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IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

A New Heuristic for $N$ -Dimensional Nearest Neighbor Realization of a Quantum Circuit

Abhoy Kole, Kamalika Datta, Indranil Sengupta

Published Apr 18, 2017• 68 citations
Publisher

Abstract

One of the main challenges in quantum computing is to ensure error-free operation of the basic quantum gates. There are various implementation technologies of quantum gates for which the distance between interacting qubits must be kept within a limit for reliable operation. This leads to the so-called requirement of neighborhood arrangements of the interacting qubits, often referred to as nearest neighbor (NN) constraint. This is typically achieved by inserting SWAP gates in the quantum circuits, where a SWAP gate between two qubits exchanges their states. Minimizing the number of SWAP gates to provide NN compliance is an important problem to solve. A number of approaches have been proposed in this regard, based on local and global ordering techniques. In this paper, a generalized approach for combined local and global ordering of qubits have been proposed that is based on an improved heuristic for cost estimation and is also scalable. The approach can be extended to N -dimensional arrangement of qubits, for any arbitrary values of N . Practical constraints, however, restrict the maximum value of N to 3. Extensive experiments on benchmark functions have been carried out to evaluate the performance in terms of SWAP gate requirements. 3-D organization of qubits shows average reductions of 6.7% and 37.4%, respectively, in the number of SWAP gates over 2-D and 1-D organizations. Also compared to the best 2-D and 1-D results reported in the literature, on the average 8.7% and 8.4% reductions, respectively, are observed.

DOI
10.1109/tcad.2017.2693284

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A New Heuristic for NNN -Dimensional Nearest Neighbor Realization of a Quantum Circuit
One of the main challenges in quantum computing is to ensure error-free operation of the basic quantum gates. There are various implementation technologies of quantum gates for which the distance between interacting qubits must be kept within a limit for reliable operation. This leads to the so-called requirement of neighborhood arrangements of the interacting qubits, often referred to as nearest neighbor (NN) constraint. This is typically achieved by inserting SWAP gates in the quantum circuits, where a SWAP gate between two qubits exchanges their states. Minimizing the number of SWAP gates to provide NN compliance is an important problem to solve. A number of approaches have been proposed in this regard, based on local and global ordering techniques. In this paper, a generalized approach for combined local and global ordering of qubits have been proposed that is based on an improved heuristic for cost estimation and is also scalable. The approach can be extended to N -dimensional arrangement of qubits, for any arbitrary values of N . Practical constraints, however, restrict the maximum value of N to 3. Extensive experiments on benchmark functions have been carried out to evaluate the performance in terms of SWAP gate requirements. 3-D organization of qubits shows average reductions of 6.7% and 37.4%, respectively, in the number of SWAP gates over 2-D and 1-D organizations. Also compared to the best 2-D and 1-D results reported in the literature, on the average 8.7% and 8.4% reductions, respectively, are observed.
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.
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.
With recent interest in reversible and quantum computation, research in synthesis of reversible and quantum circuits has increased in momentum. With additional requirements of neighborhood interactions among qubits (with two basis states) being a necessity in some physical realizations, several works on obtaining nearest neighbor quantum gate realization by inserting SWAP gates have been reported. These methods are based on two broad optimization approaches, one based on global ordering, where qubits are ordered over the whole netlist, and the other based on local ordering for minimizing SWAP gate insertions on smaller segments of netlists. Further reductions in cost are possible by using multi-valued qudits that have more than two basis states. The present paper considers a quantum circuit based on the NCV library, and proposes a better SWAP gate insertion method based on local ordering that uses an N-gate lookahead approach to reduce cost. Experimental results on benchmark circuits and comparison against published works confirm the benefits of the proposed approach, with improvements over reported works obtained in the range of 27%-43% on the average and 54%-63% in the best case. The method is also scalable for larger circuits, with the longest runtime observed as 10 minutes.
Motivated by its promising applications e.g. for database search or factorization, significant progress has been made in the development of automated design methods for quantum circuits. But in order to keep up with recent physical developments in this domain, new technological constraints have to be considered. Limited interaction distance between gate qubits is one of the most common of these constraints. This led to the development of several strategies aiming at making a given quantum circuit nearest neighbor-compliant by inserting SWAP gates into the existing structure. Usually these strategies are of heuristic nature. In this work, we present an exact approach that enables nearest neighbor-compliance by inserting a minimal number of SWAP gates. Experiments demonstrate the applicability of the approach which enabled a comparison of results obtained by heuristic methods to the actual optimum.
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 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.