Bivariate bicycle codes and the gross code

Short answer: Bivariate bicycle codes are a family of quantum low-density parity-check codes proposed for low-overhead error correction, including a "gross code" with 288 physical qubits. A 2024 Nature paper by IBM researchers reports, from simulation, that 12 logical qubits could be preserved for nearly a million syndrome cycles at a physical error rate of 0.1%. A 2025 arXiv preprint extends this to a modular "bicycle architecture". These are simulation and resource-estimate results, and no hardware demonstration is described.

The 2024 Nature paper

The abstract describes an end-to-end quantum error correction protocol for fault-tolerant memory based on a family of low-density parity-check codes. The authors report an error threshold of 0.7% for the standard circuit-based noise model, which they say is on par with the surface code, long the leading code in terms of threshold. The syndrome measurement cycle for a length-n code needs n ancillary qubits and a depth-8 circuit of CNOT gates, initializations and measurements. The required connectivity is a degree-6 graph composed of two edge-disjoint planar subgraphs.

The headline estimate is that 12 logical qubits can be preserved for nearly 1 million syndrome cycles using 288 physical qubits in total, assuming a physical error rate of 0.1%, whereas the authors say the surface code would need nearly 3,000 physical qubits for the same performance. They conclude that demonstrations of a low-overhead fault-tolerant memory are within reach of near-term processors. This is an assumption-based estimate, not a measurement.

IBM blog account

IBM published a blog post in March 2024, when the paper appeared on the cover of Nature. It calls the result a code about 10 times more efficient than prior methods and names it the gross code. It also says error correction is not a solved problem. These are statements by the company that employs the authors.

2025: the bicycle architecture

The 2025 arXiv preprint presents a modular quantum computing framework based on high-rate, low-overhead quantum LDPC codes from prior work. For two bivariate bicycle codes with distances 12 and 18, the authors construct logical instruction sets, estimate the logical error rate of each instruction under circuit noise, and develop a compilation strategy. Their end-to-end resource estimates say an order of magnitude larger logical circuits can be run with a given number of physical qubits than on surface code architectures. They anticipate further improvements from code constructions, circuit designs and compilation.

Limits

The numbers depend on the assumed 0.1% physical error rate and on the specific noise model. The required degree-6 connectivity is a hardware demand that the abstract notes but does not claim to have built. The efficiency comparisons are against the surface code in the authors' own estimates.

FAQ

What is the gross code?

The name IBM gives to a bivariate bicycle code using 288 physical qubits for 12 logical qubits in the Nature paper's estimate.

What threshold was reported?

0.7% for the standard circuit-based noise model, per the Nature abstract.

How does it compare with the surface code?

The authors estimate nearly 3,000 physical qubits for the surface code against 288 for the same performance.

Has this been demonstrated on hardware?

The pages used here describe simulations and resource estimates.

What does the 2025 preprint add?

A modular architecture with logical instruction sets and compilation for two codes of distance 12 and 18.