Quantum computers that are based on technologies like superconducting and quantum dots impose a physical constraint that requires interacting qubits to be adjacent. The initial placement of qubits and the swap gate insertion techniques affect the circuit cost. The authors proposed a global qubit ordering technique that considers fewer permutations for the number of interactions a qubit does with other qubits of its circuit. They also performed the local re‐ordering of qubits by attempting to reduce the cost as much as possible; the cost is estimated by defining a window with weights assigned in such a way that nearby gates to the current gate in question are given higher weightage. Experiments have been conducted on NCV benchmarks, and results have been compared with those of recent state‐of‐the‐art techniques. When compared with the existing works, the proposed method shows improvements of up to 53.3% for smaller benchmarks and up to 51.61% for larger benchmarks.
Quantum computers that are based on technologies like superconducting and quantum dots impose a physical constraint that requires interacting qubits to be adjacent. The initial placement of qubits and the swap gate insertion techniques affect the circuit cost. The authors proposed a global qubit ordering technique that considers fewer permutations for the number of interactions a qubit does with other qubits of its circuit. They also performed the local re‐ordering of qubits by attempting to reduce the cost as much as possible; the cost is estimated by defining a window with weights assigned in such a way that nearby gates to the current gate in question are given higher weightage. Experiments have been conducted on NCV benchmarks, and results have been compared with those of recent state‐of‐the‐art techniques. When compared with the existing works, the proposed method shows improvements of up to 53.3% for smaller benchmarks and up to 51.61% for larger benchmarks.
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.
Quantum computers that are based on superconducting and quantum dots have a fundamental requirement called Nearest Neighbour (NN) constraint satisfaction. They require interacting qubits to be directly connected (neighbours). If two non-adjacent qubits are to interact, they should be brought together first, so that interaction can occur. In this paper, we summarized state-of-the-art techniques and proposed a local ordering algorithm for transforming a given quantum circuit to a 2D NN-compliant circuit. Using the algorithm, a given circuit is decomposed into non-overlapping sub-circuits where each sub-circuit contains unique qubits. The insertion of swap gates occurs between every two consecutive sub-circuits (Ciand Ci+1) if Ci+1 do not satisfy the NN-constraint. Up to 50% reduction in swap count was obtained when compared to the most recent existing work on NCV benchmark circuits.
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.
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.
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.
A New Heuristic for N -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.