arXiv subjects

Madelyn Cain

Publications and source records attributed to Madelyn Cain.

At least 19 recordsLinked to original sources

arXiv2026

High-rate qLDPC processors

Despite significant progress on quantum low-density parity-check (qLDPC) codes, building qLDPC processors that are high-rate, high-throughput, hardware-friendly, and fast-to-decode remains a challenge. We introduce mitten codes, a family of qLDPC processor codes of encoding rate $20\%$ and check weight $9$, based on non-abelian groups. Their non-abelian structure evades distance bounds constraining abelian counterparts, allowing mitten codes to reach distance $18$ and beyond with just a few hundred data qubits. The logical operators of a mitten code are related by the group action, yielding a modular, low-overhead logical toolkit: full Clifford operations follow from bridging two reusable seed surgery gadgets or from a single fixed extractor. Furthermore, qLDPC processors based on mitten codes support high-rate surgery that executes many logical measurements in parallel, and parallel magic-state injection into all logical qubits at once. Under circuit-level noise, with our fast decoder, the $[\![300,60,14]\!]$ mitten code achieves, without extrapolation, a block logical error rate of ${\sim}10^{-11}$ per round at $0.1\%$ physical error rate (PER), while the $[\![ 975,195,\leq 24 ]\!]$ code reaches ${\sim}10^{-8}$ at $0.4\%$ PER. Decoding $15$ billion surgery experiments on the $[\![540,108,18]\!]$ code at $0.1\%$ PER, we observe only two logical failures, demonstrating a qLDPC processor capable of running ${\sim}10^{10}$ logical operations. Our decoder is compatible with sub-millisecond average latency per logical cycle, sufficient for real-time decoding on neutral atom hardware. Discovered by an end-to-end design pipeline built on sQetch, a distance estimator orders of magnitude faster than existing tools, and mapping efficiently onto near-term neutral atom and superconducting hardware, mitten codes open a practical path toward fault-tolerant quantum computation.

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arXiv2026

Shor's algorithm is possible with as few as 10,000 reconfigurable atomic qubits

Quantum computers have the potential to perform computational tasks beyond the reach of classical machines. A prominent example is Shor's algorithm for integer factorization and discrete logarithms, which is of both fundamental importance and practical relevance to cryptography. However, due to the high overhead of quantum error correction, optimized resource estimates for cryptographically relevant instances of Shor's algorithm require millions of physical qubits. Here, by leveraging advances in high-rate quantum error-correcting codes, efficient logical instruction sets, and circuit design, we show that Shor's algorithm can be executed at cryptographically relevant scales with as few as 10,000 reconfigurable atomic qubits. Increasing the number of physical qubits improves time efficiency by enabling greater parallelism; under plausible assumptions, the runtime for discrete logarithms on the P-256 elliptic curve could be just a few days for a system with 26,000 physical qubits, while the runtime for factoring RSA-2048 integers is one to two orders of magnitude longer. Recent neutral-atom experiments have demonstrated universal fault-tolerant operations below the error-correction threshold, computation on arrays of hundreds of qubits, and trapping arrays with more than 6,000 highly coherent qubits. Although substantial engineering challenges remain, our theoretical analysis indicates that an appropriately designed neutral-atom architecture could support quantum computation at cryptographically relevant scales. More broadly, these results highlight the capability of neutral atoms for fault-tolerant quantum computing with wide-ranging scientific and technological applications.

