Runs circuits at controlled noise levels and extrapolates back to the zero-noise limit — delivering better results from today's noisy hardware without requiring additional physical qubits.
Full quantum error correction requires large qubit overhead to encode each logical qubit in many physical qubits. Zero-noise extrapolation is a complementary approach for teams working with near-term hardware where qubit counts are limited: run the same circuit at several amplified noise levels, measure the degraded results, and fit a curve to extrapolate back to what the result would have been at zero noise.
The φCoherent ZNE package uses N-nacci-spaced noise scaling levels. Conventional methods use uniformly-spaced or power-of-two noise levels, producing poorly-conditioned extrapolation matrices. The N-nacci spacing gives conditioning that is 3.7 to 8.5 times better than conventional methods for the same number of noise levels, producing more accurate extrapolated results with fewer circuit runs.
Noise amplification factors are chosen at Fibonacci/N-nacci intervals, giving better-conditioned extrapolation than uniform or exponential spacing. The result is more accurate zero-noise estimates from the same number of circuit runs.
Linear, polynomial, and exponential extrapolation models are available depending on the expected noise behavior of the target circuit. The appropriate model can be selected by the scheduler or chosen manually based on circuit characterization data.
Unlike error correction codes, ZNE requires no additional physical qubits. It only requires running the same circuit multiple times at different noise scales, making it accessible on any hardware with limited qubit counts.
Works on any circuit expressed in the φCoherent type system, making it applicable to every algorithm package in the stack without modification. Mitigation runs transparently alongside normal circuit execution.
Near-term mitigation layer — ZNE is the recommended approach when qubit counts prevent full error correction. It pairs with the coherence recycler (which recovers residual coherence before ZNE runs) and the error budget allocator (whose criticality weights can guide where extrapolation budget is concentrated).
Published under the GNU AGPLv3 with whitepaper and reference implementation. Commercial licensing is available for closed-source deployments.