Evolutionary Approach to Quantum and Reversible Circuits Synthesis

Lukáč, Martin; Perkowski, Marek; Goi, Hilton; Pivtoraiko, Mikhail; Yu, Chengtao; Chung, Fu-Lai; Jeech, Hyunkoo; Kim, Byung-Guk; Kim, Yong-Duk

doi:10.1023/b:aire.0000006605.86111.79

Cited by 68 publications

(45 citation statements)

References 32 publications

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“…Table 1 shows comparison of results between the KFLD and the method from [16] and Table 2 compares our KFLD with algorithms from [1], [15] and [25]. The evaluation counts the number of gates used to built the circuit and the quantum costs of the reversible gates are computed using the method used in the contemporary CAD algorithms [11], [12], [15]. Table 1 shows the name of the function benchmark, the number of gates (G) and the quantum cost (C) for the algorithm from [16] and the number of gates and the quantum cost for the KFLD in columns one, two, three, four and five respectively.…”

Section: Resultsmentioning

confidence: 99%

Synthesis of Quantum Arrays from Kronecker Functional Lattice Diagrams

Lukáč

Shah

Perkowski

et al. 2014

IEICE Trans. Inf. & Syst.

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SUMMARYReversible logic is becoming more and more popular due to the fact that many novel technologies such as quantum computing, low power CMOS circuit design or quantum optical computing are becoming more and more realistic. In quantum computing, reversible computing is the main venue for the realization and design of classical functions and circuits. We present a new approach to synthesis of reversible circuits using Kronecker Functional Lattice Diagrams (KFLD). Unlike many of contemporary algorithms for synthesis of reversible functions that use n × n Toffoli gates, our method synthesizes functions using 3 × 3 Toffoli gates, Feynman gates and NOT gates. This reduces the quantum cost of the designed circuit but adds additional ancilla bits. The resulting circuits are always regular in a 4-neighbor model and all connections are predictable. Consequently resulting circuits can be directly mapped in to a quantum device such as quantum FPGA [14]. This is a significant advantage of our method, as it allows us to design optimum circuits for a given quantum technology.

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Section: Resultsmentioning

confidence: 99%

Synthesis of Quantum Arrays from Kronecker Functional Lattice Diagrams

Lukáč

Shah

Perkowski

et al. 2014

IEICE Trans. Inf. & Syst.

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“…This is one important reason why evolutionary approaches for the design of binary and MV reversible circuits are receiving increasing attention (see e.g. [5,6,13,14]). …”

Section: Abstract-mentioning

confidence: 99%

On Some Basic Aspects of Ternary Reversible and Quantum Computing

Moraga

2014

2014 IEEE 44th International Symposium on Multiple-Valued Logic

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Abstract-In spite of the former remarks, there are relatively few contributions in the literature related to real multiplevalued reversible circuits, as compared to contributions on binary reversible circuits. Most, if not all of them, are dedicated to ternary reversible circuits [3,15,16,20]. Some careful basic mathematical studies support these efforts (see e.g. [1,4,10,11]).Reversible circuits are realized with fan-out free, feedback free, cascades of reversible gates, where reversible gates realize bijections on a given set of p n p-valued n-tuples. These constraints suggest that the design of reversible circuits is much more difficult than that of classical ("irreversible") digital circuits. This is one important reason why evolutionary approaches for the design of binary and MV reversible circuits are receiving increasing attention (see e.g. [5,6,13,14]).The present paper has been mainly motivated by the pair of nicely selfcontained contributions [15,16], (where basic gates, a circuits design algorithm, a non-trivial test circuit, and details of low level realization are discussed), and by some open questions and suggestions found in an unfortunately unfinished-unpublished paper of Marek Perkowski and colleagues [20].The next section reviews some mathematical aspects, Pauli matrices, representation of the basic ternary values in the Bloch sphere, and the role of the VilenkinChrestenson transform. In a following section an analysis is done to determine whether Barenco et al. type of structures [2], and Sasanian-Wang-Perkowski type of structures [22,24] may be used in ternary reversible computing, with similar advantages as in the binary case. A last section is devoted to introduce the Entanglement phenomenon and its presence in ternary quantum computing. Some conclusions will close the paper.

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“…Different from the stricter linear GP schemes in Spector et al (1999a) and Rubinstein (2001), the GP system described here used linear tree structures and was built to achieve more "degrees of freedom" in the construction and evolution of quantum circuits. Lukac and Perkowski (2002) and Lukac et al (2003) proposed a generic genetic algorithm to evolve arbitrary quantum circuit specified by a goal unitary matrix. They also proposed a specific encoding method which encoded quantum circuit as a structured string of quantum gates that can reflect the parallel and sequential framework of quantum circuit.…”

Section: Related Workmentioning

confidence: 99%

Evolving quantum circuits at the gate level with a hybrid quantum-inspired evolutionary algorithm

2008

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This paper proposes an approach to evolve quantum circuits at the gate level, based on a hybrid quantuminspired evolutionary algorithm. This approach encodes quantum gates as integers and combines the cost and correctness of quantum circuits into the fitness function. A fast algorithm of matrix multiplication with Kronecker product has been proposed to speed up the calculation of matrix multiplication in individuals evaluation. This algorithm is shown to be better than the known best algorithm for matrix multiplication when a certain condition holds. The approach of evolving quantum circuits is validated by some experiments and the effects of some parameters are investigated. And finally, some features of the approach are also discussed.

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Evolutionary Approach to Quantum and Reversible Circuits Synthesis

Cited by 68 publications

References 32 publications

Synthesis of Quantum Arrays from Kronecker Functional Lattice Diagrams

Synthesis of Quantum Arrays from Kronecker Functional Lattice Diagrams

On Some Basic Aspects of Ternary Reversible and Quantum Computing

Evolving quantum circuits at the gate level with a hybrid quantum-inspired evolutionary algorithm

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