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arXiv2025

Batched high-rate logical operations for quantum LDPC codes

High-rate quantum LDPC (qLDPC) codes reduce memory overhead by densely packing many logical qubits into a single block of physical qubits. Here we extend this concept to high-rate computation by constructing \emph{batched} fault-tolerant operations that apply the same logical gate across many code blocks in parallel. By leveraging shared physical resources to execute many logical operations in parallel, these operations realize high rates in space-time and significantly reduce computational costs. For \emph{arbitrary} CSS qLDPC codes, we build batched gadgets with \emph{constant space-time overhead} (assuming fast classical computation) for (i) single-shot error correction, state preparation, and code surgeries (ii) code switching, and (iii) addressable Clifford gates. Using these batched gadgets we also construct parallel non-Clifford gates with low space-time cost. We outline principles for designing parallel quantum algorithms optimized for a batched architecture, and show in particular how lattice Hamiltonian dynamical simulations can be compiled efficiently. We also propose a near-term implementation using new self-dual Bivariate-Bicycle codes with high encoding rates ($\sim 1/10$), transversal Clifford gates, and global $T$ gates via parallel magic state cultivation, enabling Hamiltonian simulations with a lower space-time cost than analogous surface-code protocols and low-rate qLDPC protocols. These results open new paths toward scalable quantum computation via co-design of parallel quantum algorithms and high-rate fault-tolerant protocols.

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arXiv2025

Architectural mechanisms of a universal fault-tolerant quantum computer

Quantum error correction (QEC) is believed to be essential for the realization of large-scale quantum computers. However, due to the complexity of operating on the encoded `logical' qubits, understanding the physical principles for building fault-tolerant quantum devices and combining them into efficient architectures is an outstanding scientific challenge. Here we utilize reconfigurable arrays of up to 448 neutral atoms to implement all key elements of a universal, fault-tolerant quantum processing architecture and experimentally explore their underlying working mechanisms. We first employ surface codes to study how repeated QEC suppresses errors, demonstrating 2.14(13)x below-threshold performance in a four-round characterization circuit by leveraging atom loss detection and machine learning decoding. We then investigate logical entanglement using transversal gates and lattice surgery, and extend it to universal logic through transversal teleportation with 3D [[15,1,3]] codes, enabling arbitrary-angle synthesis with logarithmic overhead. Finally, we develop mid-circuit qubit re-use, increasing experimental cycle rates by two orders of magnitude and enabling deep-circuit protocols with dozens of logical qubits and hundreds of logical teleportations with [[7,1,3]] and high-rate [[16,6,4]] codes while maintaining constant internal entropy. Our experiments reveal key principles for efficient architecture design, involving the interplay between quantum logic and entropy removal, judiciously using physical entanglement in logic gates and magic state generation, and leveraging teleportations for universality and physical qubit reset. These results establish foundations for scalable, universal error-corrected processing and its practical implementation with neutral atom systems.

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arXiv2025

Resource Analysis of Low-Overhead Transversal Architectures for Reconfigurable Atom Arrays

Neutral atom arrays have recently emerged as a promising platform for fault-tolerant quantum computing. Based on these advances, including dynamically-reconfigurable connectivity and fast transversal operations, we present a low-overhead architecture that supports the layout and resource estimation of large-scale fault-tolerant quantum algorithms. Utilizing recent advances in fault tolerance with transversal gate operations, this architecture achieves a run time speed-up on the order of the code distance $d$, which we find directly translates to run time improvements of large-scale quantum algorithms. Our architecture consists of functional building blocks of key algorithmic subroutines, including magic state factories, quantum arithmetic units, and quantum look-up tables. These building blocks are implemented using efficient transversal operations, and we design space-time efficient versions of them that minimize interaction distance, thereby reducing atom move times and minimizing the volume for correlated decoding. We further propose models to estimate their logical error performance. We perform resource estimation for a large-scale implementation of Shor's factoring algorithm, one of the prototypical benchmarks for large-scale quantum algorithms, finding that 2048-bit RSA factoring can be executed with 19 million qubits in 5.6 days, for 1 ms QEC cycle times. This represents close to 50$\times$ speed-up of the run-time compared to existing estimates with similar assumptions, with no increase in space footprint.

