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IEEE International Advance Computing Conference

Design of reversible Quantum equivalents of classical circuits using Hybrid Quantum Inspired Evolutionary Algorithm

Swanti Satsangi, C. Patvardhan

Published Jun 1, 2015• 2 citations
Publisher

Abstract

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.

DOI
10.1109/iadcc.2015.7154709

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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.
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The quantum circuit is the prime factor to realize quantum computation. This paper proposes a novel quantum-inspired evolutionary computation method to synthesize quantum circuits effectively and efficiently. Recently, the Clifford+T gate library has become popular, as the T gate has a better fault-tolerant and error correction efficacy, which is essential to near-term quantum computation. The proposed quantum-inspired evolutionary computation is more flexible in constructing diverse solutions than the classical synthesis method. The entangled local search mechanism further enhances the ability to discover the optimal solutions on an efficient frontier. The encoding can be slightly changed to achieve various gate libraries circuit synthesis in the quantum or reversible Boolean circuits. The experiments demonstrate that our proposed method can be more effective in composing a compact quantum circuit than the state-of-the-art method. Meanwhile, the T-depth can attain an optimal value without ancilla bits. Furthermore, we provide an illustration to construct the function equivalent quantum circuit with the NOT, CNOT, Controlled-Square-Root-of-NOT quantum gate library (NCV). We also conduct exhaustion to prove that our synthesized circuit is an optimal solution, requiring far fewer resources in time and evaluation than exhaustion.
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.
Quantum computing is a new way of data processing based on the concept of quantum mechanics. Quantum circuit design is a process of converting a quantum gate to a series of basic gates and is divided into two general categories based on the decomposition and composition. In the second group, using evolutionary algorithms and especially genetic algorithms, multiplication of matrix gates was used to achieve the final characteristic of quantum circuit. Genetic programming is a subfield of evolutionary computing in which computer programs evolve to solve studied problems. In past research that has been done in the field of quantum circuits design, only one cost metrics (usually quantum cost) has been investigated. In this paper for the first time, a multi-objective approach has been provided to design quantum circuits using genetic programming that considers the depth and the cost of nearest neighbor metrics in addition to quantum cost metric. Another innovation of this article is the use of two-step fitness function and taking into account the equivalence of global phase in quantum gates. The results show that the proposed method is able to find a good answer in a short time.
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Recent advancements in computing speed and capacity of Artificial Intelligence (AI) algorithms have reached a saturation level in performance due to the continuous application of Moore's law which resulted in the memory wall phenomenon. Quantum computing (QC), based on the principles of quantum mechanics which include superposition and entanglement, has the potential to contribute to the advancements of AI by providing exponential speedup. Quantum computers use quantum bits, also known as qubits, as the metric to demonstrate the power of quantum technology. Qubits, the fundamental unit of quantum information can exist in two states, 0 and 1, simultaneously, leveraging the principle of superposition. Quantum gates are the building blocks of quantum circuits, operating on qubits to transform one quantum state into another, and are comparative to classical logic gates. Designing and simulating quantum circuits can be completed using the Qiskit library design by IBM. Qiskit is a cloud-based, open access platform to real quantum computers with 5 to 16 qubits. This paper offers a straightforward tutorial on implementing one, two and three-qubit quantum gates, as well as designing quantum circuits using the Qiskit library, illustrated with an example of a quantum half adder implementation.