cancer, autoimmune disease, and multiple sclerosis. To develop a clinical-grade assay for exploring microbiome-derived clinical biomarkers across disease areas, a two-phase approach is implemented. 1) Identification of the optimal sample preparation reagents using pre-mixed bacteria and healthy donor stool samples coupled with proprietary Sigma-Aldrich® bioinformatics solution. 2) Exploratory analysis of patient samples for enabling precision medicine. Study Procedure: In phase 1 study, we first compared the 16S sequencing results of two ATCC® microbiome standards (MSA 2002 and MSA 2003) across five different extraction kits (Kit A, B, C, D & E). Both microbiome standards samples were extracted in triplicate across all extraction kits. Following isolation, DNA quantity was determined by Qubit assay. DNA quality was assessed to determine purity and to confirm extracted DNA is of high molecular weight. Bacterial 16S ribosomal ribonucleic acid (rRNA) amplicons were generated via amplification of the V3/V4 hypervariable region of the 16S rRNA. Sequencing was performed using a 2x300 bp paired-end configuration on the Illumina MiSeq. Fastq files were analyzed using the Sigma-Aldrich® Microbiome Platform. The Microbiome Platform is a cloud-based service that offers best-in-class 16S-seq and WGS analysis pipelines and databases. The Platform and its methods have been extensively benchmarked using microbiome standards generated internally by MilliporeSigma and other external providers. Data Summary: The DNA yield using the extraction kit D and E is below the limit of detection (100 pg/µl) of Qubit assay as both extraction kits are intended for samples with low bacterial counts. The pre-mixed bacterial pellets at high concentrations with an input of 2 x106 cells for MSA-2002 and 1 x106 cells from MSA-2003 were not compatible with the kits. Among the remaining 3 extraction kits, kit A produced the greatest yield whereas kit B provided the least yield (Kit-A/MSA-2002: 174.25 ± 34.98; Kit-A/MSA-2003: 179.89 ± 30.18; Kit-B/MSA-2002: 27.86 ± 9.35; Kit-B/MSA-2003: 23.14 ± 6.39; Kit-C/MSA-2002: 55.19 ± 10.18; Kit-C/MSA-2003: 35.80 ± 11.41 (Mean ± SD)). Also, kit A produced the greatest yield, whereas kit B provided the least yield. The PCoA 3D visualization of the Weighted Unifrac beta diversity shows that kits A and C cluster closely together while kit B appears as an outlier. The kit A sequencing samples cluster more closely together than both the other kits. The taxonomic profiles of kit B have lower recall when compared to the known mixture profiles indicating that kit B was inefficient at detecting some of the bacteria. Conclusion: Our data demonstrated that the DNA extraction method impacts DNA concentration, purity, and microbial communities detected by next-generation sequencing analysis. Further microbiome analysis performance comparison of using healthy stool samples is underway; also, colorectal cancer patients' samples will be acquired for further explore the clinical utilities. Collectively, our comprehensive qualification approach, including the evaluation of optimal DNA extraction conditions, the inclusion of positive controls, and the implementation of a robust qualified bioinformatics pipeline, assures accurate characterization of the microbiota in a complex matrix for deciphering the deep biology and enabling precision medicine.

Keywords: 16S rRNA sequencing, analytical validation, bioinformatics pipeline, metagenomics

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4 D-Wave Quantum Computing Ising Model: A Case Study for Forecasting of Heat Waves