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arXiv2025

Fast correlated decoding of transversal logical algorithms

Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead. Recent advances have shown that by jointly decoding logical qubits in algorithms composed of transversal gates, the number of syndrome extraction rounds can be reduced by a factor of the code distance $d$, at the cost of increased classical decoding complexity. Here, we reformulate the problem of decoding transversal circuits by directly decoding relevant logical operator products as they propagate through the circuit. This procedure transforms the decoding task into one closely resembling that of a single-qubit memory propagating through time. The resulting approach leads to fast decoding and reduced problem size while maintaining high performance. Focusing on the surface code, we prove that this method enables fault-tolerant decoding with minimum-weight perfect matching, and benchmark its performance on example circuits including magic state distillation. We find that the threshold is comparable to that of a single-qubit memory, and that the total decoding run time can be, in fact, less than that of conventional lattice surgery. Our approach enables fast correlated decoding, providing a pathway to directly extend single-qubit QEC techniques to transversal algorithms.

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arXiv2025

Counterdiabatic Driving with Performance Guarantees

Counterdiabatic (CD) driving has the potential to speed up adiabatic quantum state preparation by suppressing unwanted excitations. However, existing approaches either require intractable classical computations or are based on approximations which do not have performance guarantees. We propose and analyze a non-variational, system-agnostic CD expansion method and analytically show that it converges exponentially quickly in the expansion order. In finite systems, the required resources scale inversely with the spectral gap, which we argue is asymptotically optimal. To extend our method to the thermodynamic limit and suppress errors stemming from high-frequency transitions, we leverage finite-time adiabatic protocols. In particular, we show that a time determined by the quantum speed limit is sufficient to prepare the desired ground state, without the need to optimize the adiabatic trajectory. Numerical tests of our method on the quantum Ising chain show that our method can outperform state-of-the-art variational CD approaches.

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arXiv2025

Leveraging Qubit Loss Detection in Fault Tolerant Quantum Algorithms

Qubit loss errors constitute a dominant source of noise in many quantum hardware systems, particularly in neutral atom quantum computers. We develop a theoretical framework to effectively detect and correct loss errors in logical algorithms and leverage such loss information in decoding. Considering general quantum error correction codes and logical circuits, we introduce a delayed-erasure decoder for experimentally-motivated error models which leverages information from delayed loss detection to accurately correct loss errors, even when the precise moment of the error is unknown. Using this decoder, we identify strategies for detecting and correcting loss errors based on the logical circuit structure. For deep circuits prior to logical measurement, we explore methods to integrate loss detection into syndrome extraction with minimal overhead, identifying optimal strategies depending on the qubit loss fraction in the noise and hardware capabilities. In contrast, we find that many key algorithmic subroutines involve frequent gate teleportation, shortening the circuit depth before logical measurement and naturally replacing qubits with no additional experimental overhead. We simulate this setting using a toy model algorithm for small-angle synthesis, and find a significant performance improvement as the loss fraction increases. These results provide a path forward for advancing large-scale fault tolerant quantum computation in systems with loss error detection.

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arXiv2025

Probing the Kitaev honeycomb model on a neutral-atom quantum computer

Quantum simulations of many-body systems are among the most promising applications of quantum computers. In particular, models based on strongly-correlated fermions are central to our understanding of quantum chemistry and materials problems, and can lead to exotic, topological phases of matter. However, due to the non-local nature of fermions, such models are challenging to simulate with qubit devices. Here we realize a digital quantum simulation architecture for two-dimensional fermionic systems based on reconfigurable atom arrays. We utilize a fermion-to-qubit mapping based on Kitaev's model on a honeycomb lattice, in which fermionic statistics are encoded using long-range entangled states. We prepare these states efficiently using measurement and feedforward, realize subsequent fermionic evolution through Floquet engineering with tunable entangling gates interspersed with atom rearrangement, and improve results with built-in error detection. Leveraging this fermion description of the Kitaev spin model, we efficiently prepare topological states across its complex phase diagram and verify the non-Abelian spin liquid phase by evaluating an odd Chern number. We further explore this two-dimensional fermion system by realizing tunable dynamics and directly probing fermion exchange statistics. Finally, we simulate strong interactions and study dynamics of the Fermi-Hubbard model on a square lattice. These results pave the way for digital quantum simulations of complex fermionic systems for materials science, chemistry, and high-energy physics.

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arXiv2024

Derandomized shallow shadows: Efficient Pauli learning with bounded-depth circuits

Efficiently estimating large numbers of non-commuting observables is an important subroutine of many quantum science tasks. We present the derandomized shallow shadows (DSS) algorithm for efficiently learning a large set of non-commuting observables, using shallow circuits to rotate into measurement bases. Exploiting tensor network techniques to ensure polynomial scaling of classical resources, our algorithm outputs a set of shallow measurement circuits that approximately minimizes the sample complexity of estimating a given set of Pauli strings. We numerically demonstrate systematic improvement, in comparison with state-of-the-art techniques, for energy estimation of quantum chemistry benchmarks and verification of quantum many-body systems, and we observe DSS's performance consistently improves as one allows deeper measurement circuits. These results indicate that in addition to being an efficient, low-depth, stand-alone algorithm, DSS can also benefit many larger quantum algorithms requiring estimation of multiple non-commuting observables.

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arXiv2024

Experimental Demonstration of Logical Magic State Distillation

Realizing universal fault-tolerant quantum computation is a key goal in quantum information science. By encoding quantum information into logical qubits utilizing quantum error correcting codes, physical errors can be detected and corrected, enabling substantial reduction in logical error rates. However, the set of logical operations that can be easily implemented on such encoded qubits is often constrained, necessitating the use of special resource states known as 'magic states' to implement universal, classically hard circuits. A key method to prepare high-fidelity magic states is to perform 'distillation', creating them from multiple lower fidelity inputs. Here we present the experimental realization of magic state distillation with logical qubits on a neutral-atom quantum computer. Our approach makes use of a dynamically reconfigurable architecture to encode and perform quantum operations on many logical qubits in parallel. We demonstrate the distillation of magic states encoded in d=3 and d=5 color codes, observing improvements of the logical fidelity of the output magic states compared to the input logical magic states. These experiments demonstrate a key building block of universal fault-tolerant quantum computation, and represent an important step towards large-scale logical quantum processors.

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arXiv2024

Quantum adiabatic optimization with Rydberg arrays: localization phenomena and encoding strategies

Quantum adiabatic optimization seeks to solve combinatorial problems using quantum dynamics, requiring the Hamiltonian of the system to align with the problem of interest. However, these Hamiltonians are often incompatible with the native constraints of quantum hardware, necessitating encoding strategies to map the original problem into a hardware-conformant form. While the classical overhead associated with such mappings is easily quantifiable and typically polynomial in problem size, it is much harder to quantify their overhead on the quantum algorithm, e.g., the transformation of the adiabatic timescale. In this work, we address this challenge on the concrete example of the encoding scheme proposed in [Nguyen et al., PRX Quantum 4, 010316 (2023)], which is designed to map optimization problems on arbitrarily connected graphs into Rydberg atom arrays. We consider the fundamental building blocks underlying this encoding scheme and determine the scaling of the minimum gap with system size along adiabatic protocols. Even when the original problem is trivially solvable, we find that the encoded problem can exhibit an exponentially closing minimum gap. We show that this originates from a quantum coherent effect, which gives rise to an unfavorable localization of the ground-state wavefunction. On the QuEra Aquila neutral atom machine, we observe such localization and its effect on the success probability of finding the correct solution to the encoded optimization problem. Finally, we propose quantum-aware modifications of the encoding scheme that avoid this quantum bottleneck and lead to an exponential improvement in the adiabatic performance. This highlights the crucial importance of accounting for quantum effects when designing strategies to encode classical problems onto quantum platforms.

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arXiv2024

Strategies for running the QAOA at hundreds of qubits

We explore strategies aimed at reducing the amount of computation, both quantum and classical, required to run the Quantum Approximate Optimization Algorithm (QAOA). First, following Wurtz et al. [Phys.Rev A 104:052419], we consider the standard QAOA with instance-independent "tree" parameters chosen in advance. These tree parameters are chosen to optimize the MaxCut expectation for large girth graphs. We provide extensive numerical evidence supporting the performance guarantee for tree parameters conjectured in [Phys.Rev A 103:042612] and see that the approximation ratios obtained with tree parameters are typically well beyond the conjectured lower bounds, often comparable to performing a full optimization. This suggests that in practice, the QAOA can achieve near-optimal performance without the need for parameter optimization. Next, we modify the warm-start QAOA of Tate et al. [Quantum 7:1121]. The starting state for the QAOA is now an optimized product state associated with a solution of the Goemans-Williamson (GW) algorithm. Surprisingly, the tree parameters continue to perform well for the warm-start QAOA. We find that for random 3-regular graphs with hundreds of vertices, the expected cut obtained by the warm-start QAOA at depth $p \gtrsim 3$ is comparable to that of the standard GW algorithm. Our numerics on random instances do not provide general performance guarantees but do provide substantial evidence that there exists a regime of instance sizes in which the QAOA finds good solutions at low depth without the need for parameter optimization. For each instance studied, we classically compute the expected size of the QAOA distribution of cuts; producing the actual cuts requires running on a quantum computer.

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arXiv2024

Low-Overhead Transversal Fault Tolerance for Universal Quantum Computation

Fast, reliable logical operations are essential for realizing useful quantum computers. By redundantly encoding logical qubits into many physical qubits and using syndrome measurements to detect and correct errors, one can achieve low logical error rates. However, for many practical quantum error correcting (QEC) codes such as the surface code, due to syndrome measurement errors, standard constructions require multiple extraction rounds -- on the order of the code distance $d$ -- for fault-tolerant computation, particularly considering fault-tolerant state preparation. Here, we show that logical operations can be performed fault-tolerantly with only a constant number of extraction rounds for a broad class of QEC codes, including the surface code with magic state inputs and feed-forward, to achieve ``transversal algorithmic fault tolerance". Through the combination of transversal operations and novel strategies for correlated decoding, despite only having access to partial syndrome information, we prove that the deviation from the ideal logical measurement distribution can be made exponentially small in the distance, even if the instantaneous quantum state cannot be made close to a logical codeword due to measurement errors. We supplement this proof with circuit-level simulations in a range of relevant settings, demonstrating the fault tolerance and competitive performance of our approach. Our work sheds new light on the theory of quantum fault tolerance and has the potential to reduce the space-time cost of practical fault-tolerant quantum computation by over an order of magnitude.

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arXiv2024

Quantum quench dynamics as a shortcut to adiabaticity

The ability to efficiently prepare ground states of quantum Hamiltonians via adiabatic protocols is typically limited by the smallest energy gap encountered during the quantum evolution. This presents a key obstacle for quantum simulation and realizations of adiabatic quantum algorithms in large systems, particularly when the adiabatic gap vanishes exponentially with system size. Using QuEra's Aquila programmable quantum simulator based on Rydberg atom arrays, we experimentally demonstrate a method to circumvent such limitations. Specifically, we develop and test a "sweep-quench-sweep" quantum algorithm in which the incorporation of a quench step serves as a remedy to the diverging adiabatic timescale. These quenches introduce a macroscopic reconfiguration between states separated by an extensively large Hamming distance, akin to quantum many-body scars. Our experiments show that this approach significantly outperforms the adiabatic algorithm, illustrating that such quantum quench algorithms can provide a shortcut to adiabaticity for large-scale many-body quantum systems.

