Building Perfect Quantum Arrays, One Atom at a Time

Author: Denis Avetisyan

Researchers have developed a new algorithm that efficiently rearranges neutral atoms, paving the way for more stable and scalable quantum computers.

The scaling of rearrangement moves, computed via Monte Carlo simulation at zero atom-loss probability, remains consistently near $0.55$ for occupation fractions of $0.5$ and $0.7$, but increases to approximately $0.71$ at higher fill levels, suggesting a shift in the dominant mechanism governing rearrangement as the system approaches saturation.

ATLAS, a loss-aware atom rearrangement algorithm, demonstrates improved scalability and defect reduction in neutral-atom quantum arrays.

Achieving scalable and high-fidelity quantum computation with neutral atoms hinges on assembling defect-free arrays, a challenge complicated by stochastic loading and inevitable atom loss during rearrangement. This work introduces ATLAS-an open-source algorithm for efficiently rearranging atoms-detailed in ‘ATLAS: Efficient Atom Rearrangement for Defect-Free Neutral-Atom Quantum Arrays Under Transport Loss’. Through optimized parallel moves and loss-aware planning, ATLAS demonstrates sublinear scaling and high retention rates, exceeding the performance of prior methods. Could this approach unlock the creation of substantially larger and more reliable neutral-atom quantum processors?

The Promise of Atomic Order: A New Quantum Paradigm

Neutral atom quantum computing presents a compelling alternative to more established qubit technologies by harnessing the intrinsic quantum properties of individual, neutral atoms. These atoms, typically rubidium or cesium, serve as qubits – the fundamental units of quantum information – and exhibit remarkably long coherence times, meaning their quantum states remain stable for a duration sufficient to perform complex calculations. Crucially, this approach allows for “all-to-all” connectivity, where any qubit can directly interact with any other within the array, circumventing the limitations of nearest-neighbor interactions found in many other quantum systems. This connectivity is achieved through the precise manipulation of atomic positions using optical tweezers, creating a scalable and highly interconnected quantum register. The combination of extended coherence and full connectivity positions neutral atom qubits as a particularly promising platform for realizing fault-tolerant quantum computation and tackling currently intractable computational problems.

The realization of practical quantum computation with neutral atoms hinges on the ability to perform quantum operations with extremely high fidelity. Unlike classical bits, qubits are susceptible to environmental noise, leading to errors in computation. These errors accumulate rapidly if operations aren’t nearly perfect. Crucially, the precision with which neutral atoms are arranged directly impacts the fidelity of these operations; the strength of the interactions between qubits-manipulated by lasers-is exquisitely sensitive to their relative positions. Even slight misalignments can introduce unwanted crosstalk or weaken the desired quantum gates, degrading performance. Therefore, significant research focuses on developing techniques – such as optical tweezers and holographic shaping of laser beams – to create, control, and maintain these atomic arrays with nanometer-scale precision, effectively minimizing errors and paving the way for scalable quantum processors.

The scalability of neutral atom quantum computing hinges on the ability to construct expansive, highly ordered arrays of these atomic qubits. Unlike some solid-state approaches, neutral atoms offer the potential for all-to-all connectivity, meaning any qubit can directly interact with any other, but this advantage is only fully realized with precise atomic placement. Defects within these arrays – missing atoms or atoms out of position – introduce errors and limit the complexity of computations. Current research focuses on advanced trapping and cooling techniques, including the use of optical tweezers and sophisticated laser configurations, to reliably assemble and maintain these large-scale, defect-free structures. Achieving this level of control is not merely an engineering challenge; it directly dictates the fidelity and ultimately, the computational power of neutral atom quantum processors, paving the way for tackling increasingly complex quantum algorithms and simulations.

The Art of Arrangement: Sculpting Quantum Registers

Atom rearrangement is the foundational process for creating ordered arrays of neutral atoms, specifically aiming for structures with minimal defects. This manipulation involves precisely controlling the spatial positioning of individual atoms, typically utilizing optical or magnetic trapping techniques. The resulting arrays are not simply aggregates, but rather deliberately constructed arrangements where each atom occupies a defined lattice site. Achieving defect-free structures is crucial as even single misplaced atoms can significantly alter the array’s properties and functionality, particularly in quantum computing applications where atomic position dictates qubit connectivity and coherence. The process necessitates overcoming interatomic repulsion and maintaining positional stability throughout the array construction.

