Vine codes generalize directional codes to open planar boundaries, delivering up to 28% fewer data/measure qubits at circuit distance 7 and better simulated performance than the surface code at 10^{-3} noise while using fewer total qubits.
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Shor's algorithm is possible with as few as 10,000 reconfigurable atomic qubits
Canonical reference. 100% of citing Pith papers cite this work as background.
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abstract
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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Classical codes plus SAT search yield no-go theorems limiting error detection in sub-8-qubit distillation and new minimal-qubit protocols for T-to-T (distances 4-5 on 10-11 qubits) and T-to-CCZ (distances 3-4 on 9-10 qubits).
LLM-driven evolutionary program synthesis discovers Generalized Superfast Encodings with exact distance 5 (and 6 on one instance) for molecular Hamiltonians, the first beyond distance 3.
A new LLM-guided search method called structured concept evolution discovers competitive lifted-product qLDPC code families including non-abelian constructions.
Presents planar open-boundary quantum LDPC codes with nearest-neighbor iSWAP-based syndrome extraction that outperform rotated surface codes in code-efficiency and logical error rate on finite instances like [[323,14,15]].
A parameterized quantum divide-and-conquer TSP solver achieves O*(1.865666…^n) query complexity via 4-subset partitioning and a new set-partition state preparation method, correcting prior work to show no quantum advantage below O*(2^n).
Experimental breakeven demonstration of a qLDPC code encoding 4 logical qubits in 18 physical qubits on trapped ions, with up to 9x lower logical error rate than prior superconducting implementations.
A single metasurface creates a tweezer array that traps 11,000 atoms, reported as the first platform to reach the 10,000-qubit resource scale.
Dual-species Na-Cs Rydberg array enables simultaneous non-destructive readout of multiple Pauli-Z stabilizers on four-qubit plaquettes using a single global pulse sequence after compensating geometric phase errors.
Real-time Krylov subspace methods are extended to Lindblad open quantum systems and demonstrated on a Kerr resonator for estimating the Liouvillian gap in cat qubit regimes.
An automated predecoder generator for arbitrary qLDPC codes cuts decoder utilization by up to 3963x and supports hardware scaling to tens or hundreds of thousands of logical qubits within power limits.
A graph neural network path planner and phase-aware Gerchberg-Saxton algorithm enable defect-free assembly of 10,000-atom arrays in under 6 ms, faster than typical atom loss times.
Hardware experiment on IBM devices shows reset-free LUCI achieves logical X and Z error suppression ratios of 1.75(10) and 1.93(12), competitive with surface code despite halved syndrome density.
A symmetry-co-designed high-rate QEC architecture with parallel STAR injection on bivariate bicycle codes achieves ~5.5x space savings for TFIM and Fermi-Hubbard simulations versus surface-code STAR.
GAS-SCF uses Grover adaptive search and quantum arithmetic to mark and amplify improving Fock states, offering a theoretical quadratic speedup for SCF optimization, shown via classical simulations up to 26 qubits and analysis to 330 qubits.
Full extractors for HGP codes are built to enable logical processing via PBC without compilation overhead, with sizes 50-80% of base codes and low error rates in simulations.
Nonlinear cross-entropy benchmark and heavy-output classifier enable sample-efficient distinction between noisy quantum and classical spoofers for shallow-depth all-to-all random circuits.
Concatenating quantum Reed-Solomon codes over the gross code via Galois qudits reaches teraquop regime at uniform 10^{-3} noise with reduced overhead.
PIQC proposes a distributed FTQC architecture based on molecular quantum nodes with photonic integration, nuclear registers, loss-tolerant entanglement, and Floquetified qLDPC codes.
A forced-gap post-selection strategy using repeated Relay-BP decoder runs improves logical error rates by over 4x on 72- and 144-qubit bivariate bicycle codes at fixed post-selection rate.
Experimental demonstration of a multiplexing trapped-ion QPU using sample-and-hold circuits achieves motional heating rates below 1 phonon/s and expected gate errors below 10^{-4} for sampling intervals under 50 ms.
