Author

# Martin Lukac

Other affiliations: Portland State University, Katholieke Universiteit Leuven, Tohoku University ...read more

Bio: Martin Lukac is an academic researcher from Nazarbayev University. The author has contributed to research in topics: Quantum computer & Quantum circuit. The author has an hindex of 12, co-authored 85 publications receiving 654 citations. Previous affiliations of Martin Lukac include Portland State University & Katholieke Universiteit Leuven.

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TL;DR: The evolutionary computation approach to the problem of optimal synthesis of Quantum and reversible Logic circuits and several variants of these gates have been automatically synthesized from quantum primitives for the first time.

Abstract: The paper discusses the evolutionary computation approach to the problem of optimal synthesis of Quantum and Reversible Logic circuits. Our approach uses standard Genetic Algorithm (GA) and its relative power as compared to previous approaches comes from the encoding and the formulation of the cost and fitness functions for quantum circuits synthesis. We analyze new operators and their role in synthesis and optimization processes. Cost and fitness functions for Reversible Circuit synthesis are introduced as well as local optimizing transformations. It is also shown that our approach can be used alternatively for synthesis of either reversible or quantum circuits without a major change in the algorithm. Results are illustrated on synthesized Margolus, Toffoli, Fredkin and other gates and Entanglement Circuits. This is for the first time that several variants of these gates have been automatically synthesized from quantum primitives.

93 citations

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15 Jul 2002TL;DR: A generic GA to evolve arbitrary quantum by using genetic algorithm as well as a specific encoding that reduces the time of calculating the resultant unitary matrices of chromosomes is proposed.

Abstract: In this paper we focus on a general approach of using genetic algorithm (GA) to evolve Quantum circuits (QC). We propose a generic GA to evolve arbitrary quantum. circuit specified by a (target) unitary matrix as well as a specific encoding that reduces the time of calculating the resultant unitary matrices of chromosomes. We demonstrate that, in contrast to previous approaches, our encoding allows synthesis of small quantum circuits of arbitrary type, using standard genetic operators.

79 citations

01 Jan 2003

TL;DR: An informed genetic algorithm is used to evolve arbitrary quantum circuit specified by a (target) unitary matrix, specific encoding that reduces the time of calculating the resultant unitary matrices of chromosomes, and an evolutionary algorithm specialized to permutation circuits specified by truth tables are used.

Abstract: A new approach to synthesis of permutation class of quantum logic circuits has been proposed in this paper. This approach produces better results than the previous approaches based on classical reversible logic and can be easier tuned to any particular quantum technology such as nuclear magnetic resonance (NMR). First we synthesize a library of permutation (pseudobinary) gates using a Computer-Aided-Design approach that links evolutionary and combinatorics approaches with human experience and creativity. Next the circuit is designed using these gates and standard 1*1 and 2*2 quantum gates and finally the optimizing tautological transforms are applied to the circuit, producing a sequence of quantum operations being close to operations practically realizable. These hierarchical stages can be compared to standard gate library design, generic logic synthesis and technology mapping stages of classical CAD systems, respectively. We use an informed genetic algorithm to evolve arbitrary quantum circuit specified by a (target) unitary matrix, specific encoding that reduces the time of calculating the resultant unitary matrices of chromosomes, and an evolutionary algorithm specialized to permutation circuits specified by truth tables. We outline interactive CAD approach in which the designer is a part of feedback loop in evolutionary program and the search is not for circuits of known specifications, but for any gates with high processing power and small cost for given constraints. In contrast to previous approaches, our methodology allows synthesis of both: small quantum circuits of arbitrary type (gates), and permutation class circuits that are well realizable in particular technology.

67 citations

01 Jan 2002

TL;DR: This work proposes an automated synthesis of Reversible logic circuits using Darwinian and Lamarckian Genetic Algorithms, and shows good results for synthesis of both random functions and benchmark functions with practical meaning, such as adders.

Abstract: We propose an automated synthesis of Reversible logic (RL) circuits using Darwinian and Lamarckian Genetic Algorithms (GA). Our designs are in a form of cascades of generalized gates which generalize factorized Exclusive-Or-Sum-of-Products (ESOP) circuits. GA can be used to explore the problem space of combinational functions and here it is used to evolve reversible logic circuits. We emphasize the role of problem encoding a well-designed encoding leads to improved results. Our method with well-encoded circuits is compared to standard method on classical benchmarks in GA, and shows good results for synthesis of both random functions and benchmark functions with practical meaning, such as adders.

47 citations

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19 May 2005TL;DR: An approach to test generation and fault localization for a wide category of fault models, which uses both deterministic and probabilistic tests to detect faults and uses special measurement gates to determine the internal states.

Abstract: It is believed that quantum computing will begin to have a practical impact in industry around year 2010. We propose an approach to test generation and fault localization for a wide category of fault models. While in general we follow the methods used in test of standard circuits, there are two significant differences: (2) we use both deterministic and probabilistic tests to detect faults, (2) we use special measurement gates to determine the internal states. A fault table is created that includes probabilistic information. "Probabilistic set covering" and "probabilistic adaptive trees" that generalize those known in standard circuits, are next used.

39 citations

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TL;DR: There is, I think, something ethereal about i —the square root of minus one, which seems an odd beast at that time—an intruder hovering on the edge of reality.

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.
Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

33,785 citations

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02 Jun 2003TL;DR: A transformation based algorithm for the synthesis of such a reversible circuit in terms of n /spl times/ n Toffoli gates is presented and produces very good results for larger problems.

Abstract: A digital combinational logic circuit is reversible if it maps each input pattern to a unique output pattern. Such circuits are of interest in quantum computing, optical computing, nanotechnology and low-power CMOS design. Synthesis approaches are not well developed for reversible circuits even for small numbers of inputs and outputs.In this paper, a transformation based algorithm for the synthesis of such a reversible circuit in terms of n × n Toffoli gates is presented. Initially, a circuit is constructed by a single pass through the specification with minimal look-ahead and no back-tracking. Reduction rules are then applied by simple template matching. The method produces near-optimal results for 3-input circuits and also produces very good results for larger problems.

520 citations

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KAIST

^{1}TL;DR: The results show that the updated QEA makes QEA more powerful than the previous QEA in terms of convergence speed, fitness, and robustness.

Abstract: From recent research on combinatorial optimization of the knapsack problem, quantum-inspired evolutionary algorithm (QEA) was proved to be better than conventional genetic algorithms. To improve the performance of the QEA, this paper proposes research issues on QEA such as a termination criterion, a Q-gate, and a two-phase scheme, for a class of numerical and combinatorial optimization problems. A new termination criterion is proposed which gives a clearer meaning on the convergence of Q-bit individuals. A novel variation operator H/sub /spl epsi// gate, which is a modified version of the rotation gate, is proposed along with a two-phase QEA scheme based on the analysis of the effect of changing the initial conditions of Q-bits of the Q-bit individual in the first phase. To demonstrate the effectiveness and applicability of the updated QEA, several experiments are carried out on a class of numerical and combinatorial optimization problems. The results show that the updated QEA makes QEA more powerful than the previous QEA in terms of convergence speed, fitness, and robustness.

446 citations

01 Jan 2009

TL;DR: In this paper, the authors map the vast quantities of short sequence fragments produced by next-generation sequencing platforms, and present a set of programs that can be used to map these fragments.

Abstract: Mapping the vast quantities of short sequence fragments produced by next-generation sequencing platforms is a challenge. What programs are available and how do they work?

306 citations