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IEEE International Symposium on Smart Electronic Systems (iSES)

An Efficient 2D Mapping of Quantum Circuits to Nearest Neighbor Designs

Anirban Bhattacharjee, Hafizur Rahaman

Published Dec 1, 2021• 2 citations
Publisher

Abstract

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.

DOI
10.1109/ises52644.2021.00024

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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.
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, quantum computing has gained the attention of the researchers due to its ability to perform parallel and exponentially faster computation over classical computing. One of the prominent challenges for quantum circuits is to satisfy the nearest neighbor (NN) condition, i.e., the qubits of the computing gate must be placed adjacent. Based on this fact, here, in this paper, we have proposed a heuristic synthesis workflow to realize NN circuits in 2D grid configuration. The implemented approach has been evaluated over a broad range of benchmark circuits and we have reported the best results. To validate the efficiency of the stated approach, we have compared it with the previously reported works, an average improvement of 15.94%, 8.89% and 10.98% are obtained over the existing 2D works, and 44.72% and 70.35% are obtained over existing 1D works, respectively.
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.
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 couple of years, quantum computing has come out as emerging trends of computation not only due to its immense popularity but also for its commitment towards physical realization of quantum circuit in on-chip units. At the same time, the process of physical realization has faced several design constraints and one such problem is nearest neighbor (NN) enforcement which demands all the operating qubits to be placed adjacent in the implementable circuit. Though SWAP gate embedment can transform a design into NN architecture, it still creates overhead in the design. So, designing algorithms to restrict the use of SWAPs bears high importance. Considering this fact, in this work, we are proposing a heuristic-based improved qubit placement strategy for efficient implementation of NN circuit. Two different design policies are being developed here. In the first scheme, a global reordering technique based on clustering approach is shown. In the second scheme, a local reordering technique based on look-ahead policy is developed. This look-ahead strategy considers the impact over the gates in the circuit and thereby estimates the effect using a cost metric to decide the suitable option for SWAP implementation. Furthermore, the joint use of both the ordering schemes also has been explored here. To ascertain the correctness of our design algorithms, we have tested them over a wide range of benchmarks and the obtained results are compared with some state-of-the-art design approaches. From this comparison, we have witnessed a considerable reduction on SWAP cost in our design scheme against the reported works’ results.
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.