The manipulation of individual atoms into defined arrays shares significant parallels with quantum circuit compilation. In quantum computing, a high-level algorithm is decomposed into a series of quantum gate operations – analogous to translating a desired atomic configuration into a specific sequence of physical movements. Each atom’s required position and interaction is effectively a quantum bit, or qubit, and the rearrangement process constitutes the execution of an algorithm to achieve a target quantum state, represented by the final atomic array. This translation involves mapping the abstract algorithm onto the physical constraints of the atom manipulation system, optimizing for minimal steps and error correction, much like optimizing a quantum circuit for a specific quantum processor.

Current atom rearrangement algorithms, including Modified LSAP (Linear Sum Assignment Problem) and PSCA (Phase Shift and Collision Avoidance), demonstrate feasibility for small-scale arrays but face computational complexity challenges when applied to larger systems. Modified LSAP, while efficient for minimizing total wire length, exhibits scalability issues due to its $O(n^3)$ complexity, where $n$ is the number of atoms. PSCA, offering improved performance in certain scenarios, still requires substantial computational resources for path planning and collision avoidance as array size increases. Consequently, research is focused on developing novel algorithms and optimization techniques – such as hierarchical approaches, machine learning-assisted pathfinding, and parallelization strategies – to address these limitations and enable the construction of large-scale, defect-free atom arrays.

ATLAS: A System Designed for Scalability and Resilience

ATLAS addresses the challenges of creating large-scale, defect-free neutral-atom arrays, a critical component for quantum computation and simulation. Current rearrangement algorithms often struggle with scalability and maintaining array fidelity due to atom loss during the rearrangement process. ATLAS is designed to mitigate these issues by focusing on efficient computation for larger array sizes and explicitly accounting for atom loss during the rearrangement planning stage. The algorithm aims to produce arrays with minimized defects and maximized atom retention, enabling the creation of denser and more reliable quantum systems. This is achieved through a novel combination of algorithmic strategies detailed in subsequent sections, prioritizing both scalability to larger array sizes and robustness against inevitable atom loss events.

The ATLAS algorithm employs a Two-Phase Plan-Then-Execute Framework to address the computational demands of large-scale neutral atom array rearrangement and to realistically simulate atom loss during the process. This framework decouples the rearrangement planning stage from the execution stage; the planning phase computes a complete rearrangement trajectory without considering real-time failures, while the execution phase iteratively applies the planned moves and incorporates a probabilistic model of atom loss. By separating these concerns, ATLAS reduces computational complexity, allowing for planning of rearrangements for arrays with thousands of atoms, and enables accurate modeling of the impact of atom loss on overall array fidelity. The execution phase dynamically adjusts the plan based on observed atom loss, ensuring robustness and maximizing the probability of successfully assembling the target configuration.

ATLAS employs Loss-Aware Target Sizing to proactively adjust target positions during rearrangement, accounting for anticipated atom loss and minimizing the impact on final array fidelity. This is coupled with a Parallel Transport Scheme which calculates atom movements based on maintaining constant distances to neighboring atoms; this approach reduces the cumulative displacement and associated excitation probability during transport. By strategically pre-allocating space for potential loss and optimizing movement pathways, ATLAS demonstrably achieves higher atom retention rates – up to 97% in simulations – and supports significantly increased array densities compared to traditional rearrangement algorithms. The algorithm prioritizes maintaining array connectivity throughout the process, directly contributing to improved overall performance and scalability.

Measuring Success: Retention, Fill Rate, and Velocity Profiles

ATLAS performance is fundamentally linked to both Fill Rate and Retention Rate. Fill Rate quantifies the density of atoms successfully positioned within the designated target zone; ATLAS achieves a Fill Rate exceeding 99% as demonstrated through Monte Carlo simulations. Retention Rate, conversely, measures the efficiency of atom utilization, representing the proportion of atoms remaining in the target zone after a specified operation or time period. These metrics are directly proportional to overall system efficiency; higher Fill and Retention Rates indicate a more effective and stable atom manipulation process, minimizing waste and maximizing operational throughput.

The ATLAS algorithm utilizes a Trapezoidal Velocity Profile to govern atom movement, implementing controlled acceleration and deceleration phases. This profile limits both the maximum velocity and the rate of velocity change – acceleration – experienced by each atom during relocation. By constraining these parameters, the algorithm minimizes positional errors arising from momentum and reduces the likelihood of atom loss due to instability. The Trapezoidal Velocity Profile consists of three distinct phases: a linear acceleration phase, a constant velocity phase, and a linear deceleration phase, ensuring smooth transitions and predictable atom trajectories.

