Ultra-high-rate quantum error correction codes can store many logical qubits in a single code block with few physical qubits. A fault-tolerant quantum computer, however, also requires a universal set of logical operations on individually addressable logical qubits, and the ancilla overhead of these operations may erode the advantage of the high encoding rate. Here, we propose the Cornucopia architecture, in which a universal set of logical operations is implemented at low overhead for the Cornucopia codes. In particular, we focus on the [[2844,1426,18]] Cornucopia code as an example and introduce a modular quantum computer built from such code blocks connected by bridges. Each block stores 1,426 logical qubits and serves as a universal logical processor. Exploiting the code's translation symmetry, we construct a family of reusable gadgets that individually address 1,422 logical qubits within each block. These gadgets support three universal logical instruction sets: basic, high-throughput and fixed-extractor. Excluding magic-state factories, a module with sufficient workspace to execute any instruction in the basic set requires an average of 4.1 physical qubits per logical qubit, compared with 3.0 for memory alone. The architecture thus preserves the resource advantage of ultra-high-rate quantum memory while enabling universal logical computation, providing a route towards low-overhead fault-tolerant quantum computers.
Ultra-high-rate quantum error correction codes can store many logical qubits in a single code block with few physical qubits. A fault-tolerant quantum computer, however, also requires a universal set of logical operations on individually addressable logical qubits, and the ancilla overhead of these operations may erode the advantage of the high encoding rate. Here, we propose the Cornucopia architecture, in which a universal set of logical operations is implemented at low overhead for the Cornucopia codes. In particular, we focus on the [[2844,1426,18]] Cornucopia code as an example and introduce a modular quantum computer built from such code blocks connected by bridges. Each block stores 1,426 logical qubits and serves as a universal logical processor. Exploiting the code's translation symmetry, we construct a family of reusable gadgets that individually address 1,422 logical qubits within each block. These gadgets support three universal logical instruction sets: basic, high-throughput and fixed-extractor. Excluding magic-state factories, a module with sufficient workspace to execute any instruction in the basic set requires an average of 4.1 physical qubits per logical qubit, compared with 3.0 for memory alone. The architecture thus preserves the resource advantage of ultra-high-rate quantum memory while enabling universal logical computation, providing a route towards low-overhead fault-tolerant quantum computers.
High-rate quantum low-density parity-check (qLDPC) codes encode many logical qubits with low physical-qubit overhead, but realizing efficient fault-tolerant computation on such dense encodings remains a major challenge. Generic, code-agnostic techniques such as code surgery and gate teleportation apply broadly, but are difficult to make modular, low-overhead, and fully certifiable on complex high-rate codes whose structure is left unexploited. Here we overcome these obstacles by co-designing the code together with its logical instruction set for a broad family of canonical lifted-product (LP) codes with cyclic symmetry. We show that these codes admit a canonical logical basis, in which conjugate logical operators are organized into rows and columns of cyclic orbits inherited directly from the underlying classical codes, analogous to the structure that makes hypergraph-product codes so tractable. This canonical basis enables universal logical processing using magic-state input and a constant number of reusable seed surgery gadgets---only two (resp. four) for a [[1122,148,≤20]] (resp. [[4350,1224,≤20]]) LP code. A fixed extractor smaller than half the data block also enables arbitrarily high-weight logical Pauli-product measurements (PPMs) while preserving the code's cyclic symmetry. These codes also enable rigorously fault-tolerant parallel logic, including PPMs across all logical qubits and magic-state injection from many surface codes into a full LP block. For example, a [[468,36,20]] (resp. [[952,112,17]]) code supports simultaneous measurements of arbitrary logically disjoint Pauli products with an ancilla overhead of roughly three (resp. four) times the data block size. These results advance the frontier of fault-tolerant quantum computation on ultra-high-rate quantum architectures.
Quantum low-density parity-check (qLDPC) codes offer a promising route to reducing the qubit overhead of fault tolerance, with recent ultra-high-rate constructions achieving encoding rates above one half. In this work, we develop fast and parallel logical computation methods for ultra-high-rate codes. We first utilize the group symmetries of the codes to partition the logical qubits into orbits, and then apply parallel surgery methods to implement group-invariant collections of logical Pauli-product measurements. These measurements are highly programmable, as we may arbitrarily couple logical orbits as long as each measurement is repeated across the whole orbit(s). To reduce the space and time overheads, we develop a technique called chain-map convolution, which uses the group structure to boost both the spatial and temporal distances of our protocol in a highly efficient manner. As case studies, we construct distance-preserving parallel measurement gadgets for the [[256, 68, 12]], [[576, 148, 18]] pair-partition codes, and a [[1152, 580, 12]] rate-1/2 code, with only around 2.5× space overhead and 3-4 rounds of syndrome extraction each. The same methods also enable parallel injection of cultivated magic states into high-rate codes. Finally, we extend programmability through subgroup restrictions, revealing a tradeoff between logical control and the spacetime resources required for fault tolerance and highlighting the crucial role structured parallelism plays in reducing overhead. These results provide new methods for designing qLDPC logical operations with low spacetime overhead, opening a route toward more efficient fault-tolerant quantum architectures.
