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

Architecture-Aware Synthesis of Phase Polynomials for NISQ Devices

Arianne Meijer-van de Griend, Duncan, Ross

Published Apr 13, 2020• 11 citations
Publisher

Abstract

We propose a new algorithm to synthesise quantum circuits for phase polynomials, which takes into account the qubit connectivity of the quantum computer. We focus on the architectures of currently available NISQ devices. Our algorithm generates circuits with a smaller CNOT depth than the algorithms currently used in Staq and tket, while improving the runtime with respect the former.

DOI
10.4204/eptcs.394.8

Related papers

Architecture-Aware Synthesis of Phase Polynomials for NISQ Devices

Arianne Meijer-van de Griend, Ross Duncan

We propose a new algorithm to synthesise quantum circuits for phase polynomials, which takes into account the qubit connectivity of the quantum computer.We focus on the architectures of currently available NISQ devices.Our algorithm generates circuits with a smaller CNOT depth than the algorithms currently used in Staq and t|ket , while improving the runtime with respect the former.

arXiv:2004.06052•Electronic Proceedings in Theoretical Computer Science•Nov 14, 2023•27 citations

Phase polynomials synthesis algorithms for NISQ architectures and beyond

Vivien Vandaele, Simon Martiel, Timothée Goubault de Brugière

Abstract We present a framework for the synthesis of phase polynomials that addresses both cases of full connectivity and partial connectivity for NISQ architectures. In most cases, our algorithms generate circuits with lower CNOT count and CNOT depth than the state of the art or have a significantly smaller running time for similar performances. We also provide methods that can be applied to our algorithms in order to trade an increase in the CNOT count for a decrease in execution time, thereby filling the gap between our algorithms and faster ones.

arXiv:2104.00934•Quantum Science and Technology•Mar 2, 2022•25 citations

A comparison of quantum compilers using a DAG-based or phase polynomial-based intermediate representation

Arianne Meijer-van de Griend

In the NISQ era, where quantum computing is dominated by hybrid quantum algorithms, it is important for quantum circuits to be well-optimized to reduce noise from unnecessary gates. We investigate different phase polynomial-based compilation strategies to determine the current best practices and compare them against the DAG-based Qiskit and TKET compilers. We find that phase polynomial-based compiling is very fast compared to DAG-based compiling. For long circuits, these compilers generate fewer CNOT gates than Qiskit or TKET, but for short circuits, they are quite inefficient. We also show that supplementary algorithms such as Reverse Traversal and simulated annealing mightimprove the generated CNOT count slightly, but the effect is negligible in most settings and generally not worth the additional compiler runtime. Instead, more sophisticated phase polynomial synthesis algorithms are needed.

arXiv:2304.08814•Journal of Systems and Software•Nov 7, 2024•6 citations

Quantum circuit optimizations for NISQ architectures

Beatrice Nash, Vlad Gheorghiu, Michele Mosca

Abstract Currently available quantum computing hardware platforms have limited 2-qubit connectivity among their addressable qubits. In order to run a generic quantum algorithm on such a platform, one has to transform the initial logical quantum circuit describing the algorithm into an equivalent one that obeys the connectivity restrictions. In this work we construct a circuit synthesis scheme that takes as input the qubit connectivity graph and a quantum circuit over the gate set generated by { CNOT , R Z } and outputs a circuit that respects the connectivity of the device. As a concrete application, we apply our techniques to Google’s Bristlecone 72-qubit quantum chip connectivity, IBM’s Tokyo 20-qubit quantum chip connectivity, and Rigetti’s Acorn 19-qubit quantum chip connectivity. In addition, we also compare the performance of our scheme as a function of sparseness of randomly generated quantum circuits, and discuss how to apply our techniques as a subroutine for the more general mapping problem over universal set of gates (Clifford + T).

arXiv:1904.01972•Quantum Science and Technology•Feb 25, 2020•139 citations

HOPPS: Hardware-Aware Optimal Phase Polynomial Synthesis with Blockwise Optimization for Quantum Circuits

Xinpeng Li, Ji Liu, Shuai Xu +2 more

Blocks composed of {CNOT, Rz} are ubiquitous in modern quantum applications, notably in circuits such as QAOA ansatzes and quantum adders. After compilation, many of them exhibit large CNOT counts or depths, which lowers fidelity. Therefore, we introduce HOPPS: a SAT-based hardware-aware optimal phase polynomial synthesis algorithm that could generate {CNOT, Rz} blocks with CNOT count or depth optimality. Sometime {CNOT, Rz} blocks are large, such as in QAOA ansatzes, HOPPS's pursuit of optimality limits its scalability. To address this issue, we introduce an iterative blockwise optimization strategy: large circuits are partitioned into smaller blocks, each block is optimally refined, and the process is repeated for several iterations. Empirical results show that HOPPS is more efficient comparing with existing near optimal synthesis tools. Used as a peephole optimizer, HOPPS reduces the CNOT count by up to 50.0% and the CNOT depth by up to 57.1% under OLSQ. For large QAOA circuit, after mapping by Qiskit, circuit can be reduced CNOT count and depth by up to 44.4% and 42.4% by our iterative blockwise optimization. Index Terms-Phase Polynomial, Quantum Circuit Synthesis, Quantum Circuit Optimization.

quant-pharXiv:2511.18770•Nov 25, 2025•0 citations

Quantum circuit synthesis on noisy intermediate-scale quantum devices

Shuai Yang, Guojing Tian, Jialin Zhang +1 more

In the near future of the noisy intermediate-scale quantum (NISQ) era, almost all quantum computing devices will be restricted to a specific fixed qubits connectivity architecture. Thus, the synthesis of quantum circuits with limited connectivity is urgent. We design quantum circuit synthesis algorithms for basic and essential synthesis problems, such as quantum state preparation, general unitary synthesis, and quantum isometries. For any architecture, the controlled not (cnot) count is at most 5/3 times the state-of-the-art result on complete-graph architecture. For some specific architectures, such as square-grid ones, the ratio is reduced to 1.126. The numerical simulation result is confirmatory of theoretical conclusions. Our algorithms significantly reduce by more than $50%$ additional cnot count compared to mapping algorithms. These algorithms help to implement the larger-scale algorithm in the physics device. Our results illustrate that well-designed synthesis algorithms can mitigate the problem of limited qubit connectivity in the NISQ era and may suggest the design of large-scale quantum devices.

Physical Review A•Jan 2, 2024•7 citations
We propose a new algorithm to synthesise quantum circuits for phase polynomials, which takes into account the qubit connectivity of the quantum computer. We focus on the architectures of currently available NISQ devices. Our algorithm generates circuits with a smaller CNOT depth than the algorithms currently used in Staq and tket, while improving the runtime with respect the former.
Abstract We present a framework for the synthesis of phase polynomials that addresses both cases of full connectivity and partial connectivity for NISQ architectures. In most cases, our algorithms generate circuits with lower CNOT count and CNOT depth than the state of the art or have a significantly smaller running time for similar performances. We also provide methods that can be applied to our algorithms in order to trade an increase in the CNOT count for a decrease in execution time, thereby filling the gap between our algorithms and faster ones.
In the NISQ era, where quantum computing is dominated by hybrid quantum algorithms, it is important for quantum circuits to be well-optimized to reduce noise from unnecessary gates. We investigate different phase polynomial-based compilation strategies to determine the current best practices and compare them against the DAG-based Qiskit and TKET compilers. We find that phase polynomial-based compiling is very fast compared to DAG-based compiling. For long circuits, these compilers generate fewer CNOT gates than Qiskit or TKET, but for short circuits, they are quite inefficient. We also show that supplementary algorithms such as Reverse Traversal and simulated annealing mightimprove the generated CNOT count slightly, but the effect is negligible in most settings and generally not worth the additional compiler runtime. Instead, more sophisticated phase polynomial synthesis algorithms are needed.
Abstract Currently available quantum computing hardware platforms have limited 2-qubit connectivity among their addressable qubits. In order to run a generic quantum algorithm on such a platform, one has to transform the initial logical quantum circuit describing the algorithm into an equivalent one that obeys the connectivity restrictions. In this work we construct a circuit synthesis scheme that takes as input the qubit connectivity graph and a quantum circuit over the gate set generated by { CNOT , R Z } and outputs a circuit that respects the connectivity of the device. As a concrete application, we apply our techniques to Google’s Bristlecone 72-qubit quantum chip connectivity, IBM’s Tokyo 20-qubit quantum chip connectivity, and Rigetti’s Acorn 19-qubit quantum chip connectivity. In addition, we also compare the performance of our scheme as a function of sparseness of randomly generated quantum circuits, and discuss how to apply our techniques as a subroutine for the more general mapping problem over universal set of gates (Clifford + T).
Blocks composed of {CNOT, Rz} are ubiquitous in modern quantum applications, notably in circuits such as QAOA ansatzes and quantum adders. After compilation, many of them exhibit large CNOT counts or depths, which lowers fidelity. Therefore, we introduce HOPPS: a SAT-based hardware-aware optimal phase polynomial synthesis algorithm that could generate {CNOT, Rz} blocks with CNOT count or depth optimality. Sometime {CNOT, Rz} blocks are large, such as in QAOA ansatzes, HOPPS's pursuit of optimality limits its scalability. To address this issue, we introduce an iterative blockwise optimization strategy: large circuits are partitioned into smaller blocks, each block is optimally refined, and the process is repeated for several iterations. Empirical results show that HOPPS is more efficient comparing with existing near optimal synthesis tools. Used as a peephole optimizer, HOPPS reduces the CNOT count by up to 50.0% and the CNOT depth by up to 57.1% under OLSQ. For large QAOA circuit, after mapping by Qiskit, circuit can be reduced CNOT count and depth by up to 44.4% and 42.4% by our iterative blockwise optimization. Index Terms-Phase Polynomial, Quantum Circuit Synthesis, Quantum Circuit Optimization.
In the near future of the noisy intermediate-scale quantum (NISQ) era, almost all quantum computing devices will be restricted to a specific fixed qubits connectivity architecture. Thus, the synthesis of quantum circuits with limited connectivity is urgent. We design quantum circuit synthesis algorithms for basic and essential synthesis problems, such as quantum state preparation, general unitary synthesis, and quantum isometries. For any architecture, the controlled not (cnot) count is at most 5/3 times the state-of-the-art result on complete-graph architecture. For some specific architectures, such as square-grid ones, the ratio is reduced to 1.126. The numerical simulation result is confirmatory of theoretical conclusions. Our algorithms significantly reduce by more than 5050%50 additional cnot count compared to mapping algorithms. These algorithms help to implement the larger-scale algorithm in the physics device. Our results illustrate that well-designed synthesis algorithms can mitigate the problem of limited qubit connectivity in the NISQ era and may suggest the design of large-scale quantum devices.