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IEEE Access

Nearest Neighbor Transformation of Quantum Circuits in 2D Architecture

Xueyun Cheng, Zhijin Guan, Pengcheng Zhu

Published Jan 1, 2020• 14 citations
Publisher

Abstract

In recent years, quantum computing has received extensive attention for its superior efficiency and application potential. For some physical architecture, one qubit can only interact with its adjacent qubits, SWAP gates are inserted to make a quantum circuit nearest neighbor compliant. The initial qubit placement algorithm in a 2D grid structure is proposed based on the constructed interaction cost metric model, and the method of dynamic grid decision is given. In order to obtain a better way of inserting SWAP gates, the gate level and circuit level interaction routing policies are put forward, and a heuristic pruning of interaction routing records is employed so as to reduce the runtime and additional quantum cost. Experimental results show that our proposed methods can achieve better performance than existing methods, and the average optimization rate of quantum cost is 21.76% and 17.23% respectively.

DOI
10.1109/access.2020.3043497

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In recent years, quantum computing has received extensive attention for its superior efficiency and application potential. For some physical architecture, one qubit can only interact with its adjacent qubits, SWAP gates are inserted to make a quantum circuit nearest neighbor compliant. The initial qubit placement algorithm in a 2D grid structure is proposed based on the constructed interaction cost metric model, and the method of dynamic grid decision is given. In order to obtain a better way of inserting SWAP gates, the gate level and circuit level interaction routing policies are put forward, and a heuristic pruning of interaction routing records is employed so as to reduce the runtime and additional quantum cost. Experimental results show that our proposed methods can achieve better performance than existing methods, and the average optimization rate of quantum cost is 21.76% and 17.23% respectively.
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.
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 recent years, the semiconductor industry is increasingly considering alternative computation schemes and in this conjuncture quantum computing has come up as a promising alternative due its ability to perform parallel computations (by exploiting superposition) and capacity to solve some of the intractable problems exponentially faster. But one of the criteria in the realization of quantum circuits is that corresponding descriptions demand a so-called nearest neighbour (NN) constraint to be satisfied. One of the possible solutions towards satisfying such constraints is through the insertion of SWAP gates that makes the qubit interactions within a gate adjacent. But since the incorporation of SWAP gates increases the cost of the circuits, strategies should be employed which satisfy the NN constraint while placing SWAP gates so that the cost are reduced. In this work, we propose improved design strategies to realize low-cost NN-compliant quantum circuits. Two approaches are introduced, where the first approach relies on a graph traversal process and uses heuristics in critical decision-making conditions to design a 1D NN-compliant representation. The second approach considers qubit-to-qubit interactions and realizes the circuits in a 2D platform based on some weighted metric. Both the designs are evaluated over a wide spectrum of benchmarks and results have been compared with related works. In those comparisons, we have seen that our approaches perform fairly better than the reported ones.
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.
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.
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%.