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Architecture and Compilation Co-Design for High-Rate Quantum Product Codes on Neutral Atom Arrays
Authors:
Adrian Liu,
Wan-Hsuan Lin,
Daniel Bochen Tan,
Qian Xu,
Jason Cong
Abstract:
Achieving fault-tolerant quantum computing at a practical scale demands quantum error correction (QEC) codes with high encoding rates. Quantum low-density parity-check (qLDPC) codes emerge as a promising candidate, especially given the rise of neutral atom arrays that provide dynamic long-range connectivity via atom movements. In general, synthesizing valid and efficient physical execution plans f…
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Achieving fault-tolerant quantum computing at a practical scale demands quantum error correction (QEC) codes with high encoding rates. Quantum low-density parity-check (qLDPC) codes emerge as a promising candidate, especially given the rise of neutral atom arrays that provide dynamic long-range connectivity via atom movements. In general, synthesizing valid and efficient physical execution plans for QEC is a provably hard combinatorial problem, forming a critical compilation bottleneck that worsens as code sizes grow. To overcome this complexity, we focus on an important product family of qLDPC codes with dimension-reduction properties, and propose ONEX. This framework decomposes complex 2D physical execution planning into independent 1D subproblems, each solved to optimal execution depth within practical compilation time. First, we formulate the 1D execution plan with an explicit satisfiability modulo theories (SMT) encoding. This protocol produces provably depth-optimal solutions with substantial duration reduction. Second, we develop a multi-stage compilation pipeline featuring anytime optimization, movement compaction, and iterative feedback. This pipeline maintains practical wall-clock times while providing progressive refinement and on-demand retrieval of quality solutions. Third, we evaluate ONEX in the application of hypergraph product (HGP) code memory mapped onto neutral atom arrays, achieving 3.7x to 6.1x and 29.8x to 42.1x higher clock rates than the constructive 1D algorithm and the general 2D compiler, respectively, while scaling efficiently to codes with 2,500 data qubits. Finally, we extend ONEX to zoned layouts, revealing architectural insights into the associated trade-offs, and demonstrate its applicability to the broader lifted-product (LP) code family through a representative example.
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Submitted 20 August, 2026;
originally announced August 2026.
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Strategic Plan for Neutral Atom Quantum Computation
Authors:
Adrian J. Menssen,
Tout Wang,
Michael Gullans,
Tom Manovitz,
Jacob M. Taylor,
Jason Cong,
Josiah Sinclair,
Ziv Aqua,
Daniel J. Blumenthal,
J. Pablo Bonilla Ataides,
Johannes Borregaard,
Antoine Browaeys,
Paola Cappellaro,
Soonwon Choi,
Alexandre Cooper,
Robin Côté,
Jacob P. Covey,
Alexandre Dauphin,
Ivana Dimitrova,
Matt Eichenfield,
Dirk Englund,
Jacob Freedman,
Akihisa Goban,
Brandon Grinkemeyer,
Andi Gu
, et al. (31 additional authors not shown)
Abstract:
We present a strategic plan for neutral atom quantum computation, bringing together hardware development and theory advancements to achieve the goal of practical quantum advantage. The concept of practical quantum advantage is defined, along with how to verify claims of advantage, and approaches to designing quantum algorithms that deliver practical advantage. Future directions for neutral atom qu…
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We present a strategic plan for neutral atom quantum computation, bringing together hardware development and theory advancements to achieve the goal of practical quantum advantage. The concept of practical quantum advantage is defined, along with how to verify claims of advantage, and approaches to designing quantum algorithms that deliver practical advantage. Future directions for neutral atom quantum processor hardware are described: scaling-up system size, Qubit encodings and atomic platforms, going further below threshold with neutral-atom logical-qubit performance, continuous reloading of qubits, and fast readout. We also explore opportunities for scalable integrated photonic control technologies. Alongside hardware advancements, new developments in quantum error correction and compilation of quantum circuits are proposed. Finally, we examine the opportunity of networking multiple neutral atom quantum processors together to perform distributed quantum computing and overcome possible limitations of a single system.
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Submitted 23 July, 2026;
originally announced July 2026.
