Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Circuit Theory and Applications

Quantum circuit physical design flow for 2D nearest‐neighbor architectures

Azim Farghadan, Naser Mohammadzadeh

Published Mar 17, 2017• 28 citations
Publisher

Abstract

Summary The physical design process takes a netlist generated by the logic synthesis process and places and routes the netlist on a physical platform. In some physical platforms, physical qubits must be placed on a 2D grid. Each node of the grid represents a qubit. In these platforms, performing quantum gates on non‐adjacent qubits is very error prone or hard to control. Therefore, quantum gates are limited to be performed on adjacent qubits. A communication channel of swap gates needs to be constructed if the qubits in the logical circuit are not adjacent. The algorithms used for mapping of qubits on the grid have important roles in reducing the number of swap gates and thus decreasing of the circuit latency. Focusing on this issue, in this paper, a flow for physical design of quantum circuits on a 2D grid is proposed. It contains three algorithms for finding the order of qubit placement, physical qubit placement, and routing. Simulation results show that the proposed flow not only decreases the average number of swap gates by about 16% compared with the best in the literature but also improves the average runtime by about 94% compared with it. Copyright © 2017 John Wiley & Sons, Ltd.

DOI
10.1002/cta.2335

Related papers

2D Qubit Placement of Quantum Circuits using LONGPATH

Ghosh, Mrityunjay, Nivedita Dey, Debdeep Mitra +1 more

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.

arXiv:2007.06804•Jul 14, 2020•1 citation

Mapping quantum circuits on 3D nearest-neighbor architectures

Azim Farghadan, Naser Mohammadzadeh

Abstract In some quantum technologies, an interaction is only allowed between physically adjacent qubits, hence the nearest-neighbor requirement is needed. In such technologies, quantum gates are limited to operate on adjacent qubits. To make a quantum circuit compliant with the nearest-neighbor requirement, SWAP gates are inserted into the circuit to move the interacting qubits of a gate to be adjacent to each other. The mapping of qubits on the physical environment has an important role on reducing the number of SWAP gates and thus the circuit latency. Focusing on this issue, in this paper, a method is proposed that maps a quantum circuit onto a 3D physical hardware such as a 3D optical lattice. A new methodology for this mapping problem is proposed based on a complex network spectral clustering algorithm and graph theory, which are suitable for very large scale networks. It includes three steps: finding the order of qubit mapping, placing physical qubits, and routing. Simulation results show that the proposed mapping approach not only decreases the average number of SWAP gates by about 37% but also improves the average runtime by about 87% for the 2D architecture compared to PAQCS. Moreover, it reduces the average number of SWAP gates for the 3D architecture by 17.1% compared to the best studies in the literatures.

Quantum Science and Technology•Apr 9, 2019•11 citations

Efficient Design of Quantum Circuits Using Nearest Neighbor Constraint in 3D Architecture

Leniency Marbaniang, Kamalika Datta

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.

Journal of Circuits Systems and Computers•Jun 24, 2018•5 citations

A method of mapping and nearest neighbor optimization for 2-D quantum circuits

Yuxin Zhang, Zhijin Guan, Longyong Ji +2 more

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%.

Quantum Information and Computation•Mar 1, 2020•1 citation

Fast Qubit Placement in 2D Architecture Using Nearest Neighbor Realization

Ritu Ranjan Shrivastwa, Kamalika Datta, Indranil Sengupta

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.

