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International Conference on Computing, Communication, Perception and Quantum Technology (CCPQT)

A Method of Mapping and Nearest-Neighbor for IBM QX Architecture

Chao Zhang, Zhijin Guan, Yang Qian, Shiguang Feng

Published Aug 1, 2022• 1 citation
Publisher

Abstract

In order to solve the problem of mapping a quantum circuit to IBM QX architecture and satisfy connectivity constraints. This paper presents a mapping method, which is divided into two parts: Qubit initial mapping and Nearest-neighbor optimization. To solve the problem of initial mapping of qubits, according to the execution order and interaction of quantum gates in quantum circuit, a qubit mapping order method based on the weight of qubits is proposed. Then, according to the qubit interaction degree in the coupling graph, the initial qubit mapping is completed. In order to solve the nearest-neighbor problem in the mapping process, the quantum cost of non-neighbor two-qubit gate is determined by introducing the lookahead quantum cost method. Our algorithm is evaluated on IBM Q 20. Experimental results show that the proposed algorithm can effectively complete the mapping task even in large-scale benchmark tests. The proposed method is verified by experiments and compared with the existing methods, the optimized results were obtained in 74% of the test circuits.

DOI
10.1109/ccpqt56151.2022.00076

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In order to solve the problem of mapping a quantum circuit to IBM QX architecture and satisfy connectivity constraints. This paper presents a mapping method, which is divided into two parts: Qubit initial mapping and Nearest-neighbor optimization. To solve the problem of initial mapping of qubits, according to the execution order and interaction of quantum gates in quantum circuit, a qubit mapping order method based on the weight of qubits is proposed. Then, according to the qubit interaction degree in the coupling graph, the initial qubit mapping is completed. In order to solve the nearest-neighbor problem in the mapping process, the quantum cost of non-neighbor two-qubit gate is determined by introducing the lookahead quantum cost method. Our algorithm is evaluated on IBM Q 20. Experimental results show that the proposed algorithm can effectively complete the mapping task even in large-scale benchmark tests. The proposed method is verified by experiments and compared with the existing methods, the optimized results were obtained in 74% of the test circuits.
In some practical quantum physical architectures, the qubits need to be distributed on 2-dimensional (2-D) grid structure to implement quantum computation. In order to map an 1-dimensional (1-D) quantum circuit into a 2-D grid structure and satisfy the nearest neighbor constraint of qubit interaction in the grid structure, a mapping method from 1-D quantum circuit to 2-D grid structure is proposed in this paper. This method firstly determines the order of placing qubits, and then presents the layout strategy of qubits in 2-D grid. We also proposed an algorithm for establishing interaction paths between non-adjacent qubits in 2-D grid structure, which can satisfy the physical constraints of the interaction of quantum bits in the grid in the process of mapping an 1-D quantum circuit to a 2-D grid structure. For some benchmark circuits, after using the method of this paper to place qubits, it is possible to make every 2-qubit gate in the circuit have a nearest neighbor, so that there is no need to use SWAP gate to establish channel routing. Compared with the latest available methods, the average optimization rate is 82.38%.
Quantum computers are becoming a reality today due to the rapid progress made by researchers in the last years. In the process of building quantum computers, IBM has developed several versions-starting from 5-qubit architectures like IBM QX2 and IBM QX4 to larger 16- or 20-qubit architectures. These architectures support arbitrary rotations of a single qubit and a controlled negation (CNOT) involving two qubits. The two qubit operations come with added coupling-map restrictions that only allow specific physical qubits to be the control and target qubits of the operation. In order to execute a quantum circuit on the IBM QX architecture, CNOT gates must satisfy the so-called coupling constraints of the architecture. Previous works addressed this issue with the objective of reducing the number of gates and the circuit depth. However, in this article, we show that further improvements are possible. To this end, we present a general approach for further improving the number of gate operations and depth of the mapped circuit. The proposed approach encompasses the selection of physical qubits, determining initial and local permutations efficiently to obtain the final circuit mapped to the given IBM QX architecture. Through experiments, improvements are observed over existing methods in terms of the number of gates and circuit depth.
