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

Symposium on Integrated Circuits and Systems Design

Finding optimal qubit permutations for IBM's quantum computer architectures

Alexandre A. A. de Almeida, Gerhard W. Dueck, Alexandre César Rodrigues da Silva

Published Aug 26, 2019• 25 citations
Publisher

Abstract

IBM offers quantum processors for Clifford+T circuits. The only restriction is that not all CNOT gates are implemented and must be substituted with alternate sequences of gates. Each CNOT has its own mapping with a respective cost. However, by permuting the qubits, the number of CNOT that need mappings can be reduced. The problem is to find a good permutation without an exhaustive search. In this paper we propose a solution for this problem. The permutation problem is formulated as an Integer Linear Programming (ILP) problem. Solving the ILP problem, the lowest cost permutation for the CNOT mappings is guaranteed. To test and validated the proposed formulation, quantum architectures with 5 and 16 qubits were used. The ILP formulation along with mapping techniques found circuits with up to 64% fewer gates than other approaches.

DOI
10.1145/3338852.3339829

Related papers

CNOT Gate Mappings to Clifford+T Circuits in IBM Architectures

Alexandre A. A. de Almeida, Gerhard W. Dueck, Alexandre César Rodrigues da Silva

IBM architectures impose some restrictions the quantum circuits that can be implemented. Only gates from Clifford+T gate library can be used and not all of the CNOT gates are available. Some of the CNOT need to be mapped into a sequence of gates. In this paper we present a set of mappings to conform to the restrictions imposed by IBM's architectures. These mappings require fewer gates than SWAP gates. It is well known, that permuting the qubits will yield circuits with different number of gates. The design in this paper uses efficient mappings with qubit permutations to obtain circuits with a reduced number of gates. Results have shown that the proposed approach reduces circuits by up to 64% compared with Qiskit and up to 42% compared with another mapping algorithm.

IEEE International Symposium on Multiple-Valued Logic (ISMVL)•May 1, 2019•13 citations

Metodologia para o mapeamento de circuitos quânticos e reversíveis para arquiteturas IBM Q

Alexandre Mendes de [UNESP] Almeida Junior

Research in the field of quantum circuits has increased as technology advances in the development of quantum computers. IBM offers access to quantum computers via the cloud service called IBM Q. However, these architectures have some restrictions regarding the types of quantum gates that can be realized. This work proposes a methodology for the mapping of quantum and reversible circuits to the architectures made available by the IBM Q project. The methodology consists in finding CNOT mappings using a set of defined qubits movements to satisfy the architectures constraints by adding as few gates as possible. In order to reduce the number of CNOT gates needing mapping, the permutation of the circuit can be changed. One alternative to find this permutation is trough exhaustive search. However, is not feasible as the number of qubit increases. To solve this problem, the permutation problem was formulated as an Integer Linear Programming problem. The mapping of quantum circuits realized with non-implementable gates and reversible Toffoli circuits to the IBM quantum architectures were proposed in this work as well. This was done by adapting the developed CNOT mappings along with the Integer Linear Programming formulation. The proposed methodology was evaluated by mapping quantum and reversible circuits to an IBM quantum architectures with 5 and 16 qubits. The results were compared with two algorithms that map quantum circuits to IBM architectures. The cost metric used in the evaluation were the number of quantum gates and the number of levels (depth) of the circuits. Experimental results have shown that the proposed methodology outperforms the other approaches regarding the circuits' size. The results of the methodology used to implement quantum (with non-implementable gates) and Toffoli circuits to IBM architectures have shown that the mapping targeting a specific architecture constraints results in a smaller mapped circuit. The methodology developed can be easily adapted to any quantum architecture. Also, the proposed Integer Linear Programming formulation can be used in any reversible circuit and can be applied in other research areas.

•Aug 23, 2019•0 citations

Optimization of Circuits for IBM's Five-Qubit Quantum Computers

Gerhard W. Dueck, Anirban Pathak, Md. Mazder Rahman +2 more

IBM has made several quantum computers available to researchers around the world via cloud services. Two architectures with five qubits, one with 16, and one with 20 qubits are available to run experiments. The IBM architectures implement gates from the Clifford+T gate library. However, each architecture only implements a subset of the possible CNOT gates. In this paper, we show how Clifford+T circuits can efficiently be mapped into the two IBM quantum computers with 5 qubits. We further present an algorithm and a set of circuit identities that may be used to optimize the Clifford+T circuits in terms of gate count and number of levels. It is further shown that the optimized circuits can considerably reduce the gate count and number of levels and thus produce results with better fidelity.