ATLAS achieves a retention rate of 0.89 when operating on a 16×16 target size, indicating efficient atom utilization. This performance surpasses that of the PSCA method. Furthermore, ATLAS exhibits a sublinear move scaling factor of approximately 0.47, meaning the computational cost increases slower than linearly with the number of atoms moved. This scaling is comparable to the performance of leading multitweezer techniques, demonstrating competitive efficiency in large-scale atom manipulation.

Monte Carlo simulations demonstrate that retention rate decreases with both increasing lattice size and atom-loss probability, with a noticeable drop at higher loss probabilities due to iteration limits, though retention would otherwise remain around 80%.

Beyond Current Limits: The Trajectory of Scalable Quantum Systems

ATLAS signifies a notable advancement in the pursuit of scalable quantum computation by leveraging the unique properties of neutral atoms. This innovative platform achieves high-fidelity control and entanglement of individual atoms, arranged in precisely defined arrays – a critical requirement for executing complex quantum algorithms. Unlike some existing architectures where scaling introduces substantial overhead, ATLAS demonstrates a linear relationship between array size and computational capacity; this means that doubling the number of qubits only requires a proportionate increase in control infrastructure, potentially circumventing a major bottleneck in building fault-tolerant quantum computers. The system’s efficiency in creating defect-free arrays, coupled with its scalable architecture, positions it as a promising pathway toward realizing the full potential of quantum computation and achieving quantum advantage over classical computers.

The realization of practical quantum computation hinges on the ability to assemble large, highly ordered arrays of qubits – the quantum equivalent of bits. Defects within these arrays introduce errors that rapidly corrupt quantum information, severely limiting the complexity of algorithms that can be successfully executed. Consequently, achieving high-fidelity qubit arrangements is not merely a technical challenge, but a fundamental prerequisite for reaching the threshold where quantum computers can outperform classical computers – a state known as quantum advantage. Each additional qubit added to a defective array exponentially increases the probability of error, while defect-free architectures allow for the implementation of sophisticated error correction schemes, maintaining the delicate quantum states necessary for complex calculations and unlocking the full potential of quantum computation. The pursuit of these scalable, high-fidelity architectures represents a critical frontier in the development of fault-tolerant quantum computers.

Continued development centers on refining the Automated Tool for Lattice Assembly (ATLAS), a platform poised to overcome scalability bottlenecks in neutral atom quantum computing. Unlike architectures that experience a rapid increase in complexity – scaling at a rate of $N^{3/2}$ as the number of qubits, denoted by N, grows – ATLAS maintains a linear relationship between system size and the number of atoms required for initial assembly. This efficient scaling promises to significantly reduce the resources needed to construct large-scale quantum processors. Current research is directed towards enhancing atom rearrangement techniques and improving individual qubit control, with the overarching goal of unlocking the full potential of quantum computation by building systems capable of tackling previously intractable problems.

The pursuit of defect-free neutral-atom arrays, as detailed in this work with the ATLAS algorithm, echoes a fundamental truth about complex systems. It isn’t about building perfection, but rather coaxing order from inherent imperfections. The algorithm’s success isn’t in eliminating loss – a futile endeavor – but in accommodating it, rearranging the remaining atoms into a functional configuration. This resonates with a sentiment shared by Richard Feynman: “The first principle is that you must not fool yourself – and you are the easiest person to fool.” The illusion of complete control, of a perfectly scalable architecture, is precisely what this research sidesteps. ATLAS acknowledges the inevitable entropy, the atoms lost to the process, and designs for resilience within that reality. Scalability, it seems, isn’t a destination, but a continuous negotiation with the unpredictable.

What Lies Ahead?

The presentation of ATLAS feels less like a solution and more like a careful charting of the inevitable losses to come. Each optimized rearrangement, each minimized defect, merely delays the entropic tide. The algorithm addresses transport loss with admirable ingenuity, but the system, as a whole, remains exquisitely sensitive to the realities of physical manipulation. A ‘defect-free’ array is a transient illusion, a temporary reprieve from the decay inherent in any assembled system.

Scalability, predictably, remains the central preoccupation. But pursuing larger arrays without a fundamental shift in architectural thinking feels like building ever-more-complex sandcastles closer to the waterline. The focus will inevitably drift from simply moving atoms to understanding-and perhaps even embracing-the emergent properties of imperfect arrangements. Perhaps the true breakthroughs will not involve preventing loss, but harnessing it.

One anticipates a proliferation of increasingly sophisticated loss-aware algorithms, each a refined prediction of failure. Documentation, of course, will become a historical record of strategies that once worked, before the system inevitably evolves beyond them. The interesting question isn’t how to build a perfect array, but what novel computational substrates can emerge from controlled imperfection.

Original article: https://arxiv.org/pdf/2511.16303.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/