scholarly journals Synthesis of quantum circuits based on incompletely specified functions and if-decision diagrams

2021 ◽  
pp. 84-97
Author(s):  
Anatoly A. Prihozhy
Keyword(s):  
Boolean Function ◽  
Quantum Circuit ◽  
Binary Decision Diagram ◽  
Quantum Circuits ◽  
Graph Representation ◽  
Decision Diagrams ◽  
Decomposition Products ◽  
Binary Decision ◽  
Binary Diagram ◽  
Functional Specification

The problem of synthesis and optimisation of logical reversible and quantum circuits from functional descriptions represented as decision diagrams is considered. It is one of the key problems being solved with the aim of creating quantum computing technology and quantum computers. A new method of stepwise transformation of the initial functional specification to a quantum circuit is proposed, which provides for the following project states: reduced ordered binary decision diagram, if-decision diagram, functional if-decision diagram, reversible circuit and quantum circuit. The novelty of the method consists in extending the Shannon and Davio expansions of a Boolean function on a single variable to the expansions of the same Boolean function on another function with obtaining decomposition products that are represented by incompletely defined Boolean functions. Uncertainty in the decomposition products gives remarkable opportunities for minimising the graph representation of the specified function. Instead of two outgoing branches of the binary diagram vertex, three outgoing branches of the if-diagram vertex are generated, which increase the level of parallelism in reversible and quantum circuits. For each transformation step, appropriate mapping rules are proposed that reduce the number of lines, gates and the depth of the reversible and quantum circuit. The comparison of new results with the results given by the known method of mapping the vertices of binary decision diagram into cascades of reversible and quantum gates shows a significant improvement in the quality of quantum circuits that are synthesised by the proposed method.

Embedded Nanowire Network Growth and Node Device Fabrication for GaAs-Based High-Density Hexagonal Binary Decision Diagram Quantum Circuits

2006 ◽  
Vol 45 (4B) ◽  
pp. 3614-3620 ◽  
Author(s):  
Takahiro Tamura ◽  
Isao Tamai ◽  
Seiya Kasai ◽  
Taketomo Sato ◽  
Hideki Hasegawa ◽  
...  
Keyword(s):  
Binary Decision Diagram ◽  
Device Fabrication ◽  
High Density ◽  
Quantum Circuits ◽  
Network Growth ◽  
Binary Decision ◽  
Nanowire Network

scholarly journals Calculation of selection probabilities of stack filters through BDD

2004 ◽  
Vol 17 (3) ◽  
pp. 421-442
Author(s):  
Suzana Stojkovic ◽  
Jaakko Astola ◽  
Karen Egiazarian
Keyword(s):  
Boolean Function ◽  
Spectral Method ◽  
Binary Decision Diagrams ◽  
Decision Diagrams ◽  
Binary Decision ◽  
Stack Filters ◽  
Selection Probabilities ◽  
Exponential Complexity

This paper presents a procedure for calculation of selection probabilities of stack filters using Binary decision diagrams (BDDs) to represent the positive Boolean function that defines the stack filter. The procedure is derived by a modification of the spectral method for calculation of selection probabilities of stack filters. The usage of BDDs, instead of vectors overcomes the exponential complexity of the corresponding spectral method and extends application of the spectral method to stack filters with large windows widths.

scholarly journals WPG-Controlled Quantum BDD Circuits with BDD Architecture on GaAs-Based Hexagonal Nanowire Network Structure

2012 ◽  
Vol 2012 ◽  
pp. 1-6
Author(s):  
Hong-Quan ZHao ◽  
Seiya Kasai
Keyword(s):  
Quantum Logic ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Combinational Circuit ◽  
Quantum Devices ◽  
Binary Decision ◽  
One Dimensional ◽  
Nanowire Network ◽  
Dimensional Electron Gas ◽  
Very High

