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Soft Computing

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

Shengchao Ding, Zhi Hao Jin, Qing Yang

Published Jan 28, 2008• 21 citations
Publisher
DOI
10.1007/s00500-007-0273-9

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This paper illustrates the application of a Hybrid Quantum Inspired Evolutionary Algorithm (HQIEA) in evolving a variety of Quantum equivalents of classical circuits. Taking the matrix corresponding to an oracle as input, this HIQEA designs classical circuits using quantum gates. A library consisting of single, two and three qubit Quantum gates and the desired circuit matrix were given as input and algorithm was able to successfully design half adder, full adder and binary-gray conversion circuits apart from circuits for two, three and four qubit Boolean functions, using Quantum gates. The circuits obtained compare favorably with earlier attempts in terms of number of gates, ancillary inputs and garbage outputs required for constructing these circuits and the time taken to evolve them.
Quantum oracles play key roles in the studies of quantum computation and quantum information. But implementing quantum oracles efficiently with universal quantum gates is a hard work. Motivated by genetic programming, this paper proposes a novel approach to evolve quantum oracles with a hybrid quantum-inspired evolutionary algorithm. The approach codes quantum circuits with numerical values and combines the cost and correctness of quantum circuits into the fitness function. To speed up the calculation of matrix multiplication in the evaluation of individuals, a fast algorithm of matrix multiplication with Kronecker product is also presented. The experiments show the validity and the effects of some parameters of the presented approach. And some characteristics of the novel approach are discussed too.
In this work, a novel Hybrid Quantum Genetic Algorithm (HQGA) for the 0-1 Knapsack Problem (KP) is presented. It is based on quantum computing principles, such as qubits, superposition, and entanglement of states. The HQGA was simulated in the Qiskit simulator. Qiskit simulator is a platform developed by IBM that allows working with quantum computers at the level of circuits, pulses, and algorithms. The performance of HQGA is evaluated in three strongly correlated KP data sets, and computational results are compared with a Quantum-Inspired Evolutionary Algorithm (QIEA), a modified version of a QIEA (QIEA-Q), and a modified version of the HQGA (HQGA-Q). Experimental results demonstrate that the proposed HQGA can obtain the best solutions in all the KP data sets, and performs well on robustness.