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Entangling logical qubits without physical operations
Authors:
Jin Ming Koh,
Anqi Gong,
Andrei C. Diaconu,
Daniel Bochen Tan,
Alexandra A. Geim,
Michael J. Gullans,
Norman Y. Yao,
Mikhail D. Lukin,
Shayan Majidy
Abstract:
Fault-tolerant logical entangling gates are essential for scalable quantum computing, but are limited by the error rates and overheads of physical two-qubit gates and measurements. To address this limitation, we introduce phantom codes-quantum error-correcting codes that realize entangling gates between all logical qubits in a code block purely through relabelling of physical qubits during compila…
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Fault-tolerant logical entangling gates are essential for scalable quantum computing, but are limited by the error rates and overheads of physical two-qubit gates and measurements. To address this limitation, we introduce phantom codes-quantum error-correcting codes that realize entangling gates between all logical qubits in a code block purely through relabelling of physical qubits during compilation, yielding perfect fidelity with no spatial or temporal overhead. We present a systematic study of such codes. First, we identify phantom codes using complementary numerical and analytical approaches. We exhaustively enumerate all $2.71 \times 10^{10}$ inequivalent CSS codes up to $n=14$ and identify additional instances up to $n=21$ via SAT-based methods. We then construct higher-distance phantom-code families using quantum Reed-Muller codes and the binarization of qudit codes. Across all identified codes, we characterize other supported fault-tolerant logical Clifford and non-Clifford operations. Second, through end-to-end noisy simulations with state preparation, full QEC cycles, and realistic physical error rates, we demonstrate scalable advantages of phantom codes over the surface code across multiple tasks. We observe a one-to-two order-of-magnitude reduction in logical infidelity at comparable qubit overhead for GHZ-state preparation and Trotterized many-body simulation tasks, given a modest preselection acceptance rate. Our work establishes phantom codes as a viable architectural route to fault-tolerant quantum computation with scalable benefits for workloads with dense local entangling structure, and introduces general tools for systematically exploring the broader landscape of quantum error-correcting codes.
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Submitted 28 January, 2026;
originally announced January 2026.
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Magic tricycles: Efficient magic state generation with finite block-length quantum LDPC codes
Authors:
Varun Menon,
J. Pablo Bonilla-Ataides,
Rohan Mehta,
Andi Gu,
Daniel Bochen Tan,
Mikhail D. Lukin
Abstract:
The preparation of high-fidelity non-Clifford (magic) states is an essential subroutine for universal quantum computation, but imposes substantial space-time overhead. Magic state factories based on high rate and distance quantum low-density parity check (LDPC) codes equipped with transversal non-Clifford gates can potentially reduce these overheads significantly, by circumventing the need for mul…
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The preparation of high-fidelity non-Clifford (magic) states is an essential subroutine for universal quantum computation, but imposes substantial space-time overhead. Magic state factories based on high rate and distance quantum low-density parity check (LDPC) codes equipped with transversal non-Clifford gates can potentially reduce these overheads significantly, by circumventing the need for multiple rounds of distillation and by producing a large number of magic states in a single code-block. As a step towards realizing efficient, fault-tolerant magic state production, we introduce a class of finite block-length quantum LDPC codes which we name tricycle codes, generalizing the well-known bicycle codes to three homological dimensions. These codes can support constant-depth physical circuits that implement logical $CCZ$ gates between three code blocks. To construct these constant-depth $CCZ$ circuits, we develop new analytical and numerical techniques that apply to a broad class of three-dimensional homological and balanced product codes. We further show that tricycle codes enable single-shot state-preparation and error correction, leading to a highly efficient magic-state generation protocol. Numerical simulations of specific codes confirm robust performance under circuit-level noise, demonstrating a high circuit-noise threshold of $>0.5\%$. With modest post-selection, certain tricycle codes of block-lengths of only $50-100$ qubits are shown to achieve logical error-rates of $6\times 10^{-10}$ or lower. Finally, we construct optimal depth syndrome extraction circuits for tricycle codes and present a protocol for implementing them efficiently on a reconfigurable neutral atom platform.
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Submitted 6 November, 2025; v1 submitted 14 August, 2025;
originally announced August 2025.