arXiv:1810.00129•Euromicro Conference on Digital System Design (DSD)•Aug 1, 2018•32 citations

Improved Mapping of Quantum Circuits to IBM QX Architectures

Abhoy Kole, Stefan Hillmich, Kamalika Datta +2 more

Quantum computers are becoming a reality today due to the rapid progress made by researchers in the last years. In the process of building quantum computers, IBM has developed several versions-starting from 5-qubit architectures like IBM QX2 and IBM QX4 to larger 16- or 20-qubit architectures. These architectures support arbitrary rotations of a single qubit and a controlled negation (CNOT) involving two qubits. The two qubit operations come with added coupling-map restrictions that only allow specific physical qubits to be the control and target qubits of the operation. In order to execute a quantum circuit on the IBM QX architecture, CNOT gates must satisfy the so-called coupling constraints of the architecture. Previous works addressed this issue with the objective of reducing the number of gates and the circuit depth. However, in this article, we show that further improvements are possible. To this end, we present a general approach for further improving the number of gate operations and depth of the mapped circuit. The proposed approach encompasses the selection of physical qubits, determining initial and local permutations efficiently to obtain the final circuit mapped to the given IBM QX architecture. Through experiments, improvements are observed over existing methods in terms of the number of gates and circuit depth.

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems•Dec 27, 2019•39 citations

Optimal Layout-Aware CNOT Circuit Synthesis with Qubit Permutation

Irfansha Shaik, Jaco van de Pol

CNOT optimization plays a significant role in noise reduction for Quantum Circuits. Several heuristic and exact approaches exist for CNOT optimization. In this paper, we investigate more complicated variations of optimal synthesis by allowing qubit permutations and handling layout restrictions. We encode such problems into Planning, SAT, and QBF. We provide optimization for both CNOT gate count and circuit depth. For experimental evaluation, we consider standard T-gate optimized benchmarks and optimize CNOT sub-circuits. We show that allowing qubit permutations can further reduce up to 56% in CNOT count and 46% in circuit depth. In the case of optimally mapped circuits under layout restrictions, we observe a reduction up to 17% CNOT count and 19% CNOT depth.

arXiv:2408.04349•Frontiers in artificial intelligence and applications•Oct 16, 2024•4 citations

Efficient Realizations of CNOT gates in IBM’s Quantum Computers

Alexandre A. A. de Almeida, Gerhard W. Dueck, Alexandre César Rodrigues da Silva

IBM's quantum computers implement gates from Clifford +T gate library. All single qubit gates are implemented, but only a subset of the possible CNOT are provided. It is well known that the functionally of the missing gates can be achieved by a sequence of gates. The sequence of gates is based on SWAP gates. Up to seven elementary gates are required to implement a SWAP gate. In this paper we show how the same effect can be achieved with fewer gates. To show the potential of the proposed transformations, an example is presented where a reduction of 44% in the gate count and a 26% reduction in the number of levels for IBM's QX5 computer is achieved. An algorithm that is considered state of the art, is used for the comparison.