Realizing practical quantum computers requires quantum error correction, but the most widely implemented approach, the planar surface code, demands a substantial physical qubit overhead. Here, we demonstrate that partitioning quantum processors into manageable, flat modules with non-local inter-module connections provides a natural solution. By wiring sparse, static boundary connections between Euclidean planar modules, we construct modular hyperbolic surface and color codes, based on new families of semi-hyperbolic codes. Using modular syndrome extraction circuits and efficient neural network and matching decoders, our circuit-level simulations show that this modular memory design can reduce the physical qubit overhead by tenfold or more compared to the surface code, even under elevated inter-module seam error rates. Projecting to larger system sizes, we find modular codes with encoding rate k/n=1/16 and distance d≥22, exceeding both the rate and distance of the [[288,12,18]] two-gross bivariate bicycle code while using mostly nearest-neighbor gates within planar modules, and implying an over 30× overhead reduction relative to surface codes. We develop fault-tolerant walking circuits for implementing logic via code automorphisms, which we co-design with low-weight, highly symmetrical logical bases and a modular extractor system that is ≈4.5× smaller than the code itself. Combining these methods, our modular memory can be used as dense storage in a universal fault-tolerant architecture, unlocking the efficiency of high-rate codes without sacrificing the fabrication advantages of planar modules.
Quantum error correction offers a path from fragile physical qubits to reliable quantum computation, but the resource cost of conventional architectures remains a central obstacle to useful machines. This thesis develops a full-stack approach based on high-rate quantum low-density parity-check (qLDPC) codes, which encode many logical qubits per block and can substantially reduce fault-tolerance overhead. Its central premise is that favorable code parameters are useful only when memory, hardware, logical operations, decoding, and interconnects are designed together. Quantum memories based on hypergraph-product, lifted-product, spatially coupled, and balanced-product codes provide the underlying algebraic structure, while reconfigurable neutral-atom arrays realize their nonlocal connectivity through parallel optical control, high-fidelity Rydberg gates, and loss-resolving readout. Universal logical computation is enabled through teleportation, homomorphic gates, and finite-block-length tricycle constructions for low-cost non-Clifford resource states. Structure-aware neural decoders learn spatial, temporal, and gate-induced correlations while remaining compatible with real-time feed-forward, and high-rate entanglement-distillation protocols extend the same constant-overhead principles to quantum interconnects. Together, these results outline an integrated route toward practical fault-tolerant quantum computers built from high-rate quantum codes.
Suppressing errors is the central challenge for useful large-scale quantum computing. While quantum error correction promises a viable solution to this challenge, existing codes typically suffer from trade-offs among encoding efficiency, error threshold, and hardware feasibility. Here, we introduce Cornucopia codes, a family of practical, hardware-efficient quantum low-density parity-check codes that achieve an ultra-high encoding rate exceeding 1/2 while maintaining a pseudo-threshold exceeding 0.4% under the standard circuit-level noise model. Inspired by recent affine-permutation-based code constructions and the long-range connectivity available in reconfigurable neutral-atom arrays, we adopt a structured code geometry in which the code layout, atom rearrangement, and syndrome-extraction schedule are co-designed. This structure enables nonlocal syndrome measurements through simple, parallel atom rearrangements. A complete syndrome extraction cycle measures all X- and Z-type checks in parallel with 12 entangling layers, independent of the code size. The resulting threshold is comparable to those of the surface code and bivariate bicycle codes. In particular, a single code block [[2844,1426,18]] encodes 1,426 distance-18 logical qubits, achieving an extrapolated logical error rate of 2.6×10−16 (1.9×10−31) per logical qubit per cycle, assuming the physical error rate of 0.1% (0.01%). By comparison, a bivariate bicycle code implementation would require more than 68,000 physical qubits to encode the same number of logical qubits at a comparable logical error rate. These results bring demonstrations of ultra-low-overhead quantum error correction within the reach of near-term quantum processors.
Quantum low-density parity-check (qLDPC) codes can achieve high encoding rates and good code distance scaling, providing a promising route to low-overhead fault-tolerant quantum computing. However, the long-range connectivity required to implement such codes makes their physical realization challenging. Here, we propose a hardware-efficient scheme to perform fault-tolerant quantum computation with high-rate qLDPC codes on reconfigurable atom arrays, directly compatible with recently demonstrated experimental capabilities. Our approach utilizes the product structure inherent in many qLDPC codes to implement the non-local syndrome extraction circuit via atom rearrangement, resulting in effectively constant overhead in practically relevant regimes. We prove the fault tolerance of these protocols, perform circuit-level simulations of memory and logical operations with these codes, and find that our qLDPC-based architecture starts to outperform the surface code with as few as several hundred physical qubits at a realistic physical error rate of 10−3. We further find that less than 3000 physical qubits are sufficient to obtain over an order of magnitude qubit savings compared to the surface code, and quantum algorithms involving thousands of logical qubits can be performed using less than 105 physical qubits. Our work paves the way for explorations of low-overhead quantum computing with qLDPC codes at a practical scale, based on current experimental technologies.