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Compilation of QCrank Encoding Algorithm for a Dynamically Programmable Qubit Array Processor
Authors:
Jan Balewski,
Wan-Hsuan Lin,
Anupam Mitra,
Milan Kornjača,
Stefan Ostermann,
Pedro L. S. Lopes,
Daniel Bochen Tan,
Jason Cong
Abstract:
Algorithm and hardware-aware compilation co-design is essential for the efficient deployment of near-term quantum programs. We present a compilation case-study implementing QCrank -- an efficient encoding protocol for storing sequenced real-valued classical data in a quantum state -- targeting neutral atom-based Dynamically Programmable Qubit Arrays (DPQAs). We show how key features of neutral-ato…
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Algorithm and hardware-aware compilation co-design is essential for the efficient deployment of near-term quantum programs. We present a compilation case-study implementing QCrank -- an efficient encoding protocol for storing sequenced real-valued classical data in a quantum state -- targeting neutral atom-based Dynamically Programmable Qubit Arrays (DPQAs). We show how key features of neutral-atom arrays such as high qubits count, operation parallelism, multi-zone architecture, and natively reconfigurable connectivity can be used to inform effective algorithm deployment. We identify algorithmic and circuit features that signal opportunities to implement them in a hardware-efficient manner. To evaluate projected hardware performance, we define a realistic noise model for DPQAs using parameterized Pauli channels, implement it in Qiskit circuit simulators, and assess QCrank's accuracy for writing and reading back 24-320 real numbers into 6-20 qubits. We compare DPQA results with simulated performances of Quantinuum's H1-1E and with experimental results from IBM Fez, highlighting promising accuracy scaling for DPQAs.
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Submitted 15 July, 2025; v1 submitted 14 July, 2025;
originally announced July 2025.
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Assessing Quantum Layout Synthesis Tools via Known Optimal-SWAP Cost Benchmarks
Authors:
Shuohao Ping,
Wan-Hsuan Lin,
Daniel Bochen Tan,
Jason Cong
Abstract:
Quantum layout synthesis (QLS) is a critical step in quantum program compilation for superconducting quantum computers, involving the insertion of SWAP gates to satisfy hardware connectivity constraints. While previous works have introduced SWAP-free benchmarks with known-optimal depths for evaluating QLS tools, these benchmarks overlook SWAP count - a key performance metric. Real-world applicatio…
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Quantum layout synthesis (QLS) is a critical step in quantum program compilation for superconducting quantum computers, involving the insertion of SWAP gates to satisfy hardware connectivity constraints. While previous works have introduced SWAP-free benchmarks with known-optimal depths for evaluating QLS tools, these benchmarks overlook SWAP count - a key performance metric. Real-world applications often require SWAP gates, making SWAP-free benchmarks insufficient for fully assessing QLS tool performance. To address this limitation, we introduce QUBIKOS, a benchmark set with provable-optimal SWAP counts and non-trivial circuit structures. For the first time, we are able to quantify the optimality gaps of SWAP gate usages of the leading QLS algorithms, which are surprisingly large: LightSabre from IBM delivers the best performance with an optimality gap of 63x, followed by ML-QLS with an optimality gap of 117x. Similarly, QMAP and t|ket> exhibit significantly larger gaps of 250x and 330x, respectively. This highlights the need for further advancements in QLS methodologies. Beyond evaluation, QUBIKOS offers valuable insights for guiding the development of future QLS tools, as demonstrated through an analysis of a suboptimal case in LightSABRE. This underscores QUBIKOS's utility as both an evaluation framework and a tool for advancing QLS research.
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Submitted 4 March, 2025; v1 submitted 12 February, 2025;
originally announced February 2025.
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Reuse-Aware Compilation for Zoned Quantum Architectures Based on Neutral Atoms
Authors:
Wan-Hsuan Lin,
Daniel Bochen Tan,
Jason Cong
Abstract:
Quantum computing architectures based on neutral atoms offer large scales and high-fidelity operations. They can be heterogeneous, with different zones for storage, entangling operations, and readout. Zoned architectures improve computation fidelity by shielding idling qubits in storage from side-effect noise, unlike monolithic architectures where all operations occur in a single zone. However, su…
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Quantum computing architectures based on neutral atoms offer large scales and high-fidelity operations. They can be heterogeneous, with different zones for storage, entangling operations, and readout. Zoned architectures improve computation fidelity by shielding idling qubits in storage from side-effect noise, unlike monolithic architectures where all operations occur in a single zone. However, supporting these flexible architectures with efficient compilation remains challenging. In this paper, we propose ZAC, a scalable compiler for zoned architectures. ZAC minimizes data movement overhead between zones with qubit reuse, i.e., keeping them in the entanglement zone if an immediate entangling operation is pending. Other innovations include novel data placement and instruction scheduling strategies in ZAC, a flexible specification of zoned architectures, and an intermediate representation for zoned architectures, ZAIR. Our evaluation shows that zoned architectures equipped with ZAC achieve a 22x improvement in fidelity compared to monolithic architectures. Moreover, ZAC is shown to have a 10% fidelity gap on average compared to the ideal solution. This significant performance enhancement enables more efficient and reliable quantum circuit execution, enabling advancements in quantum algorithms and applications. ZAC is open source at https://github.com/UCLA-VAST/ZAC
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Submitted 25 February, 2026; v1 submitted 18 November, 2024;
originally announced November 2024.
