Research and Technical Notes
We read external research with its sources, explain N/M design decisions and make small experiments runnable again. Literature records belong to their respective researchers.
How we investigate
Scientific publications, software design notes and educational experiments are different kinds of evidence. We present each in its own context.
Literature readings
We link real publications, author information and DOI or arXiv records, summarising findings with their scope and limitations.
Our technical notes
We explain N/M syntax, runtime and toolchain decisions through guides and RFC documents.
Reproducible experiments
We keep code, parameters and model assumptions visible, linking small examples to Playground and laboratories for another run.
N/M development
Technical notes for our software
These records are language design and product documentation, not peer-reviewed scientific publications.
Design of classical functions
Inspect function parameters, return values and bounded execution decisions in NM-RFC-0035.
Open the noteCapabilities and implementation limits
Read available, preview and experimental features alongside target and runtime restrictions.
Open the noteN/M language guide
Follow syntax and supported examples in the product’s usage guide.
Open the noteReproducible educational experiment
Surface-code resource estimate
This panel runs the same N/M example as Playground and the learning laboratory. It is a starting point for inspecting circuit resources and how selected assumptions affect the estimate.
These numbers are approximate estimates from N/M’s simplified resource model. They are not physical QPU measurements, calibrated hardware performance or evidence of error-correction success.
Runnable source
FTQC resource estimate example
Runtime output
FTQC estimate: surface code d=7, logical qubits 3, physical qubits ~294, T-count 16, T-depth 6, magic states 16, runtime ~0.048 ms
Continue with a comparison
Inspect small hybrid examples and classical comparisons in Quantum AI. Read the results alongside data, model and evaluation limits.
03 / Sources and experiments
Literature sources
The publications and standards announcement below are external sources. Their authors and results are not QuantumSoftware’s.
4 sources shown
Quantum error correction below the surface code threshold
Google Quantum AI and Collaborators — Nature 638 (2025); online publication in 2024
Examines decreasing logical error rates with code distance in specified surface-code experiments. This memory experiment alone is not a demonstration of a universal fault-tolerant quantum computer.
First publication: · DOI: 10.1038/s41586-024-08449-y
Quantum Machine Learning in Feature Hilbert Spaces
Maria Schuld and Nathan Killoran — Physical Review Letters 122, 040504 (2019)
Discusses quantum data encoding through feature spaces and kernel methods. A result on one dataset does not establish a speed or accuracy advantage for every machine learning task.
First publication: · DOI: 10.1103/PhysRevLett.122.040504
OpenQASM 3: A broader and deeper quantum assembly language
Andrew W. Cross et al. — arXiv:2104.14722 (2021); ACM Transactions on Quantum Computing (2022)
Describes a language design that extends classical control, timing and quantum program representation. N/M export support does not mean the complete OpenQASM standard is implemented.
First publication: · DOI: 10.1145/3505636
NIST releases first three finalized post-quantum cryptography standards
National Institute of Standards and Technology (NIST) — Standards announcement; FIPS 203, 204 and 205 (2024)
The 2024 announcement introduces ML-KEM, ML-DSA and SLH-DSA standards. Post-quantum cryptography runs on classical systems and does not require a quantum computer.
First publication: