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

arXiv:2607.08212

Möbius-Guided Diagonal-Gate Compilation with Native Multiqubit Controlled-Phase Gates on Neutral-Atom Processors

Hairuo Huang, Yanwu Gu, Chen Huang, Xi Zhao, Meng-Jun Hu, Dong E. Liu, Jingbo Wang

quant-phSubmitted Jul 9, 2026• Announced Jul 10, 2026• 0 citations• Revised Jul 30, 2026 (v2)
v1 · Jul 9, 2026v2 · Jul 30, 2026
arXivHTMLPDF

Abstract

Diagonal gates are ubiquitous primitives in quantum algorithms, from phase oracles, hypergraph-state preparation, and multi-control logic to Hamiltonian simulation of spin models and digitized lattice field theories, where Ising interactions and local potential terms are diagonal in the encoded basis. Standard compilers, however, often lower diagonal structure into one- and two-qubit gates before neutral-atom hardware can exploit native Rydberg-mediated multiqubit controlled-phase operations. We propose a Möbius-guided compiler that maps a diagonal phase function to a phase hypergraph via subset-lattice Möbius inversion. The hypergraph retains the support and angle of each many-body phase term, allowing sparse or local high-order structure to be routed as native multiqubit controlled-phase candidates when feasible and decomposed otherwise. The neutral-atom scheduler accounts for atom motion, interaction-zone constraints, blockade feasibility, and error costs, enabling a direct comparison between native high-order execution and decomposed alternatives. Benchmarks against routed ZAP and ZX-calculus baselines show improved estimated success for algorithmic instances with exploitable three- and four-body phase terms, and comparable performance on predominantly two-body instances. These results provide a feasible compilation strategy for more fully exploiting the native capabilities of neutral-atom hardware, using atom reconfigurability and Rydberg-mediated multiqubit phase operations as practical resources for more efficient quantum computation.

Comments
21 pages, 10 figures

Related papers

Multi-controlled Phase Gate Synthesis with ZX-calculus applied to Neutral Atom Hardware

Korbinian Staudacher, L. Schmid, Johannes Zeiher +2 more

Quantum circuit synthesis describes the process of converting arbitrary unitary operations into a gate sequence of a fixed universal gate set, usually defined by the operations native to a given hardware platform. Most current synthesis algorithms are designed to synthesize towards a set of single qubit rotations and an additional entangling two qubit gate, such as CX, CZ, or the Molmer Sorensen gate. However, with the emergence of neutral atom based hardware and their native support for gates with more than two qubits, synthesis approaches tailored to these new gate sets become necessary. In this work, we present an approach to synthesize multi controlled phase gates using ZX calculus. By representing quantum circuits as graph like ZX diagrams, one can utilize the distinct graph structure of diagonal gates to identify multi controlled phase gates inherently present in some quantum circuits even if none were explicitly defined in the original circuit. We evaluate the approach on a wide range of benchmark circuits and compare them to the standard Qiskit synthesis regarding its circuit execution time for neutral atom based hardware with native support of multi controlled gates. Our results show possible advantages for current state of the art hardware and represent the first exact synthesis algorithm supporting arbitrary sized multi controlled phase gates.

arXiv:2403.10864•Electronic Proceedings in Theoretical Computer Science•Aug 9, 2024•4 citations

Blockade-induced exchange primitives for scalable neutral-atom QPU

Mohammadsadegh Khazali, Klaus Mølmer

Many quantum hardware platforms natively support either phase or exchange operations, yet converting between these two forms of control typically incurs substantial overhead. Rydberg-blockade neutral-atom arrays are highly developed for phase control, while controlled exchange is usually obtained only through depth-intensive decompositions. Here, controlled exchange is realized as a native, blockade-programmed phenomenon in a collective excited manifold. Target atoms are engineered such that two competing exchange pathways between |01> and |10> destructively interfere, while a single collective four-photon channel mediated by a symmetric Rydberg excitation remains resonant and drives a direct SWAP, with all other qubit configurations undergoing an identity action. Exchange conditionality follows from blockade: exciting a control atom to a Rydberg state shifts and blocks the target collective resonance, suppressing exchange, whereas leaving the control in the ground manifold enables exchange in a single step. Anisotropic control-target interactions give rise to selective blockade, enabling coherent programmability of exchange among specific target pairs. This yields a family of controlled-SWAP primitives with process fidelities above 99% and an order-of-magnitude reduction in circuit depth and Rydberg-state exposure time compared with decomposed implementations. The same principle generalizes to multi-control and multiplexed controlled-exchange operations, providing compact hardware-level primitives for conditional information routing in extended neutral-atom arrays. More broadly, engineering interaction-tuned near-degeneracies in collective manifolds offers a route to programmable non-diagonal multiqubit operations across quantum platforms.

