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DEStech Transactions on Engineering and Technology Research

Quantum State Analysis and Optimal Logic Synthesis for Linear Nearest Neighbor Architecture

Hai Cheng Xu, Zhijin Guan, Xueyun Cheng, Pengcheng Zhu

Published Mar 14, 2017• 0 citations
Publisher

Abstract

Real quantum computing technologies have different restrictions and constraints which need to be considered during circuit synthesis. In certain technologies, only physically adjacent qubits can interact. It is common to use a pair of SWAP gates to bring the control and target qubits of any quantum gate to adjacent lines and maintain correct circuit functionality. This paper introduces a new method to synthesize linear nearest neighbor quantum circuit on the base of the analysis of quantum state in circuit. For all 3-qubit quantum circuit, experimental results shows that our algorithm can reduce the quantum cost by approximately 30% on average compared with one recent proposed method.

DOI
10.12783/dtetr/icca2016/6070

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Real quantum computing technologies have different restrictions and constraints which need to be considered during circuit synthesis. In certain technologies, only physically adjacent qubits can interact. It is common to use a pair of SWAP gates to bring the control and target qubits of any quantum gate to adjacent lines and maintain correct circuit functionality. This paper introduces a new method to synthesize linear nearest neighbor quantum circuit on the base of the analysis of quantum state in circuit. For all 3-qubit quantum circuit, experimental results shows that our algorithm can reduce the quantum cost by approximately 30% on average compared with one recent proposed method.
Synthesis and optimization of quantum circuits have received significant attention from researchers in recent years. Developments in the physical realization of qubits in quantum computing have led to new physical constraints to be addressed. One of the most important constraints that is considered by many researchers is the nearest neighbor constraint which limits the interaction distance between qubits for quantum gate operations. Various works have been reported in the literature that deal with nearest neighbor compliance in multi-dimensional (mostly 1D and 2D) qubit arrangements. This is normally achieved by inserting SWAP gates in the gate netlist to bring the interacting qubits closer together. The main objective function to minimize here is the number of SWAP gates. The present paper proposes an efficient qubit placement strategy in a three-dimensional (3D) grid that considers not only qubit interactions but also the relative positions of the gates in the circuit. Experimental evaluation on a number of benchmark circuits show that the proposed method reduces the number of SWAP gates by 16.2% to 47.0% on the average as compared to recently published works.
In this paper, a synthesis method is proposed based on vector transformation for linear nearest neighbor quantum circuits.Its aim is to construct a linear nearest neighbor quantum circuit, and to reduce the quantum cost of the linear reversible circuit.The vector representation of the sequence of the circuit lines and qubits of quantum gate is given in this method.It realizes the nearest neighbor of the quantum circuit by moving the position of the qubits vector elements, and it does not cause confusion due to comparison and transformation of two vector elements in the circuit.The number of SWAP gates needed to make the quantum circuit nearest neighbors is given, and its correctness is proven.Compared with the current quantum circuit synthesis algorithms, the average optimization rate of the quantum cost is 39.69% for typical benchmark circuits.The algorithm can be applied to all quantum circuits of 2-qubit quantum gates, and can be used in large quantum circuits.
Design and synthesis of quantum circuits have gained huge momentum during the last few years. With various physical constraint sone of the major issues is in making quantum circuits nearest neighbor complaint. The existing one and two dimensional architectures for the placement of qubits does not scale well for larger circuits. The situation thus demands for a faster approach to solve the problem. To make a quantum circuit nearest neighbor compliant, SWAP gates are inserted in the quantum gate circuit to bring the interacting qubits of a gate adjacent. We have proposed a faster method with a simple yet effective algorithm to minimize the number of SWAP gates for adjacent interactions. The time required for processing does not exceed one second even for larger benchmark circuits. The proposed method is found to reduce the number of SWAP gates on an average by 9.5% compared to the best results in previous works on 2D architectures, and by 45.7% compared to the best results on 1D architecture.
In order to realize the linear nearest neighbor(LNN) of quantum circuits and reduce the quantum cost of the linear reversible quantum circuits, a method of synthesizing and optimizing linear reversible quantum circuits based on matrix multiplication is proposed. This method shows the matrix representation of linear quantum circuits by proposing the matrix representation of the CNOT gate and the SWAP gate. The rule of judging whether a two-qubit quantum circuit is in LNN state is proposed. The LNN realization by adding SWAP gates is proposed and the equivalence of two ways of adding SWAP gates is proved. The elimination rules of SWAP gates between two overlapped adjacent quantum gates in different cases are proposed, which reduce the quantum cost of quantum circuits after realizing the LNN architecture. We propose a particular algorithm to realize the LNN, which can effectively reduce the quantum cost and improve calculation efficiency by inserting the SWAP gates on parallel computing devices. Experiments show that the quantum cost can be improved by 34.31% on average and the speed-up ratio of the GPU-based algorithm can reach 4 times compared with the CPU-based algorithm.
Linear Nearest Neighbor (LNN) synthesis in reversible circuits has emerged as an important issue in terms of technological implementation for quantum computation. The objective is to obtain a LNN architecture with minimum gate cost. As achieving optimal synthesis is a hard problem, heuristic methods have been proposed in recent literature. In this work we present a graph partitioning based approach for LNN synthesis with reduction in circuit cost. In particular, the number of SWAP gates required to convert a given gate-level quantum circuit to its equivalent LNN configuration is minimized. Our algorithm determines the reordering of indices of the qubit line(s) for both single control and multiple controlled gates. Experimental results for placing the target qubits of Multiple Controlled Toffoli (MCT) library of benchmark circuits show a significant reduction in gate count and quantum gate cost compared to those of related research works.
In the present era of computation, quantum computing may offer a new direction as it allows to solve certain problems significantly faster than classical solutions. But it also has been found that there are several constrains in performing a successful realization of quantum circuits. One such constraint is the nearest neighbor (NN) criterion which states that qubits which interact with each other have to be adjacent. Motivated by this objective, in this work we propose a linear qubit placement technique that effectively rearranges the qubits and transforms quantum circuits to improved NN-based designs by inserting SWAPs. Furthermore, for placing these SWAPs in appropriate positions, we implemented a look-ahead strategy that considers the effect of the rest of the gates and computes a corresponding impact value which guides the insertion of the SWAP gates. To this extent, we consider three different strategies to evaluate the corresponding "look-ahead effects" and their influence on existing gates. At the end of this work, we have evaluated the developed methodology over a wide range of benchmarks and compared the results with existing related works. In this comparison, we have seen that the proposed technique outperforms the related works and provides substantial reductions in SWAP overhead.