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Quantum State Preparation Circuit Optimization Exploiting Don't Cares
Authors:
Hanyu Wang,
Daniel Bochen Tan,
Jason Cong
Abstract:
Quantum state preparation initializes the quantum registers and is essential for running quantum algorithms. Designing state preparation circuits that entangle qubits efficiently with fewer two-qubit gates enhances accuracy and alleviates coupling constraints on devices. Existing methods synthesize an initial circuit and leverage compilers to reduce the circuit's gate count while preserving the un…
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Quantum state preparation initializes the quantum registers and is essential for running quantum algorithms. Designing state preparation circuits that entangle qubits efficiently with fewer two-qubit gates enhances accuracy and alleviates coupling constraints on devices. Existing methods synthesize an initial circuit and leverage compilers to reduce the circuit's gate count while preserving the unitary equivalency. In this study, we identify numerous conditions within the quantum circuit where breaking local unitary equivalences does not alter the overall outcome of the state preparation (i.e., don't cares). We introduce a peephole optimization algorithm that identifies such unitaries for replacement in the original circuit. Exploiting these don't care conditions, our algorithm achieves a 36% reduction in the number of two-qubit gates compared to prior methods.
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Submitted 2 September, 2024;
originally announced September 2024.
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Compilation for Dynamically Field-Programmable Qubit Arrays with Efficient and Provably Near-Optimal Scheduling
Authors:
Daniel Bochen Tan,
Wan-Hsuan Lin,
Jason Cong
Abstract:
Dynamically field-programmable qubit arrays based on neutral atoms feature high fidelity and highly parallel gates for quantum computing. However, it is challenging for compilers to fully leverage the novel flexibility offered by such hardware while respecting its various constraints. In this study, we break down the compilation for this architecture into three tasks: scheduling, placement, and ro…
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Dynamically field-programmable qubit arrays based on neutral atoms feature high fidelity and highly parallel gates for quantum computing. However, it is challenging for compilers to fully leverage the novel flexibility offered by such hardware while respecting its various constraints. In this study, we break down the compilation for this architecture into three tasks: scheduling, placement, and routing. We formulate these three problems and present efficient solutions to them. Notably, our scheduling based on graph edge-coloring is provably near-optimal in terms of the number of two-qubit gate stages (at most one more than the optimum). As a result, our compiler, Enola, reduces this number of stages by 3.7x and improves the fidelity by 5.9x compared to OLSQ-DPQA, the current state of the art. Additionally, Enola is highly scalable, e.g., within 30 minutes, it can compile circuits with 10,000 qubits, a scale sufficient for the current era of quantum computing. Enola is open source at https://github.com/UCLA-VAST/Enola
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Submitted 2 November, 2024; v1 submitted 23 May, 2024;
originally announced May 2024.