quant-pharXiv:2511.22214•Nov 28, 2025•0 citations

Parametrized multiqubit gates for neutral-atom quantum platforms

Madhav Mohan, Julius de Hond, S. J. J. M. F. Kokkelmans

A clever choice and design of gate sets can reduce the depth of a quantum circuit, and can improve the quality of the solution one obtains from a quantum algorithm. This is especially important for near-term quantum computers that suffer from various sources of error that propagate with the circuit depth. Parametrized gates in particular have found use in both near-term algorithms and circuit compilation. The one- and two-qubit versions of these gates have been demonstrated on various computing architectures. The neutral-atom platform has the capability to implement native $N$-qubit gates (for $N\ensuremath{\ge}2$). However, one needs to first find the control functions that implement these gates on the hardware. We study the numerical optimization of neural networks towards obtaining families of controls---laser pulses to excite an atom to Rydberg states---that implement phase gates with one and two controls, the ${\mathrm{C}}_{1}\phantom{\rule{-0.1em}{0ex}}\mathrm{P}$ and ${\mathrm{C}}_{2}\phantom{\rule{-0.1em}{0ex}}\mathrm{P}$ gates, respectively, on neutral-atom hardware. The pulses we obtain have a duration significantly shorter than the loss time scale, set by decay from the Rydberg state. In addition, they do not require single-site addressability and are smooth. Hence, we expect our gates to have immediate benefits for quantum algorithms implemented on current neutral-atom hardware.

Physical Review Applied•May 27, 2025•4 citations

General circuit mapping algorithm for neutral atom quantum computers

Neven Gentil, Rianne S. Lous, Aida Todri-Sanial

Neutral atom quantum computers (NAQC) are emerging as a promising, scalable quantum computing platform because of their long qubit coherence, flexible qubit arrangement, and multiqubit gate capabilities. However, circuit execution often requires physically moving qubits, making compilation a critical optimization challenge. We propose a circuit independent mathematical framework built on graph-theoretic combinatorial optimization that determines the minimal number of required qubit transfers. This model captures spatial constraints specific to NAQC platforms with zone-limited gate operations and multi-qubit gates. From this framework, we encode the qubit mapping problem as a nonlinear integer program and solve it using a genetic algorithm, enabling trade-offs between minimizing the total traveled distance and the number of parallel transfer operations. Compared to the state-of-the-art scalable compiler for zoned architectures, our approach consistently finds fewer transfers. Depending on the optimization focus, our method produces shorter traveled distances or fewer parallel transfer operations. This work provides both theoretical guaranties and a practical tool for efficient, architecture-aware quantum circuit compilation. As a result, practitioners can generate hardware-aware mappings that reduce movement-induced errors and better exploit atom transfer parallelism, directly improving execution efficiency on NAQC devices.

quant-pharXiv:2606.20503•Jun 19, 2026•0 citations

Structure-Aware Compilation for Scalable Neutral-Atom Quantum Computing

Dekuan Dong, Fengyu Zou, Hengzhun Chen +2 more

We study the compilation of structured quantum gate families on two-dimensional neutral-atom arrays, aiming to reduce addressing and transport overhead under realistic hardware constraints. For single-qubit gates, we exploit the algebraic structures of gate families at the matrix level, enabling efficient rank-one decompositions over appropriate algebraic structures and thereby reducing the number of addressing layers. For controlled-Z (C-Z) gates, we formulate the transport scheduling problem using graph-theoretic models, leading to efficient compilation algorithms under realistic transport constraints. We provide provable performance guarantees for the proposed methods and validate them through extensive numerical experiments. Across representative single-qubit gate families, our methods reduce the number of addressing layers by up to a factor of two compared with naïve row- or column-wise implementations. For C-Z gates, our scheduling strategy reduces the required number of atom transport operations by approximately 50\%. When applied to QAOA circuits for MaxCut, the proposed framework reduces transport cost by more than 30\% on average. These results show that the physical constraints of neutral-atom hardware can be converted into algebraic and graph-theoretic structure, turning a hardware-level scheduling bottleneck into tractable decomposition and coloring problems.

quant-pharXiv:2607.01787•Jul 3, 2026•0 citations

Parametrized multiqubit gate design for neutral-atom based quantum platforms

Madhav Mohan, Julius de Hond, S. J. J. M. F. Kokkelmans

A clever choice and design of gate sets can reduce the depth of a quantum circuit, and can improve the quality of the solution one obtains from a quantum algorithm. This is especially important for near-term quantum computers that suffer from various sources of error that propagate with the circuit depth. Parametrized gates in particular have found use in both near-term algorithms and circuit compilation. The one- and two-qubit versions of these gates have been demonstrated on various computing architectures. The neutral atom platform has the capability to implement native $N$-qubit gates (for $N \geq 2$). However, one needs to first find the control functions that implement these gates on the hardware. We study the numerical optimization of neural networks towards obtaining families of controls $-$ laser pulses to excite an atom to Rydberg states $-$ that implement phase gates with one and two controls, the $\mathrm{C_1P}$ and $\mathrm{C_2P}$ gates respectively, on neutral atom hardware. The pulses we obtain have a duration significantly shorter than the loss time scale, set by decay from the Rydberg state. Further, they do not require single-site addressability and are smooth. Hence, we expect our gates to have immediate benefits for quantum algorithms implemented on current neutral atom hardware.

arXiv:2411.19785•Nov 29, 2024•0 citations
Diagonal gates are ubiquitous primitives in quantum algorithms, from phase oracles, hypergraph-state preparation, and multi-control logic to Hamiltonian simulation of spin models and digitized lattice field theories, where Ising interactions and local potential terms are diagonal in the encoded basis. Standard compilers, however, often lower diagonal structure into one- and two-qubit gates before neutral-atom hardware can exploit native Rydberg-mediated multiqubit controlled-phase operations. We propose a Möbius-guided compiler that maps a diagonal phase function to a phase hypergraph via subset-lattice Möbius inversion. The hypergraph retains the support and angle of each many-body phase term, allowing sparse or local high-order structure to be routed as native multiqubit controlled-phase candidates when feasible and decomposed otherwise. The neutral-atom scheduler accounts for atom motion, interaction-zone constraints, blockade feasibility, and error costs, enabling a direct comparison between native high-order execution and decomposed alternatives. Benchmarks against routed ZAP and ZX-calculus baselines show improved estimated success for algorithmic instances with exploitable three- and four-body phase terms, and comparable performance on predominantly two-body instances. These results provide a feasible compilation strategy for more fully exploiting the native capabilities of neutral-atom hardware, using atom reconfigurability and Rydberg-mediated multiqubit phase operations as practical resources for more efficient quantum computation.
Quantum circuit synthesis describes the process of converting arbitrary unitary operations into a gate sequence of a fixed universal gate set, usually defined by the operations native to a given hardware platform. Most current synthesis algorithms are designed to synthesize towards a set of single qubit rotations and an additional entangling two qubit gate, such as CX, CZ, or the Molmer Sorensen gate. However, with the emergence of neutral atom based hardware and their native support for gates with more than two qubits, synthesis approaches tailored to these new gate sets become necessary. In this work, we present an approach to synthesize multi controlled phase gates using ZX calculus. By representing quantum circuits as graph like ZX diagrams, one can utilize the distinct graph structure of diagonal gates to identify multi controlled phase gates inherently present in some quantum circuits even if none were explicitly defined in the original circuit. We evaluate the approach on a wide range of benchmark circuits and compare them to the standard Qiskit synthesis regarding its circuit execution time for neutral atom based hardware with native support of multi controlled gates. Our results show possible advantages for current state of the art hardware and represent the first exact synthesis algorithm supporting arbitrary sized multi controlled phase gates.
Many quantum hardware platforms natively support either phase or exchange operations, yet converting between these two forms of control typically incurs substantial overhead. Rydberg-blockade neutral-atom arrays are highly developed for phase control, while controlled exchange is usually obtained only through depth-intensive decompositions. Here, controlled exchange is realized as a native, blockade-programmed phenomenon in a collective excited manifold. Target atoms are engineered such that two competing exchange pathways between |01> and |10> destructively interfere, while a single collective four-photon channel mediated by a symmetric Rydberg excitation remains resonant and drives a direct SWAP, with all other qubit configurations undergoing an identity action. Exchange conditionality follows from blockade: exciting a control atom to a Rydberg state shifts and blocks the target collective resonance, suppressing exchange, whereas leaving the control in the ground manifold enables exchange in a single step. Anisotropic control-target interactions give rise to selective blockade, enabling coherent programmability of exchange among specific target pairs. This yields a family of controlled-SWAP primitives with process fidelities above 99% and an order-of-magnitude reduction in circuit depth and Rydberg-state exposure time compared with decomposed implementations. The same principle generalizes to multi-control and multiplexed controlled-exchange operations, providing compact hardware-level primitives for conditional information routing in extended neutral-atom arrays. More broadly, engineering interaction-tuned near-degeneracies in collective manifolds offers a route to programmable non-diagonal multiqubit operations across quantum platforms.
A clever choice and design of gate sets can reduce the depth of a quantum circuit, and can improve the quality of the solution one obtains from a quantum algorithm. This is especially important for near-term quantum computers that suffer from various sources of error that propagate with the circuit depth. Parametrized gates in particular have found use in both near-term algorithms and circuit compilation. The one- and two-qubit versions of these gates have been demonstrated on various computing architectures. The neutral-atom platform has the capability to implement native NNN-qubit gates (for $N\ensuremath{\ge}2$). However, one needs to first find the control functions that implement these gates on the hardware. We study the numerical optimization of neural networks towards obtaining families of controls---laser pulses to excite an atom to Rydberg states---that implement phase gates with one and two controls, the C1P{\mathrm{C}}_{1}\phantom{\rule{-0.1em}{0ex}}\mathrm{P}C1​P and C2P{\mathrm{C}}_{2}\phantom{\rule{-0.1em}{0ex}}\mathrm{P}C2​P gates, respectively, on neutral-atom hardware. The pulses we obtain have a duration significantly shorter than the loss time scale, set by decay from the Rydberg state. In addition, they do not require single-site addressability and are smooth. Hence, we expect our gates to have immediate benefits for quantum algorithms implemented on current neutral-atom hardware.
Neutral atom quantum computers (NAQC) are emerging as a promising, scalable quantum computing platform because of their long qubit coherence, flexible qubit arrangement, and multiqubit gate capabilities. However, circuit execution often requires physically moving qubits, making compilation a critical optimization challenge. We propose a circuit independent mathematical framework built on graph-theoretic combinatorial optimization that determines the minimal number of required qubit transfers. This model captures spatial constraints specific to NAQC platforms with zone-limited gate operations and multi-qubit gates. From this framework, we encode the qubit mapping problem as a nonlinear integer program and solve it using a genetic algorithm, enabling trade-offs between minimizing the total traveled distance and the number of parallel transfer operations. Compared to the state-of-the-art scalable compiler for zoned architectures, our approach consistently finds fewer transfers. Depending on the optimization focus, our method produces shorter traveled distances or fewer parallel transfer operations. This work provides both theoretical guaranties and a practical tool for efficient, architecture-aware quantum circuit compilation. As a result, practitioners can generate hardware-aware mappings that reduce movement-induced errors and better exploit atom transfer parallelism, directly improving execution efficiency on NAQC devices.
We study the compilation of structured quantum gate families on two-dimensional neutral-atom arrays, aiming to reduce addressing and transport overhead under realistic hardware constraints. For single-qubit gates, we exploit the algebraic structures of gate families at the matrix level, enabling efficient rank-one decompositions over appropriate algebraic structures and thereby reducing the number of addressing layers. For controlled-Z (C-Z) gates, we formulate the transport scheduling problem using graph-theoretic models, leading to efficient compilation algorithms under realistic transport constraints. We provide provable performance guarantees for the proposed methods and validate them through extensive numerical experiments. Across representative single-qubit gate families, our methods reduce the number of addressing layers by up to a factor of two compared with naïve row- or column-wise implementations. For C-Z gates, our scheduling strategy reduces the required number of atom transport operations by approximately 50\%. When applied to QAOA circuits for MaxCut, the proposed framework reduces transport cost by more than 30\% on average. These results show that the physical constraints of neutral-atom hardware can be converted into algebraic and graph-theoretic structure, turning a hardware-level scheduling bottleneck into tractable decomposition and coloring problems.
A clever choice and design of gate sets can reduce the depth of a quantum circuit, and can improve the quality of the solution one obtains from a quantum algorithm. This is especially important for near-term quantum computers that suffer from various sources of error that propagate with the circuit depth. Parametrized gates in particular have found use in both near-term algorithms and circuit compilation. The one- and two-qubit versions of these gates have been demonstrated on various computing architectures. The neutral atom platform has the capability to implement native NNN-qubit gates (for N≥2N \geq 2N≥2). However, one needs to first find the control functions that implement these gates on the hardware. We study the numerical optimization of neural networks towards obtaining families of controls −-− laser pulses to excite an atom to Rydberg states −-− that implement phase gates with one and two controls, the C1P\mathrm{C_1P}C1​P and C2P\mathrm{C_2P}C2​P gates respectively, on neutral atom hardware. The pulses we obtain have a duration significantly shorter than the loss time scale, set by decay from the Rydberg state. Further, they do not require single-site addressability and are smooth. Hence, we expect our gates to have immediate benefits for quantum algorithms implemented on current neutral atom hardware.