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

Lecture notes in computer science

Quokka#: Quantum Computing with #SAT

Jingyi Mei, Dekel Zak, Muhammad Osama, Tim J. Coopmans, Alfons Laarman

Published Jan 1, 2026• 0 citations
Publisher

Abstract

Abstract We present , a versatile, open-source Python library for quantum circuit analysis. reduces various simulation, verification, and synthesis tasks to weighted model counting (#SAT). It supports universal quantum circuits and a wide variety of gates. provides multiple encodings based on different algebraic bases and equivalence-checking methods, enabling key performance trade-offs. Moreover, the new version of adds approximate equivalence checking, which is crucial in its synthesis algorithms, since it enables translation between arbitrary gate sets. Its synthesis engine is depth-optimal, making it well-suited to real-world quantum computing. This paper demonstrates the design, extensibility, and use of .

DOI
10.1007/978-3-032-32537-2_19

Related papers

Quokka#: Quantum Computing with #SAT

Jingyi Mei, Dekel Zak, Muhammad Osama +2 more

We present Quokka#, a versatile, open-source Python library for quantum circuit analysis. Quokka# reduces various simulation, verification, and synthesis tasks to weighted model counting (#SAT). It supports universal quantum circuits and a wide variety of gates. Quokka# provides multiple encodings based on different algebraic bases and equivalence-checking methods, enabling key performance trade-offs. Moreover, the new version of Quokka# adds approximate equivalence checking, which is crucial in its synthesis algorithms, since it enables translation between arbitrary gate sets. Its synthesis engine is depth-optimal, making it well-suited to real-world quantum computing. This paper demonstrates the design, extensibility, and use of Quokka#.

quant-pharXiv:2605.16509•May 19, 2026•0 citations

Equivalence Checking of Quantum Circuits by Model Counting

Jingyi Mei, Tim J. Coopmans, Marcello Bonsangue +1 more

Abstract Verifying equivalence between two quantum circuits is a hard problem, that is nonetheless crucial in compiling and optimizing quantum algorithms for real-world devices. This paper gives a Turing reduction of the (universal) quantum circuits equivalence problem to weighted model counting (WMC). Our starting point is a folklore theorem showing that equivalence checking of quantum circuits can be done in the so-called Pauli-basis. We combine this insight with a WMC encoding of quantum circuit simulation, which we extend with support for the Toffoli gate. Finally, we prove that the weights computed by the model counter indeed realize the reduction. With an open-source implementation, we demonstrate that this novel approach can outperform a state-of-the-art equivalence-checking tool based on ZX calculus and decision diagrams.

arXiv:2403.18813•Lecture notes in computer science•Jan 1, 2024•15 citations

qSAT: Design of an Efficient Quantum Satisfiability Solver for Hardware Equivalence Checking

Abhoy Kole, Mohammed Elkacem Djeridane, Lennart Weingarten +2 more

The use of Boolean Satisfiability (SAT) solver for hardware verification incurs exponential runtime in several instances. In this work, we have proposed an efficient quantum SAT (qSAT) solver for equivalence checking of Boolean circuits employing Grover’s algorithm. The Exclusive-Sum-of-Product (ESOP)-based generation of the Conjunctive Normal Form (CNF) equivalent clauses demands less qubits and minimizes the gates and depth of quantum circuit interpretation. The consideration of reference circuits for verification affecting Grover’s iterations and quantum resources are also presented as a case study. Experimental results are presented assessing the benefits of the proposed verification approach using open source Qiskit platform and IBM quantum computer.

arXiv:2409.03917•ACM Journal on Emerging Technologies in Computing Systems•Apr 10, 2025•1 citation

A SAT Encoding for Optimal Clifford Circuit Synthesis

Sarah Schneider, Lukas Burgholzer, Robert Wille

Executing quantum algorithms on a quantum computer requires compilation to representations that conform to all restrictions imposed by the device. Due to devices' limited coherence times and gate fidelities, the compilation process has to be optimized as much as possible. To this end, an algorithm's description first has to be synthesized using the device's gate library. In this paper, we consider the optimal synthesis of Clifford circuits---an important subclass of quantum circuits, with various applications. Such techniques are essential to establish lower bounds for (heuristic) synthesis methods and gauging their performance. Due to the huge search space, existing optimal techniques are limited to a maximum of six qubits. The contribution of this work is twofold: First, we propose an optimal synthesis method for Clifford circuits based on encoding the task as a satisfiability (SAT) problem and solving it using a SAT solver in conjunction with a binary search scheme. The resulting tool is demonstrated to synthesize optimal circuits for up to 26 qubits---more than four times as many as the current state of the art. Second, we experimentally show that the overhead introduced by state-of-the-art heuristics exceeds the lower bound by 27 % on average. The resulting tool is publicly available at https://github.com/cda-tum/qmap.