A hot-zone architecture for OQFT on reconfigurable neutral-atom hardware yields tunable latency via 2-4 zones, converging to roughly 500 extra logical ancillae and 128-qubit peak parallelism for half-time performance on 256-2048 bit instances.
A qubit-reduction method for hypergraph product codes preserves dimension, distance, and fault-tolerance properties, producing smaller codes such as [[441,64,6]] from [[610,64,6]] with comparable noise performance and compatibility with logical gates.
Shor's algorithm generates and consumes magic resources in direct proportion to the difficulty of the underlying factoring problem.
citing papers explorer
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Vine Codes: Low-Overhead Quantum LDPC Codes on a Planar Square Grid
Vine codes generalize directional codes to open planar boundaries, delivering up to 28% fewer data/measure qubits at circuit distance 7 and better simulated performance than the surface code at 10^{-3} noise while using fewer total qubits.
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Exploring the landscape of compact magic-state distillation factories
Classical codes plus SAT search yield no-go theorems limiting error detection in sub-8-qubit distillation and new minimal-qubit protocols for T-to-T (distances 4-5 on 10-11 qubits) and T-to-CCZ (distances 3-4 on 9-10 qubits).
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Evolving Quantum Error-Correcting Encodings for Molecular Simulation
LLM-driven evolutionary program synthesis discovers Generalized Superfast Encodings with exact distance 5 (and 6 on one instance) for molecular Hamiltonians, the first beyond distance 3.
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Large-Language-Model Discovery of Quantum LDPC Codes through Structured Concept Evolution
A new LLM-guided search method called structured concept evolution discovers competitive lifted-product qLDPC code families including non-abelian constructions.
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Nearest-neighbour gates are all you need: High-rate quantum low-density parity-check codes on a planar grid
Presents planar open-boundary quantum LDPC codes with nearest-neighbor iSWAP-based syndrome extraction that outperform rotated surface codes in code-efficiency and logical error rate on finite instances like [[323,14,15]].
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Towards Implementable Quantum Divide and Conquer: A TSP Solver with Improved Exponential Base over Held-Karp
A parameterized quantum divide-and-conquer TSP solver achieves O*(1.865666…^n) query complexity via 4-subset partitioning and a new set-partition state preparation method, correcting prior work to show no quantum advantage below O*(2^n).
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Breakeven demonstration of quantum low-density parity-check codes
Experimental breakeven demonstration of a qLDPC code encoding 4 logical qubits in 18 physical qubits on trapped ions, with up to 9x lower logical error rate than prior superconducting implementations.
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Trapping 11,000 Atoms in a Tweezer Array Generated by a Single Metasurface
A single metasurface creates a tweezer array that traps 11,000 atoms, reported as the first platform to reach the 10,000-qubit resource scale.
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Multi-Qubit Stabilizer Readout on a Dual-Species Rydberg Array
Dual-species Na-Cs Rydberg array enables simultaneous non-destructive readout of multiple Pauli-Z stabilizers on four-qubit plaquettes using a single global pulse sequence after compensating geometric phase errors.
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Real-time Krylov Diagonalisation for Open Quantum Systems
Real-time Krylov subspace methods are extended to Lindblad open quantum systems and demonstrated on a Kerr resonator for estimating the Liouvillian gap in cat qubit regimes.
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Mitigating Classical Resource Costs in Quantum Error Correction via Generalized qLDPC Predecoding
An automated predecoder generator for arbitrary qLDPC codes cuts decoder utilization by up to 3963x and supports hardware scaling to tens or hundreds of thousands of logical qubits within power limits.
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An Algorithm for Fast Assembling Large-Scale Defect-Free Atom Arrays
A graph neural network path planner and phase-aware Gerchberg-Saxton algorithm enable defect-free assembly of 10,000-atom arrays in under 6 ms, faster than typical atom loss times.
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LUCI on IBM Hardware: Error Suppression with Almost Half Syndrome Density
Hardware experiment on IBM devices shows reset-free LUCI achieves logical X and Z error suppression ratios of 1.75(10) and 1.93(12), competitive with surface code despite halved syndrome density.