Authors: Dmytro Zubov, Francesco Volponi


In this paper, D-Wave quantum computing Ising model is used for the forecasting of positive extremes of daily mean air temperature. Forecast models are designed with two to five qubits, which represent 2-, 3-, 4-, and 5-day historical data respectively. Ising model’s real-valued weights and dimensionless coefficients are calculated using daily mean air temperatures from 119 places around the world, as well as sea level (Aburatsu, Japan). In comparison with current methods, this approach is better suited to predict heat wave values because it does not require the estimation of a probability distribution from scarce observations. Proposed forecast quantum computing algorithm is simulated based on traditional computer architecture and combinatorial optimization of Ising model parameters for the Ronald Reagan Washington National Airport dataset with 1-day lead-time on learning sample (1975-2010 yr). Analysis of the forecast accuracy (ratio of successful predictions to total number of predictions) on the validation sample (2011-2014 yr) shows that Ising model with three qubits has 100 % accuracy, which is quite significant as compared to other methods. However, number of identified heat waves is small (only one out of nineteen in this case). Other models with 2, 4, and 5 qubits have 20 %, 3.8 %, and 3.8 % accuracy respectively. Presented three-qubit forecast model is applied for prediction of heat waves at other five locations: Aurel Vlaicu, Romania – accuracy is 28.6 %; Bratislava, Slovakia – accuracy is 21.7 %; Brussels, Belgium – accuracy is 33.3 %; Sofia, Bulgaria – accuracy is 50 %; Akhisar, Turkey – accuracy is 21.4 %. These predictions are not ideal, but not zeros. They can be used independently or together with other predictions generated by different method(s). The loss of human life, as well as environmental, economic, and material damage, from extreme air temperatures could be reduced if some of heat waves are predicted. Even a small success rate implies a large socio-economic benefit.

Keywords: heat wave, D-wave, forecast, Ising model, quantum computing

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3 Detailed Quantum Circuit Design and Evaluation of Grover's Algorithm for the Bounded Degree Traveling Salesman Problem Using the Q# Language

Authors: Wenjun Hou, Marek Perkowski


The Traveling Salesman problem is famous in computing and graph theory. In short, it asks for the Hamiltonian cycle of the least total weight in a given graph with N nodes. All variations on this problem, such as those with K-bounded-degree nodes, are classified as NP-complete in classical computing. Although several papers propose theoretical high-level designs of quantum algorithms for the Traveling Salesman Problem, no quantum circuit implementation of these algorithms has been created up to our best knowledge. In contrast to previous papers, the goal of this paper is not to optimize some abstract complexity measures based on the number of oracle iterations, but to be able to evaluate the real circuit and time costs of the quantum computer. Using the emerging quantum programming language Q# developed by Microsoft, which runs quantum circuits in a quantum computer simulation, an implementation of the bounded-degree problem and its respective quantum circuit were created. To apply Grover’s algorithm to this problem, a quantum oracle was designed, evaluating the cost of a particular set of edges in the graph as well as its validity as a Hamiltonian cycle. Repeating the Grover algorithm with an oracle that finds successively lower cost each time allows to transform the decision problem to an optimization problem, finding the minimum cost of Hamiltonian cycles. N log₂ K qubits are put into an equiprobablistic superposition by applying the Hadamard gate on each qubit. Within these N log₂ K qubits, the method uses an encoding in which every node is mapped to a set of its encoded edges. The oracle consists of several blocks of circuits: a custom-written edge weight adder, node index calculator, uniqueness checker, and comparator, which were all created using only quantum Toffoli gates, including its special forms, which are Feynman and Pauli X. The oracle begins by using the edge encodings specified by the qubits to calculate each node that this path visits and adding up the edge weights along the way. Next, the oracle uses the calculated nodes from the previous step and check that all the nodes are unique. Finally, the oracle checks that the calculated cost is less than the previously-calculated cost. By performing the oracle an optimal number of times, a correct answer can be generated with very high probability. The oracle of the Grover Algorithm is modified using the recalculated minimum cost value, and this procedure is repeated until the cost cannot be further reduced. This algorithm and circuit design have been verified, using several datasets, to generate correct outputs.

Keywords: quantum computing, quantum circuit optimization, quantum algorithms, hybrid quantum algorithms, quantum programming, Grover’s algorithm, traveling salesman problem, bounded-degree TSP, minimal cost, Q# language

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2 Analytical Solutions of Josephson Junctions Dynamics in a Resonant Cavity for Extended Dicke Model