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arXiv2024

Fault-tolerant compiling of classically hard IQP circuits on hypercubes

Realizing computationally complex quantum circuits in the presence of noise and imperfections is a challenging task. While fault-tolerant quantum computing provides a route to reducing noise, it requires a large overhead for generic algorithms. Here, we develop and analyze a hardware-efficient, fault-tolerant approach to realizing complex sampling circuits. We co-design the circuits with the appropriate quantum error correcting codes for efficient implementation in a reconfigurable neutral atom array architecture, constituting what we call a fault-tolerant compilation of the sampling algorithm. Specifically, we consider a family of $[[2^D , D, 2]]$ quantum error detecting codes whose transversal and permutation gate set can realize arbitrary degree-$D$ instantaneous quantum polynomial (IQP) circuits. Using native operations of the code and the atom array hardware, we compile a fault-tolerant and fast-scrambling family of such IQP circuits in a hypercube geometry, realized recently in the experiments by Bluvstein et al. [Nature 626, 7997 (2024)]. We develop a theory of second-moment properties of degree-$D$ IQP circuits for analyzing hardness and verification of random sampling by mapping to a statistical mechanics model. We provide evidence that sampling from hypercube IQP circuits is classically hard to simulate and analyze the linear cross-entropy benchmark (XEB) in comparison to the average fidelity. To realize a fully scalable approach, we first show that Bell sampling from degree-$4$ IQP circuits is classically intractable and can be efficiently validated. We further devise new families of $[[O(d^D),D,d]]$ color codes of increasing distance $d$, permitting exponential error suppression for transversal IQP sampling. Our results highlight fault-tolerant compiling as a powerful tool in co-designing algorithms with specific error-correcting codes and realistic hardware.

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arXiv2024

Correlated decoding of logical algorithms with transversal gates

Quantum error correction is believed to be essential for scalable quantum computation, but its implementation is challenging due to its considerable space-time overhead. Motivated by recent experiments demonstrating efficient manipulation of logical qubits using transversal gates (Bluvstein et al., Nature 626, 58-65 (2024)), we show that the performance of logical algorithms can be substantially improved by decoding the qubits jointly to account for error propagation during transversal entangling gates. We find that such correlated decoding improves the performance of both Clifford and non-Clifford transversal entangling gates, and explore two decoders offering different computational runtimes and accuracies. In particular, by leveraging the deterministic propagation of stabilizer measurement errors through transversal Clifford gates, we find that correlated decoding enables the number of noisy syndrome extraction rounds between these gates to be reduced from $O(d)$ to $O(1)$ in Clifford circuits, where $d$ is the code distance. We verify numerically that this approach substantially reduces the space-time cost of deep logical Clifford circuits. These results demonstrate that correlated decoding provides a major advantage in early fault-tolerant computation, as realized in recent experiments, and further indicate it has considerable potential to reduce the space-time cost in large-scale logical algorithms.

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arXiv2023

Logical quantum processor based on reconfigurable atom arrays

Suppressing errors is the central challenge for useful quantum computing, requiring quantum error correction for large-scale processing. However, the overhead in the realization of error-corrected ``logical'' qubits, where information is encoded across many physical qubits for redundancy, poses significant challenges to large-scale logical quantum computing. Here we report the realization of a programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits. Utilizing logical-level control and a zoned architecture in reconfigurable neutral atom arrays, our system combines high two-qubit gate fidelities, arbitrary connectivity, as well as fully programmable single-qubit rotations and mid-circuit readout. Operating this logical processor with various types of encodings, we demonstrate improvement of a two-qubit logic gate by scaling surface code distance from d=3 to d=7, preparation of color code qubits with break-even fidelities, fault-tolerant creation of logical GHZ states and feedforward entanglement teleportation, as well as operation of 40 color code qubits. Finally, using three-dimensional [[8,3,2]] code blocks, we realize computationally complex sampling circuits with up to 48 logical qubits entangled with hypercube connectivity with 228 logical two-qubit gates and 48 logical CCZ gates. We find that this logical encoding substantially improves algorithmic performance with error detection, outperforming physical qubit fidelities at both cross-entropy benchmarking and quantum simulations of fast scrambling. These results herald the advent of early error-corrected quantum computation and chart a path toward large-scale logical processors.

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