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Fast and Parallel High-Rate STAR Architecture for Megaquop Quantum Simulation
A symmetry-co-designed high-rate QEC architecture with parallel STAR injection on bivariate bicycle codes achieves ~5.5x space savings for TFIM and Fermi-Hubbard simulations versus surface-code STAR.
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Quantum-Accelerated Self-Consistent Field: A Hybrid Algorithm
GAS-SCF uses Grover adaptive search and quantum arithmetic to mark and amplify improving Fock states, offering a theoretical quadratic speedup for SCF optimization, shown via classical simulations up to 26 qubits and analysis to 330 qubits.
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Full Extractors for Logical Processing in Hypergraph Product Codes
Full extractors for HGP codes are built to enable logical processing via PBC without compilation overhead, with sizes 50-80% of base codes and low error rates in simulations.
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Sample-efficient benchmarking of shallow all-to-all random quantum circuits
Nonlinear cross-entropy benchmark and heavy-output classifier enable sample-efficient distinction between noisy quantum and classical spoofers for shallow-depth all-to-all random circuits.
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Concatenating Algebraic Codes over High-Rate Quantum LDPC Codes
Concatenating quantum Reed-Solomon codes over the gross code via Galois qudits reaches teraquop regime at uniform 10^{-3} noise with reduced overhead.
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PIQC: Scalable Distributed Quantum Computing via Photonic Integration of Designed Molecular Quantum Nodes
PIQC proposes a distributed FTQC architecture based on molecular quantum nodes with photonic integration, nuclear registers, loss-tolerant entanglement, and Floquetified qLDPC codes.
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Forced Gap Post-Selection for Quantum LDPC Codes and their Operations
A forced-gap post-selection strategy using repeated Relay-BP decoder runs improves logical error rates by over 4x on 72- and 144-qubit bivariate bicycle codes at fixed post-selection rate.
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Demonstration of a Multiplexing Trapped Ion Quantum Processing Unit
Experimental demonstration of a multiplexing trapped-ion QPU using sample-and-hold circuits achieves motional heating rates below 1 phonon/s and expected gate errors below 10^{-4} for sampling intervals under 50 ms.
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Towards Deploying Optimistic Quantum Fourier Transforms: An Architecture-Algorithm Co-Design Study
A hot-zone architecture for OQFT on reconfigurable neutral-atom hardware yields tunable latency via 2-4 zones, converging to roughly 500 extra logical ancillae and 128-qubit peak parallelism for half-time performance on 256-2048 bit instances.
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Spatial overhead reduction for 2D hypergraph product codes
A qubit-reduction method for hypergraph product codes preserves dimension, distance, and fault-tolerance properties, producing smaller codes such as [[441,64,6]] from [[610,64,6]] with comparable noise performance and compatibility with logical gates.
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The true cost of factoring: Linking magic and number-theoretic complexity in Shor's algorithm
Shor's algorithm generates and consumes magic resources in direct proportion to the difficulty of the underlying factoring problem.
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Factoring $2048$ bit RSA integers with a half-million-qubit modular atomic processor
A modular atomic processor with 500,000 qubits factors 2048-bit RSA numbers in roughly the same time as a single large module when inter-module Bell-pair communication runs at 10^5 per second.
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Adaptable Continuous Variable Quantum Network with Finite Size Security
Experimental demonstration of an active 1:4 CV-QKD quantum network in the finite-size regime with adaptable protocols achieving 0.19 bits per channel use over 11 km channels.
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Architecting Early Fault Tolerant Neutral Atoms Systems with Quantum Advantage
A teleportation-based parallelization architecture for neutral-atom quantum error correction delivers up to 3x speedup over extractor methods at fixed space cost and enables simulated quantum advantage at 11,495 atoms and 15-hour runtime.
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Fault-Tolerant Quantum Computing with Trapped Ions: The Walking Cat Architecture
A trapped-ion architecture based on LDPC codes and cat-state factories achieves 110 logical qubits and one million T gates per day using 2514 physical qubits, with estimates for Heisenberg model simulation on 100 sites in one month using 10000 qubits.