IEEE International Symposium on Nanoelectronic and Information Systems (iNIS)•Dec 1, 2015•42 citations

A Transformation-Based Quantum Physical Synthesis Approach for Nearest-Neighbor Architectures

Golriz Hoseinimanesh, Naser Mohammadzadeh

The physical synthesis concept for quantum circuits, the interaction between synthesis and physical design processes, was first introduced in our previous work. This concept inspires us to propose some techniques that can minimize the number of extra inserted SWAP operations required to run a circuit on a nearest-neighbor architecture. Minimizing the number of SWAP operations potentially decreases the latency and error probability of a quantum circuit. Focusing on this concept, we present a physical synthesis technique based on transformation rules to decrease the number of SWAP operations in nearest-neighbor architectures. After the qubits of a circuit are mapped onto the physical qubits provided by the target architecture, our procedure is fed by this mapping information. Our method uses the obtained placement and scheduling information to apply some transformation rules to the original netlist to decrease the number of extra SWAP gates required for running the circuit on the architecture. We follow two policies in applying a transformation rule, greedy and simulated-annealing-based policies. Simulation results show that the proposed technique decreases the average number of extra SWAP operations by about 20.6% and 24.1% based on greedy and simulated-annealing-based policies, respectively, compared with the best in the literature.

Quantum Reports•Aug 15, 2021•2 citations
Summary The physical design process takes a netlist generated by the logic synthesis process and places and routes the netlist on a physical platform. In some physical platforms, physical qubits must be placed on a 2D grid. Each node of the grid represents a qubit. In these platforms, performing quantum gates on non‐adjacent qubits is very error prone or hard to control. Therefore, quantum gates are limited to be performed on adjacent qubits. A communication channel of swap gates needs to be constructed if the qubits in the logical circuit are not adjacent. The algorithms used for mapping of qubits on the grid have important roles in reducing the number of swap gates and thus decreasing of the circuit latency. Focusing on this issue, in this paper, a flow for physical design of quantum circuits on a 2D grid is proposed. It contains three algorithms for finding the order of qubit placement, physical qubit placement, and routing. Simulation results show that the proposed flow not only decreases the average number of swap gates by about 16% compared with the best in the literature but also improves the average runtime by about 94% compared with it. Copyright © 2017 John Wiley & Sons, Ltd.
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.
Abstract In some quantum technologies, an interaction is only allowed between physically adjacent qubits, hence the nearest-neighbor requirement is needed. In such technologies, quantum gates are limited to operate on adjacent qubits. To make a quantum circuit compliant with the nearest-neighbor requirement, SWAP gates are inserted into the circuit to move the interacting qubits of a gate to be adjacent to each other. The mapping of qubits on the physical environment has an important role on reducing the number of SWAP gates and thus the circuit latency. Focusing on this issue, in this paper, a method is proposed that maps a quantum circuit onto a 3D physical hardware such as a 3D optical lattice. A new methodology for this mapping problem is proposed based on a complex network spectral clustering algorithm and graph theory, which are suitable for very large scale networks. It includes three steps: finding the order of qubit mapping, placing physical qubits, and routing. Simulation results show that the proposed mapping approach not only decreases the average number of SWAP gates by about 37% but also improves the average runtime by about 87% for the 2D architecture compared to PAQCS. Moreover, it reduces the average number of SWAP gates for the 3D architecture by 17.1% compared to the best studies in the literatures.
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 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%.
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.
The physical synthesis concept for quantum circuits, the interaction between synthesis and physical design processes, was first introduced in our previous work. This concept inspires us to propose some techniques that can minimize the number of extra inserted SWAP operations required to run a circuit on a nearest-neighbor architecture. Minimizing the number of SWAP operations potentially decreases the latency and error probability of a quantum circuit. Focusing on this concept, we present a physical synthesis technique based on transformation rules to decrease the number of SWAP operations in nearest-neighbor architectures. After the qubits of a circuit are mapped onto the physical qubits provided by the target architecture, our procedure is fed by this mapping information. Our method uses the obtained placement and scheduling information to apply some transformation rules to the original netlist to decrease the number of extra SWAP gates required for running the circuit on the architecture. We follow two policies in applying a transformation rule, greedy and simulated-annealing-based policies. Simulation results show that the proposed technique decreases the average number of extra SWAP operations by about 20.6% and 24.1% based on greedy and simulated-annealing-based policies, respectively, compared with the best in the literature.