Authors: S.I.Mukhin, S. Seidov, A. Mukherjee


The Dicke model is a key tool for the description of correlated states of quantum atomic systems, excited by resonant photon absorption and subsequently emitting spontaneous coherent radiation in the superradiant state. The Dicke Hamiltonian (DH) is successfully used for the description of the dynamics of the Josephson Junction (JJ) array in a resonant cavity under applied current. In this work, we have investigated a generalized model, which is described by DH with a frustrating interaction term. This frustrating interaction term is explicitly the infinite coordinated interaction between all the spin half in the system. In this work, we consider an array of N superconducting islands, each divided into two sub-islands by a Josephson Junction, taken in a charged qubit / Cooper Pair Box (CPB) condition. The array is placed inside the resonant cavity. One important aspect of the problem lies in the dynamical nature of the physical observables involved in the system, such as condensed electric field and dipole moment. It is important to understand how these quantities behave with time to define the quantum phase of the system. The Dicke model without frustrating term is solved to find the dynamical solutions of the physical observables in analytic form. We have used Heisenberg’s dynamical equations for the operators and on applying newly developed Rotating Holstein Primakoff (HP) transformation and DH we have arrived at the four coupled nonlinear dynamical differential equations for the momentum and spin component operators. It is possible to solve the system analytically using two-time scales. The analytical solutions are expressed in terms of Jacobi's elliptic functions for the metastable ‘bound luminosity’ dynamic state with the periodic coherent beating of the dipoles that connect the two double degenerate dipolar ordered phases discovered previously. In this work, we have proceeded the analysis with the extended DH with a frustrating interaction term. Inclusion of the frustrating term involves complexity in the system of differential equations and it gets difficult to solve analytically. We have solved semi-classical dynamic equations using the perturbation technique for small values of Josephson energy EJ. Because the Hamiltonian contains parity symmetry, thus phase transition can be found if this symmetry is broken. Introducing spontaneous symmetry breaking term in the DH, we have derived the solutions which show the occurrence of finite condensate, showing quantum phase transition. Our obtained result matches with the existing results in this scientific field.

Keywords: Dicke Model, nonlinear dynamics, perturbation theory, superconductivity

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1 An Adiabatic Quantum Optimization Approach for the Mixed Integer Nonlinear Programming Problem

Authors: Maxwell Henderson, Tristan Cook, Justin Chan Jin Le, Mark Hodson, YoungJung Chang, John Novak, Daniel Padilha, Nishan Kulatilaka, Ansu Bagchi, Sanjoy Ray, John Kelly


We present a method of using adiabatic quantum optimization (AQO) to solve a mixed integer nonlinear programming (MINLP) problem instance. The MINLP problem is a general form of a set of NP-hard optimization problems that are critical to many business applications. It requires optimizing a set of discrete and continuous variables with nonlinear and potentially nonconvex constraints. Obtaining an exact, optimal solution for MINLP problem instances of non-trivial size using classical computation methods is currently intractable. Current leading algorithms leverage heuristic and divide-and-conquer methods to determine approximate solutions. Creating more accurate and efficient algorithms is an active area of research. Quantum computing (QC) has several theoretical benefits compared to classical computing, through which QC algorithms could obtain MINLP solutions that are superior to current algorithms. AQO is a particular form of QC that could offer more near-term benefits compared to other forms of QC, as hardware development is in a more mature state and devices are currently commercially available from D-Wave Systems Inc. It is also designed for optimization problems: it uses an effect called quantum tunneling to explore all lowest points of an energy landscape where classical approaches could become stuck in local minima. Our work used a novel algorithm formulated for AQO to solve a special type of MINLP problem. The research focused on determining: 1) if the problem is possible to solve using AQO, 2) if it can be solved by current hardware, 3) what the currently achievable performance is, 4) what the performance will be on projected future hardware, and 5) when AQO is likely to provide a benefit over classical computing methods. Two different methods, integer range and 1-hot encoding, were investigated for transforming the MINLP problem instance constraints into a mathematical structure that can be embedded directly onto the current D-Wave architecture. For testing and validation a D-Wave 2X device was used, as well as QxBranch’s QxLib software library, which includes a QC simulator based on simulated annealing. Our results indicate that it is mathematically possible to formulate the MINLP problem for AQO, but that currently available hardware is unable to solve problems of useful size. Classical general-purpose simulated annealing is currently able to solve larger problem sizes, but does not scale well and such methods would likely be outperformed in the future by improved AQO hardware with higher qubit connectivity and lower temperatures. If larger AQO devices are able to show improvements that trend in this direction, commercially viable solutions to the MINLP for particular applications could be implemented on hardware projected to be available in 5-10 years. Continued investigation into optimal AQO hardware architectures and novel methods for embedding MINLP problem constraints on to those architectures is needed to realize those commercial benefits.

Keywords: adiabatic quantum optimization, mixed integer nonlinear programming, quantum computing, NP-hard

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