arXiv:2208.11713•Asia and South Pacific Design Automation Conference (ASP-DAC)•Jan 16, 2023•17 citations

Quantum-Chiplet: A Novel Python-Based Efficient and Scalable Design Methodology for Quantum Circuit Verification and Implementation

Kao, Yu-Ting, Haoyu Lu, Yeong-Jar Chang +1 more

Analysis and verification of quantum circuits are highly challenging, given the exponential dependence of the number of states on the number of qubits. For analytical derivation, we propose a new quantum polynomial representation (QPR) to facilitate the analysis of massively parallel quantum computation and detect subtle errors. For the verification of quantum circuits, we introduce Quantum-Chiplet, a hierarchical quantum behavior modeling methodology that facilitates rapid integration and simulation. Each chiplet is systematically transformed into quantum gates. For circuits involving n qubits and k quantum gates, the design complexity is reduced from "greater than O(2^n)" to O(k). This approach provides an open-source solution, enabling a highly customized solution for quantum circuit simulation within the native Python environment, thereby reducing reliance on traditional simulation packages. A quantum amplitude estimation example demonstrates that this method significantly improves the design process, with more than 10x speed-up compared to IBM Qiskit at 14 qubits.

arXiv:2503.10054•Mar 13, 2025•0 citations

Synthesis and Optimization of Encoding Circuits for Fault-Tolerant Quantum Computation

Tom Peham, Matthew Steinberg, Robert Wille +1 more

Preparing arbitrary logical states is a central primitive for universal fault-tolerant quantum computation and the cost of encoded-state preparation contributes directly to the overall resource overhead. This makes the synthesis of efficient general-state encoding circuits an important problem, particularly with respect to two-qubit gate count and circuit depth. Yet the synthesis of such encoders has been studied less extensively than general Clifford circuit synthesis or the preparation of specific logical Pauli-eigenstates. In this work, we develop methods for synthesizing efficient encoders for arbitrary stabilizer codes. We formulate encoder synthesis as a search over stabilizer tableaus and introduce greedy and rollout-based algorithms that exploit the freedom among stabilizer-equivalent realizations of the same encoding isometry. For code families with a modular structure, such as generalized concatenated and holographic codes, we show how large encoders can be assembled from optimized local constituent encoders, and we use SMT-based exact synthesis to obtain optimal local circuits for small instances. We further evaluate the proposed methods on a broad set of stabilizer codes, including holographic and quantum low-density parity-check (qLDPC) codes, and compare them against recent encoder-synthesis methods and existing constructions from the literature, obtaining improvements of up to 43% in two-qubit gate count and up to 70% in depth. Our results support the optimization of encoded-state preparation in several fault-tolerant quantum-computing schemes, and all methods are openly available as part of the Munich Quantum Toolkit.

quant-pharXiv:2605.15266•May 18, 2026•0 citations
Abstract We present , a versatile, open-source Python library for quantum circuit analysis. reduces various simulation, verification, and synthesis tasks to weighted model counting (#SAT). It supports universal quantum circuits and a wide variety of gates. provides multiple encodings based on different algebraic bases and equivalence-checking methods, enabling key performance trade-offs. Moreover, the new version of adds approximate equivalence checking, which is crucial in its synthesis algorithms, since it enables translation between arbitrary gate sets. Its synthesis engine is depth-optimal, making it well-suited to real-world quantum computing. This paper demonstrates the design, extensibility, and use of .
We present Quokka#, a versatile, open-source Python library for quantum circuit analysis. Quokka# reduces various simulation, verification, and synthesis tasks to weighted model counting (#SAT). It supports universal quantum circuits and a wide variety of gates. Quokka# provides multiple encodings based on different algebraic bases and equivalence-checking methods, enabling key performance trade-offs. Moreover, the new version of Quokka# adds approximate equivalence checking, which is crucial in its synthesis algorithms, since it enables translation between arbitrary gate sets. Its synthesis engine is depth-optimal, making it well-suited to real-world quantum computing. This paper demonstrates the design, extensibility, and use of Quokka#.
Abstract Verifying equivalence between two quantum circuits is a hard problem, that is nonetheless crucial in compiling and optimizing quantum algorithms for real-world devices. This paper gives a Turing reduction of the (universal) quantum circuits equivalence problem to weighted model counting (WMC). Our starting point is a folklore theorem showing that equivalence checking of quantum circuits can be done in the so-called Pauli-basis. We combine this insight with a WMC encoding of quantum circuit simulation, which we extend with support for the Toffoli gate. Finally, we prove that the weights computed by the model counter indeed realize the reduction. With an open-source implementation, we demonstrate that this novel approach can outperform a state-of-the-art equivalence-checking tool based on ZX calculus and decision diagrams.
The use of Boolean Satisfiability (SAT) solver for hardware verification incurs exponential runtime in several instances. In this work, we have proposed an efficient quantum SAT (qSAT) solver for equivalence checking of Boolean circuits employing Grover’s algorithm. The Exclusive-Sum-of-Product (ESOP)-based generation of the Conjunctive Normal Form (CNF) equivalent clauses demands less qubits and minimizes the gates and depth of quantum circuit interpretation. The consideration of reference circuits for verification affecting Grover’s iterations and quantum resources are also presented as a case study. Experimental results are presented assessing the benefits of the proposed verification approach using open source Qiskit platform and IBM quantum computer.
Executing quantum algorithms on a quantum computer requires compilation to representations that conform to all restrictions imposed by the device. Due to devices' limited coherence times and gate fidelities, the compilation process has to be optimized as much as possible. To this end, an algorithm's description first has to be synthesized using the device's gate library. In this paper, we consider the optimal synthesis of Clifford circuits---an important subclass of quantum circuits, with various applications. Such techniques are essential to establish lower bounds for (heuristic) synthesis methods and gauging their performance. Due to the huge search space, existing optimal techniques are limited to a maximum of six qubits. The contribution of this work is twofold: First, we propose an optimal synthesis method for Clifford circuits based on encoding the task as a satisfiability (SAT) problem and solving it using a SAT solver in conjunction with a binary search scheme. The resulting tool is demonstrated to synthesize optimal circuits for up to 26 qubits---more than four times as many as the current state of the art. Second, we experimentally show that the overhead introduced by state-of-the-art heuristics exceeds the lower bound by 27 % on average. The resulting tool is publicly available at https://github.com/cda-tum/qmap.
Analysis and verification of quantum circuits are highly challenging, given the exponential dependence of the number of states on the number of qubits. For analytical derivation, we propose a new quantum polynomial representation (QPR) to facilitate the analysis of massively parallel quantum computation and detect subtle errors. For the verification of quantum circuits, we introduce Quantum-Chiplet, a hierarchical quantum behavior modeling methodology that facilitates rapid integration and simulation. Each chiplet is systematically transformed into quantum gates. For circuits involving n qubits and k quantum gates, the design complexity is reduced from "greater than O(2^n)" to O(k). This approach provides an open-source solution, enabling a highly customized solution for quantum circuit simulation within the native Python environment, thereby reducing reliance on traditional simulation packages. A quantum amplitude estimation example demonstrates that this method significantly improves the design process, with more than 10x speed-up compared to IBM Qiskit at 14 qubits.
Preparing arbitrary logical states is a central primitive for universal fault-tolerant quantum computation and the cost of encoded-state preparation contributes directly to the overall resource overhead. This makes the synthesis of efficient general-state encoding circuits an important problem, particularly with respect to two-qubit gate count and circuit depth. Yet the synthesis of such encoders has been studied less extensively than general Clifford circuit synthesis or the preparation of specific logical Pauli-eigenstates. In this work, we develop methods for synthesizing efficient encoders for arbitrary stabilizer codes. We formulate encoder synthesis as a search over stabilizer tableaus and introduce greedy and rollout-based algorithms that exploit the freedom among stabilizer-equivalent realizations of the same encoding isometry. For code families with a modular structure, such as generalized concatenated and holographic codes, we show how large encoders can be assembled from optimized local constituent encoders, and we use SMT-based exact synthesis to obtain optimal local circuits for small instances. We further evaluate the proposed methods on a broad set of stabilizer codes, including holographic and quantum low-density parity-check (qLDPC) codes, and compare them against recent encoder-synthesis methods and existing constructions from the literature, obtaining improvements of up to 43% in two-qubit gate count and up to 70% in depth. Our results support the optimization of encoded-state preparation in several fault-tolerant quantum-computing schemes, and all methods are openly available as part of the Munich Quantum Toolkit.