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IEICE Transactions on Information and Systems

Mapping a Quantum Circuit to 2D Nearest Neighbor Architecture by Changing the Gate Order

Wakaki Hattori, Shigeru Yamashita

Published Oct 31, 2019• 7 citations
Publisher

Abstract

This paper proposes a new approach to optimize the number of necessary SWAP gates when we perform a quantum circuit on a two-dimensional (2D) NNA. Our new idea is to change the order of quantum gates (if possible) so that each sub-circuit has only gates performing on adjacent qubits. For each sub-circuit, we utilize a SAT solver to find the best qubit placement such that the sub-circuit has only gates on adjacent qubits. Each sub-circuit may have a different qubit placement such that we do not need SWAP gates for the sub-circuit. Thus, we insert SWAP gates between two sub-circuits to change the qubit placement which is desirable for the following sub-circuit. To reduce the number of such SWAP gates between two sub-circuits, we utilize A* algorithm.

DOI
10.1587/transinf.2018edp7439

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Journal of Circuits Systems and Computers•Jun 24, 2018•5 citations
This paper proposes a new approach to optimize the number of necessary SWAP gates when we perform a quantum circuit on a two-dimensional (2D) NNA. Our new idea is to change the order of quantum gates (if possible) so that each sub-circuit has only gates performing on adjacent qubits. For each sub-circuit, we utilize a SAT solver to find the best qubit placement such that the sub-circuit has only gates on adjacent qubits. Each sub-circuit may have a different qubit placement such that we do not need SWAP gates for the sub-circuit. Thus, we insert SWAP gates between two sub-circuits to change the qubit placement which is desirable for the following sub-circuit. To reduce the number of such SWAP gates between two sub-circuits, we utilize A* algorithm.
We propose an efficient approach to optimize the number of necessary SWAP gates when we perform a quantum circuit on IBM Q system. Our idea is to change the order of quantum gates (if possible) so that each sub-circuit has only gates performing on adjacent qubits. For each sub-circuit, we utilize a SAT solver to find the best qubit placement such that the subcircuit has only gates on adjacent qubits. Each sub-circuit may have a different qubit placement such that we do not need SWAP gates for the sub-circuit. Thus, we insert SWAP gates between two sub-circuits to change the qubit placement which is desirable for the following sub-circuit. To reduce the number of such SWAP gates between two sub-circuits, we utilize A* algorithm.
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 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.
Abstract In some quantum technologies, an interaction is only allowed between physically adjacent qubits, hence the nearest-neighbor requirement is needed. In such technologies, quantum gates are limited to operate on adjacent qubits. To make a quantum circuit compliant with the nearest-neighbor requirement, SWAP gates are inserted into the circuit to move the interacting qubits of a gate to be adjacent to each other. The mapping of qubits on the physical environment has an important role on reducing the number of SWAP gates and thus the circuit latency. Focusing on this issue, in this paper, a method is proposed that maps a quantum circuit onto a 3D physical hardware such as a 3D optical lattice. A new methodology for this mapping problem is proposed based on a complex network spectral clustering algorithm and graph theory, which are suitable for very large scale networks. It includes three steps: finding the order of qubit mapping, placing physical qubits, and routing. Simulation results show that the proposed mapping approach not only decreases the average number of SWAP gates by about 37% but also improves the average runtime by about 87% for the 2D architecture compared to PAQCS. Moreover, it reduces the average number of SWAP gates for the 3D architecture by 17.1% compared to the best studies in the literatures.
In order to achieve speedup over conventional classical computing for finding solution of computationally hard problems, quantum computing was introduced. Quantum algorithms can be simulated in a pseudo quantum environment, but implementation involves realization of quantum circuits through physical synthesis of quantum gates. This requires decomposition of complex quantum gates into a cascade of simple one qubit and two qubit gates. The methodological framework for physical synthesis imposes a constraint regarding placement of operands (qubits) and operators. If physical qubits can be placed on a grid, where each node of the grid represents a qubit then quantum gates can only be operated on adjacent qubits, otherwise SWAP gates must be inserted to convert non-Linear Nearest Neighbor architecture to Linear Nearest Neighbor architecture. Insertion of SWAP gates should be made optimal to reduce cumulative cost of physical implementation. A schedule layout generation is required for placement and routing apriori to actual implementation. In this paper, two algorithms are proposed to optimize the number of SWAP gates in any arbitrary quantum circuit. The first algorithm is intended to start with generation of an interaction graph followed by finding the longest path starting from the node with maximum degree. The second algorithm optimizes the number of SWAP gates between any pair of non-neighbouring qubits. Our proposed approach has a significant reduction in number of SWAP gates in 1D and 2D NTC architecture.
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.