What was shown
Quantum computers make errors constantly. To get a reliable result, many fragile physical qubits are combined to act as one dependable unit, called a logical qubit. The standard method, the surface code, needs many physical qubits for each dependable unit. This paper studies another family, quantum LDPC codes, which need fewer. Their catch is wiring: some connections reach far across the chip and would cross each other. The authors split the connections into a small number of layers, like the floors of a building, so that within each floor no lines cross. They then simulated the whole scheme on classical computers, with noise included in every step of the calculation. Nothing was built, and nothing ran on quantum hardware. The result is a calculation, not a measurement.
“We observe a circuit-noise threshold of 0.28% for a positive-rate code family using 49 physical qubits per logical qubit. For a physical error rate of 10⁻⁴, this family reaches a logical error rate of 10⁻¹⁵ using fourteen times fewer physical qubits than the surface code.”
— Abstract, in: Constant-overhead quantum error correction with thin planar connectivity1
- How it was done: simulated on classical computers, not run on quantum hardware
- Qubits: The result counts 49 physical qubits for each dependable unit, in a simulated code family, not a built machine.
- Error correction: The simulation assumed error correction that copes with noise in every step of the calculation, using quantum LDPC codes.
- Compared against classical computing: no comparison stated in the paper
Who it affects
This concerns makers of quantum hardware and companies that expect to buy large, reliable quantum machines one day. For someone in such a company, nothing changes today: no machine with this wiring exists. If it can be built, the same reliability would need a much smaller machine. A sensible question to put to hardware vendors is whether their design allows long-range connections that do not cross.
Quantum computing vendors and their customers: McKinsey & Company estimates $43B to $71B by 2035 — quantum computing market size (vendor side) (Quantum Technology Monitor, April 2026, p. 8).
This figure is an estimate, not a measurement: McKinsey & Company is a consultancy with its own quantum advisory business. It covers a whole use case, not the result of this paper.
What is still missing
The fourteen-fold saving is a numerical estimate extrapolated from simulations. No hardware with long-range, non-crossing connections arranged in several layers has been built. The authors say experimental progress exists, for instance with light-based links, but it is unclear which of these approaches could be scaled to larger systems. A further open engineering problem is shielding the layers from interfering with each other while the data qubits take part in all layers at once.
This paper lowers the number of physical qubits, compared with the approach it improves on: fourteen times fewer. The quotation below says what is reduced. It is a calculation on paper, not a machine that runs it.
“For a physical error rate of 10⁻⁴, this family reaches a logical error rate of 10⁻¹⁵ using fourteen times fewer physical qubits than the surface code.”
Who is working on it
The paper (September 2021) lists its authors' affiliations as: Institut quantique; Département de physique, Université de Sherbrooke; Microsoft Quantum; Microsoft Research. That is who signed this work — it is not a ranking of who is ahead.
This strengthens quantum LDPC codes with a positive rate, meaning a steady share of useful units, as a lower-overhead alternative to the surface code. It applies to hardware that can offer long-range, non-crossing connections arranged in planar layers.
How this brief was made
This brief was written by software, not by a person: a language model read the full text of the paper, and code then checked every quotation, number and name in this brief against that text before it was published. The rules are set out under Method. Responsible for the rules and for this page: Georg Singer. The paper is a preprint that has not been peer-reviewed. Georg Singer holds no shares in any company or institution named in this brief (as of October 2026).