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International Conference on VLSI Design

A Dynamic Programming Based Graph Traversal Approach for Efficient Implementation of Nearest Neighbor Architecture in 2D

Sneha Lahiri, Megha Kesh, Rupsa Mandal, Anirban Bhattacharjee, Sovan Bhattacharya, Dola Sinha, Chandan Bandyopadhyay, Laxmidhar Biswal, Robert Wille, Rolf Drechsler

Published Jan 6, 2024• 1 citation
Publisher

Abstract

In the fascinating realm of quantum circuit design, tackling the intricacies of swap gate insertion presents a host of challenges. Among these, the prominent issue of the nearest neighbor condition emerges as a pivotal hurdle. This constraint not only shapes the layout and connectivity of the quantum circuit but also amplifies the complexity of orchestrating efficient quantum computations. While navigating the Quantum Realm, unraveling the overhead conundrum in swap Gate insertion, motivated us to propose an efficient 2D transformation scheme for NN quantum circuit realization with a primary objective of forming efficient NN structures while minimizing SWAP usage. The design phase involves the introduction of a new parameter to calculate qubit interactions in the circuit. We then employ a dynamic graph-based algorithm to determine the qubit interaction order. Finally, the resultant order is placed on the suitable grid to calculate the number of SWAP gates required. Our approach is extensively tested with various benchmarks, and it outperforms some state-of-the-art design works. In addition to this work, we also have shown how this NN designs can be transformed into Clifford +T based NN compliant architecture to get fault-tolerant property.

DOI
10.1109/vlsid60093.2024.00057

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In the fascinating realm of quantum circuit design, tackling the intricacies of swap gate insertion presents a host of challenges. Among these, the prominent issue of the nearest neighbor condition emerges as a pivotal hurdle. This constraint not only shapes the layout and connectivity of the quantum circuit but also amplifies the complexity of orchestrating efficient quantum computations. While navigating the Quantum Realm, unraveling the overhead conundrum in swap Gate insertion, motivated us to propose an efficient 2D transformation scheme for NN quantum circuit realization with a primary objective of forming efficient NN structures while minimizing SWAP usage. The design phase involves the introduction of a new parameter to calculate qubit interactions in the circuit. We then employ a dynamic graph-based algorithm to determine the qubit interaction order. Finally, the resultant order is placed on the suitable grid to calculate the number of SWAP gates required. Our approach is extensively tested with various benchmarks, and it outperforms some state-of-the-art design works. In addition to this work, we also have shown how this NN designs can be transformed into Clifford +T based NN compliant architecture to get fault-tolerant property.
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 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.
Since decades, quantum computing has received tremendous attention among the researchers due to its dominance over classical computing. But simultaneously it has faced some design challenges and implementation constraints in this long run. One such constraint to build quantum circuits is to satisfy the so-called Nearest Neighbor (NN) property in the implemented circuits. Using SWAP gates, this constraint can be satisfied. But this leads to another design issue, namely how to determine such NN designs with a minimum use of SWAP gates. In way to further explore this area, in this work, we propose a heuristic approach for efficient NN complaint representation of quantum circuits in 2D space. The developed technique is segmented in three stages - qubit selection, qubit placement and SWAP gate insertion. The stated approach has been tested over a wide spectrum of benchmarks and reductions in cost parameters are observed. Improvement of more than 17%, 3% over 2D designs and 35%, 22% over 1D designs on SWAP count and quantum cost can be reported, 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.
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.
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.