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A SAT Scalpel for Lattice Surgery: Representation and Synthesis of Subroutines for Surface-Code Fault-Tolerant Quantum Computing
Authors:
Daniel Bochen Tan,
Murphy Yuezhen Niu,
Craig Gidney
Abstract:
Quantum error correction is necessary for large-scale quantum computing. A promising quantum error correcting code is the surface code. For this code, fault-tolerant quantum computing (FTQC) can be performed via lattice surgery, i.e., splitting and merging patches of code. Given the frequent use of certain lattice-surgery subroutines (LaS), it becomes crucial to optimize their design in order to m…
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Quantum error correction is necessary for large-scale quantum computing. A promising quantum error correcting code is the surface code. For this code, fault-tolerant quantum computing (FTQC) can be performed via lattice surgery, i.e., splitting and merging patches of code. Given the frequent use of certain lattice-surgery subroutines (LaS), it becomes crucial to optimize their design in order to minimize the overall spacetime volume of FTQC. In this study, we define the variables to represent LaS and the constraints on these variables. Leveraging this formulation, we develop a synthesizer for LaS, LaSsynth, that encodes a LaS construction problem into a SAT instance, subsequently querying SAT solvers for a solution. Starting from a baseline design, we can gradually invoke the solver with shrinking spacetime volume to derive more compact designs. Due to our foundational formulation and the use of SAT solvers, LaSsynth can exhaustively explore the design space, yielding optimal designs in volume. For example, it achieves 8% and 18% volume reduction respectively over two states-of-the-art human designs for the 15-to-1 T-factory, a bottleneck in FTQC.
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Submitted 30 August, 2024; v1 submitted 28 April, 2024;
originally announced April 2024.
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Depth-Optimal Addressing of 2D Qubit Array with 1D Controls Based on Exact Binary Matrix Factorization
Authors:
Daniel Bochen Tan,
Shuohao Ping,
Jason Cong
Abstract:
Reducing control complexity is essential for achieving large-scale quantum computing. However, reducing control knobs may compromise the ability to independently address each qubit. Recent progress in neutral atom-based platforms suggests that rectangular (row-column) addressing may strike a balance between control granularity and flexibility for 2D qubit arrays. This scheme allows addressing qubi…
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Reducing control complexity is essential for achieving large-scale quantum computing. However, reducing control knobs may compromise the ability to independently address each qubit. Recent progress in neutral atom-based platforms suggests that rectangular (row-column) addressing may strike a balance between control granularity and flexibility for 2D qubit arrays. This scheme allows addressing qubits on the intersections of a set of rows and columns each time. While quadratically reducing controls, it may necessitate more depth. We formulate the depth-optimal rectangular addressing problem as exact binary matrix factorization, an NP-hard problem also appearing in communication complexity and combinatorial optimization. We introduce a satisfiability modulo theories-based solver for this problem, and a heuristic, row packing, performing close to the optimal solver on various benchmarks. Furthermore, we discuss rectangular addressing in the context of fault-tolerant quantum computing, leveraging a natural two-level structure.
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Submitted 22 March, 2024; v1 submitted 24 January, 2024;
originally announced January 2024.
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Q-Pilot: Field Programmable Qubit Array Compilation with Flying Ancillas
Authors:
Hanrui Wang,
Daniel Bochen Tan,
Pengyu Liu,
Yilian Liu,
Jiaqi Gu,
Jason Cong,
Song Han
Abstract:
Neutral atom arrays have become a promising platform for quantum computing, especially the field programmable qubit array (FPQA) endowed with the unique capability of atom movement. This feature allows dynamic alterations in qubit connectivity during runtime, which can reduce the cost of executing long-range gates and improve parallelism. However, this added flexibility introduces new challenges i…
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Neutral atom arrays have become a promising platform for quantum computing, especially the field programmable qubit array (FPQA) endowed with the unique capability of atom movement. This feature allows dynamic alterations in qubit connectivity during runtime, which can reduce the cost of executing long-range gates and improve parallelism. However, this added flexibility introduces new challenges in circuit compilation. Inspired by the placement and routing strategies for FPGAs, we propose to map all data qubits to fixed atoms while utilizing movable atoms to route for 2-qubit gates between data qubits. Coined flying ancillas, these mobile atoms function as ancilla qubits, dynamically generated and recycled during execution. We present Q-Pilot, a scalable compiler for FPQA employing flying ancillas to maximize circuit parallelism. For two important quantum applications, quantum simulation and the Quantum Approximate Optimization Algorithm (QAOA), we devise domain-specific routing strategies. In comparison to alternative technologies such as superconducting devices or fixed atom arrays, Q-Pilot effectively harnesses the flexibility of FPQA, achieving reductions of 1.4x, 27.7x, and 6.3x in circuit depth for 100-qubit random, quantum simulation, and QAOA circuits, respectively.
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Submitted 11 September, 2024; v1 submitted 25 November, 2023;
originally announced November 2023.