One-dimensional nanowire quantum devices and basic quantum logic AND and OR unit on hexagonal nanowire units controlled by wrap gate (WPG) were designed and fabricated on GaAs-based one-dimensional electron gas (1-DEG) regular nanowire network with hexagonal topology. These basic quantum logic units worked correctly at 35 K, and clear quantum conductance was achieved on the node device, logic AND circuit unit, and logic OR circuit unit. Binary-decision-diagram- (BDD-) based arithmetic logic unit (ALU) is realized on GaAs-based regular nanowire network with hexagonal topology by the same fabrication method as that of the quantum devices and basic circuits. This BDD-based ALU circuit worked correctly at room temperature. Since these quantum devices and circuits are basic units of the BDD ALU combinational circuit, the possibility of integrating these quantum devices and basic quantum circuits into the BDD-based quantum circuit with more complicated structures was discussed. We are prospecting the realization of quantum BDD combinational circuitries with very small of energy consumption and very high density of integration.

scholarly journals Retrieving and Saving Meaningful Keywords in Unstructured PDF Documents using Binary Decision Diagrams

2019 ◽  
Vol 8 (3) ◽  
pp. 1950-1955
Keyword(s):  
Boolean Functions ◽  
Binary Decision Diagrams ◽  
Portable Document Format ◽  
Unstructured Data ◽  
Decision Diagrams ◽  
Boolean Operations ◽  
Binary Decision ◽  
Binary Diagram ◽  
Textual Data ◽  
New Framework

With the growing intricacy in data engendered and processed across sundry platforms today, the desideratum for consistency has grown. Structured data is utilized for a number of purposes which is not feasible with unstructured data. The purpose of this study was to convert data from unstructured format to structured in portable document format with the help of new framework using the concept of Binary Decision Diagrams and Boolean operations. Binary decision diagrams are data structures for representing Boolean functions taking Boolean as input and generating Boolean as output and hence creating a binary diagram. This research is mainly carried out to show how we can store large number of data easily in the form of bits. The entire focus is on retrieving the meaningful information from unstructured textual data in PDF documents using Boolean operations and bag model, thus, saving the meaningful keywords in the form of binary decision trees. Later on clustering the documents based on commonalities between the documents. This research presents a way for increasing the efficiency of converting unstructured data to structured in PDF and saving huge number of data in the form of bits using this novel framework

scholarly journals Connectivity matrix model of quantum circuits and its application to distributed quantum circuit optimization

2021 ◽  
Vol 20 (7) ◽  
Author(s):  
Ismail Ghodsollahee ◽  
Zohreh Davarzani ◽  
Mariam Zomorodi ◽  
Paweł Pławiak ◽  
Monireh Houshmand ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Quantum Computer ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Connectivity Matrix ◽  
Circuit Optimization ◽  
Novel Approach ◽  
The Matrix ◽  
Minimum Number ◽  
Two Phases

AbstractAs quantum computation grows, the number of qubits involved in a given quantum computer increases. But due to the physical limitations in the number of qubits of a single quantum device, the computation should be performed in a distributed system. In this paper, a new model of quantum computation based on the matrix representation of quantum circuits is proposed. Then, using this model, we propose a novel approach for reducing the number of teleportations in a distributed quantum circuit. The proposed method consists of two phases: the pre-processing phase and the optimization phase. In the pre-processing phase, it considers the bi-partitioning of quantum circuits by Non-Dominated Sorting Genetic Algorithm (NSGA-III) to minimize the number of global gates and to distribute the quantum circuit into two balanced parts with equal number of qubits and minimum number of global gates. In the optimization phase, two heuristics named Heuristic I and Heuristic II are proposed to optimize the number of teleportations according to the partitioning obtained from the pre-processing phase. Finally, the proposed approach is evaluated on many benchmark quantum circuits. The results of these evaluations show an average of 22.16% improvement in the teleportation cost of the proposed approach compared to the existing works in the literature.

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