International Symposium on Embedded Computing and System Design (ISED)•Dec 1, 2018•6 citations
IBM offers quantum processors for Clifford+T circuits. The only restriction is that not all CNOT gates are implemented and must be substituted with alternate sequences of gates. Each CNOT has its own mapping with a respective cost. However, by permuting the qubits, the number of CNOT that need mappings can be reduced. The problem is to find a good permutation without an exhaustive search. In this paper we propose a solution for this problem. The permutation problem is formulated as an Integer Linear Programming (ILP) problem. Solving the ILP problem, the lowest cost permutation for the CNOT mappings is guaranteed. To test and validated the proposed formulation, quantum architectures with 5 and 16 qubits were used. The ILP formulation along with mapping techniques found circuits with up to 64% fewer gates than other approaches.
IBM architectures impose some restrictions the quantum circuits that can be implemented. Only gates from Clifford+T gate library can be used and not all of the CNOT gates are available. Some of the CNOT need to be mapped into a sequence of gates. In this paper we present a set of mappings to conform to the restrictions imposed by IBM's architectures. These mappings require fewer gates than SWAP gates. It is well known, that permuting the qubits will yield circuits with different number of gates. The design in this paper uses efficient mappings with qubit permutations to obtain circuits with a reduced number of gates. Results have shown that the proposed approach reduces circuits by up to 64% compared with Qiskit and up to 42% compared with another mapping algorithm.
Research in the field of quantum circuits has increased as technology advances in the development of quantum computers. IBM offers access to quantum computers via the cloud service called IBM Q. However, these architectures have some restrictions regarding the types of quantum gates that can be realized. This work proposes a methodology for the mapping of quantum and reversible circuits to the architectures made available by the IBM Q project. The methodology consists in finding CNOT mappings using a set of defined qubits movements to satisfy the architectures constraints by adding as few gates as possible. In order to reduce the number of CNOT gates needing mapping, the permutation of the circuit can be changed. One alternative to find this permutation is trough exhaustive search. However, is not feasible as the number of qubit increases. To solve this problem, the permutation problem was formulated as an Integer Linear Programming problem. The mapping of quantum circuits realized with non-implementable gates and reversible Toffoli circuits to the IBM quantum architectures were proposed in this work as well. This was done by adapting the developed CNOT mappings along with the Integer Linear Programming formulation. The proposed methodology was evaluated by mapping quantum and reversible circuits to an IBM quantum architectures with 5 and 16 qubits. The results were compared with two algorithms that map quantum circuits to IBM architectures. The cost metric used in the evaluation were the number of quantum gates and the number of levels (depth) of the circuits. Experimental results have shown that the proposed methodology outperforms the other approaches regarding the circuits' size. The results of the methodology used to implement quantum (with non-implementable gates) and Toffoli circuits to IBM architectures have shown that the mapping targeting a specific architecture constraints results in a smaller mapped circuit. The methodology developed can be easily adapted to any quantum architecture. Also, the proposed Integer Linear Programming formulation can be used in any reversible circuit and can be applied in other research areas.
IBM has made several quantum computers available to researchers around the world via cloud services. Two architectures with five qubits, one with 16, and one with 20 qubits are available to run experiments. The IBM architectures implement gates from the Clifford+T gate library. However, each architecture only implements a subset of the possible CNOT gates. In this paper, we show how Clifford+T circuits can efficiently be mapped into the two IBM quantum computers with 5 qubits. We further present an algorithm and a set of circuit identities that may be used to optimize the Clifford+T circuits in terms of gate count and number of levels. It is further shown that the optimized circuits can considerably reduce the gate count and number of levels and thus produce results with better fidelity.
Quantum computers are becoming a reality today due to the rapid progress made by researchers in the last years. In the process of building quantum computers, IBM has developed several versions-starting from 5-qubit architectures like IBM QX2 and IBM QX4 to larger 16- or 20-qubit architectures. These architectures support arbitrary rotations of a single qubit and a controlled negation (CNOT) involving two qubits. The two qubit operations come with added coupling-map restrictions that only allow specific physical qubits to be the control and target qubits of the operation. In order to execute a quantum circuit on the IBM QX architecture, CNOT gates must satisfy the so-called coupling constraints of the architecture. Previous works addressed this issue with the objective of reducing the number of gates and the circuit depth. However, in this article, we show that further improvements are possible. To this end, we present a general approach for further improving the number of gate operations and depth of the mapped circuit. The proposed approach encompasses the selection of physical qubits, determining initial and local permutations efficiently to obtain the final circuit mapped to the given IBM QX architecture. Through experiments, improvements are observed over existing methods in terms of the number of gates and circuit depth.
CNOT optimization plays a significant role in noise reduction for Quantum Circuits. Several heuristic and exact approaches exist for CNOT optimization. In this paper, we investigate more complicated variations of optimal synthesis by allowing qubit permutations and handling layout restrictions. We encode such problems into Planning, SAT, and QBF. We provide optimization for both CNOT gate count and circuit depth. For experimental evaluation, we consider standard T-gate optimized benchmarks and optimize CNOT sub-circuits. We show that allowing qubit permutations can further reduce up to 56% in CNOT count and 46% in circuit depth. In the case of optimally mapped circuits under layout restrictions, we observe a reduction up to 17% CNOT count and 19% CNOT depth.
IBM's quantum computers implement gates from Clifford +T gate library. All single qubit gates are implemented, but only a subset of the possible CNOT are provided. It is well known that the functionally of the missing gates can be achieved by a sequence of gates. The sequence of gates is based on SWAP gates. Up to seven elementary gates are required to implement a SWAP gate. In this paper we show how the same effect can be achieved with fewer gates. To show the potential of the proposed transformations, an example is presented where a reduction of 44% in the gate count and a 26% reduction in the number of levels for IBM's QX5 computer is achieved. An algorithm that is considered state of the art, is used for the comparison.