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GreenPeas: Unlocking Adaptive Quantum Error Correction with Just-in-Time Decoding Hypergraphs
GreenPeas delivers a just-in-time GPU compiler for decoding hypergraphs that achieves >10x speedup on surface and bivariate bicycle codes, unlocking circuit-level decoding for adaptive quantum error correction.
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QLLVM: A Scalable Quantum-Classical Co-Compilation Framework based on LLVM
QLLVM delivers an LLVM-based end-to-end co-compiler that unifies classical HPC and quantum programs into one executable, with a three-stage quantum path via MLIR and QIR that reduces circuit depth and gate counts on MQTBench versus prior compilers.
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Fast measurement of neutral atoms with a multi-atom gate
A multi-atom Rydberg gate with N ancillae enables N-fold photon collection for fast neutral-atom measurement, achieving infidelity below 10^{-3} in 6 μs with N=5 in Cs-Rb simulations.
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Heterogeneous architectures enable a 138x reduction in physical qubit requirements for fault-tolerant quantum computing under detailed accounting
Heterogeneous quantum architectures with task-specific hardware and QEC encodings deliver up to 138x lower physical-qubit overhead than monolithic baselines for fault-tolerant algorithms, including RSA-2048 factoring at 190k-381k qubits.
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Phase-Stable Hologram Updates for Large-Scale Neutral-Atom Array Reconfiguration
WPGS algorithm enforces inter-frame phase continuity in holographic tweezers to suppress refresh-induced atom loss and speed up updates for large neutral-atom arrays.
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Time-Bin BB84 QKD System Using Indium Phosphide and Silicon Nitride Photonic Integrated Circuits
Demonstration of dual-chip InP-SiN time-bin BB84 QKD system with QBER below 4% and kbps secret key rates over 150-250 km fiber using finite-key security analysis.
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Distribution Complexity of Electronic Structure Simulations on Quantum Supercomputers
An algorithm is presented for estimating distribution complexity of electronic structure Hamiltonians, with O(N^3) entanglement estimation per fragment and quadratic/exponential reductions in distribution cost for quantum and classical interconnects.
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Hardware-Tailored Resource Estimation for Magic-State Distillation on Silicon Spin Qubits
Resource estimation for magic-state distillation on silicon spin qubits finds 42% overhead reduction via optimized pulses and ~3x physical footprint reduction with biased codes versus surface code.
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Space-Time Tradeoffs of Pauli-Based Computation in Distributed qLDPC Architectures
Large qLDPC blocks in distributed quantum computing enable Pauli-based computation to run up to 10x faster than surface codes for optimization algorithms by using spare nodes to bypass serialization bottlenecks.
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Quantum resonance encryption for secure data storage and communication with quantum kicked top
Proposes a quantum encryption protocol based on quantum kicked top dynamics at resonance that allows perfect recovery by authorized users while rendering intercepted states mixed to eavesdroppers with built-in tampering detection.
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Real-Time Quantum Error Correction System Stack: Architecture, Algorithms, and Engineering Practice
A white paper proposing a six-layer system stack for real-time quantum error correction, with benchmarks of decoders for surface and qLDPC codes and latency models.
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Minimally Destructive Fast Imaging of Single Atoms in an Optical Tweezer Array with Coherent Excitation
A coherent pi-pulse imaging scheme on ytterbium-174 atoms achieves 99.89% discrimination fidelity and 98.8% survival in 17.6 μs with roughly half the heating rate of prior incoherent methods.
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Benchmarking a machine-learning differential equations solver on a neutral-atom logical processor
Logical quantum kernels outperform physical ones when solving differential equations on a neutral-atom processor, with gains traced to noise error detection in the logical encoding.
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Probing the Planck scale with quantum computation
A 500-logical-qubit quantum computer could reject laboratory-confined theories by surpassing the Planck-scale operation rate of 2^491 m^{-3} s^{-1}, with a 1600-qubit machine limited by the observable universe.
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Metasurfaces for neutral-atom trapping
Review of optical metasurfaces enabling large-scale neutral-atom trapping arrays for quantum information technologies.
- Towards Ultra-High-Rate Quantum Error Correction with Reconfigurable Atom Arrays