Optimization based on QC (quantum cost) for quantum circuits and the LNN (Linear Nearest Neighbor) Architecture are the bases for mapping quantum logic circuits into physical systems. The correlation between the underlying optimization and the upper layer of quantum logic design is an important issue that needs to be emphasized during the mapping process. In order to improve the efficiency and robustness for the above problems, a fast optimization algorithm for LNN architecture based on quantum weight is proposed. Based on quantum priority, a wire sequence initialization method is designed. Then the neighboring arrangement rule of the NCV gate library circuit and the optimization algorithm are given. The experimental results show that the proposed strategies can effectively reduce the QC and the number of inserted SWAP gates. The average optimization rate reaches 12.3% compared to the corresponding results.
Abstract Recently, quantum computing is considered as a promising future computing paradigm. However, when implementing quantum circuits on a quantum device, it is necessary to ensure that quantum circuits satisfy nearest‐neighbor architecture constraints. When performing nearest‐neighbor architecture mapping for quantum circuits, it is inevitable to introduce SWAP gates, which will increase the overhead and reduce the fidelity. Therefore, it is crucial to complete the mapping with the minimum SWAP. In this paper, a 2D nearest‐neighbor architecture mapping method for quantum circuits is proposed based on deep reinforcement learning. In the initial mapping, an isomorphic graph initial mapping search algorithm is designed to quickly find the isomorphic graph between quantum circuit and architecture constraint graph. For quantum circuits without isomorphic graph mapping, the reordering algorithm of qubit impact factors is designed to obtain the initial placement position of qubits. In the SWAP gate addition, a qubit local reordering algorithm based on dueling deep‐Q‐network is designed to reduce SWAP gates. Experiments on the benchmark set B131 and IBM Q20 Tokyo verify that the proposed method can add fewer SWAP gates. Compared with the state‐of‐the‐art method, the average running time is accelerated by 63.1%, and the average SWAP gates added are reduced by 24.7%.
The recent progress in the physical realization of quantum computers (the first publicly available ones---IBM's QX architectures---have been launched in 2017) has motivated research on automatic methods that aid users in running quantum circuits on them. Here, certain physical constraints given by the architectures which restrict the allowed interactions of the involved qubits have to be satisfied. Thus far, this has been addressed by inserting SWAP and H operations. However, it remains unknown whether existing methods add a minimum number of SWAP and H operations or, if not, how far they are away from that minimum---an NP-complete problem. In this work, weaddress this by formulating the mapping task as a symbolic optimization problem that is solved using reasoning engines like Boolean satisfiability solvers. By this, we do not only provide a method that maps quantum circuits to IBM's QX architectures with a minimal number of SWAP and H operations, but also show by experimental evaluation that the number of operations added by IBM's heuristic solution exceeds the lower bound by more than 100% on average. An implementation of the proposed methodology is publicly available at http://iic.jku.at/eda/research/ibm_qx_mapping.
In the last few years, tremendous improvement in the field of quantum computing has been witnessed. Although quantum technologies such as ion-trap, NMR, quantum dots have emerged as the promising platforms for implementing quantum circuits but these technologies have faced several design issues. One such important design problem is the nearest neighbor condition, which requires the qubits to interact with adjacent neighbors. This problem can be addressed by adding SWAP gates in the circuit. By doing so, the overhead in the circuit increases thus NN designs with minimum number of SWAP gates need to be developed. Focusing on this, here, in this work, we introduce a heuristic design method for efficient NN realization of quantum circuits in 2D architecture. Our NN transformation process is carried out in two phases, where initially in the first phase, the input circuit is mapped to 2D configuration using a qubit placement strategy and then in the second phase NN designs are obtained through SWAP gate insertion. At the end, the design algorithm has been evaluated over a large set of benchmark functions and the results are compared with some of the existing works. From this comparison, it is seen that our proposed method performs better than the reported works.