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Atomique: A Quantum Compiler for Reconfigurable Neutral Atom Arrays
Authors:
Hanrui Wang,
Pengyu Liu,
Daniel Bochen Tan,
Yilian Liu,
Jiaqi Gu,
David Z. Pan,
Jason Cong,
Umut A. Acar,
Song Han
Abstract:
The neutral atom array has gained prominence in quantum computing for its scalability and operation fidelity. Previous works focus on fixed atom arrays (FAAs) that require extensive SWAP operations for long-range interactions. This work explores a novel architecture reconfigurable atom arrays (RAAs), also known as field programmable qubit arrays (FPQAs), which allows for coherent atom movements du…
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The neutral atom array has gained prominence in quantum computing for its scalability and operation fidelity. Previous works focus on fixed atom arrays (FAAs) that require extensive SWAP operations for long-range interactions. This work explores a novel architecture reconfigurable atom arrays (RAAs), also known as field programmable qubit arrays (FPQAs), which allows for coherent atom movements during circuit execution under some constraints. Such atom movements, which are unique to this architecture, could reduce the cost of long-range interactions significantly if the atom movements could be scheduled strategically.
In this work, we introduce Atomique, a compilation framework designed for qubit mapping, atom movement, and gate scheduling for RAA. Atomique contains a qubit-array mapper to decide the coarse-grained mapping of the qubits to arrays, leveraging MAX k-Cut on a constructed gate frequency graph to minimize SWAP overhead. Subsequently, a qubit-atom mapper determines the fine-grained mapping of qubits to specific atoms in the array and considers load balance to prevent hardware constraint violations. We further propose a router that identifies parallel gates, schedules them simultaneously, and reduces depth. We evaluate Atomique across 20+ diverse benchmarks, including generic circuits (arbitrary, QASMBench, SupermarQ), quantum simulation, and QAOA circuits. Atomique consistently outperforms IBM Superconducting, FAA with long-range gates, and FAA with rectangular and triangular topologies, achieving significant reductions in depth and the number of two-qubit gates.
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Submitted 14 November, 2024; v1 submitted 25 November, 2023;
originally announced November 2023.
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Compiling Quantum Circuits for Dynamically Field-Programmable Neutral Atoms Array Processors
Authors:
Daniel Bochen Tan,
Dolev Bluvstein,
Mikhail D. Lukin,
Jason Cong
Abstract:
Dynamically field-programmable qubit arrays (DPQA) have recently emerged as a promising platform for quantum information processing. In DPQA, atomic qubits are selectively loaded into arrays of optical traps that can be reconfigured during the computation itself. Leveraging qubit transport and parallel, entangling quantum operations, different pairs of qubits, even those initially far away, can be…
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Dynamically field-programmable qubit arrays (DPQA) have recently emerged as a promising platform for quantum information processing. In DPQA, atomic qubits are selectively loaded into arrays of optical traps that can be reconfigured during the computation itself. Leveraging qubit transport and parallel, entangling quantum operations, different pairs of qubits, even those initially far away, can be entangled at different stages of the quantum program execution. Such reconfigurability and non-local connectivity present new challenges for compilation, especially in the layout synthesis step which places and routes the qubits and schedules the gates. In this paper, we consider a DPQA architecture that contains multiple arrays and supports 2D array movements, representing cutting-edge experimental platforms. Within this architecture, we discretize the state space and formulate layout synthesis as a satisfiability modulo theories problem, which can be solved by existing solvers optimally in terms of circuit depth. For a set of benchmark circuits generated by random graphs with complex connectivities, our compiler OLSQ-DPQA reduces the number of two-qubit entangling gates on small problem instances by 1.7x compared to optimal compilation results on a fixed planar architecture. To further improve scalability and practicality of the method, we introduce a greedy heuristic inspired by the iterative peeling approach in classical integrated circuit routing. Using a hybrid approach that combined the greedy and optimal methods, we demonstrate that our DPQA-based compiled circuits feature reduced scaling overhead compared to a grid fixed architecture, resulting in 5.1X less two-qubit gates for 90 qubit quantum circuits. These methods enable programmable, complex quantum circuits with neutral atom quantum computers, as well as informing both future compilers and future hardware choices.
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Submitted 1 July, 2024; v1 submitted 6 June, 2023;
originally announced June 2023.