Fibonacci-structured quantum error correction code families that encode logical qubits in groups of physical qubits, protecting quantum information from hardware noise with provable guarantees.
Every physical qubit in a real device is constantly subject to errors — gate imperfections, environmental interference, and crosstalk from neighboring qubits. Quantum error correction addresses this by encoding each logical qubit into a carefully designed pattern of multiple physical qubits, so that errors affecting individual physical qubits can be detected and corrected before they corrupt the logical information.
The φCoherent error correction codes apply Fibonacci mathematics to this problem, producing code families whose error tolerance scales according to Fibonacci numbers. This gives more efficient use of physical qubits at each error-tolerance level compared to codes with uniform scaling.
The foundational one-dimensional code family. Each logical qubit is encoded across multiple physical qubits, with the number of physical qubits at each protection level following the Fibonacci sequence. Provides provable single-qubit error correction with efficient scaling.
Two-dimensional codes that protect against both bit-flip and phase-flip errors simultaneously, organized in a Fibonacci-scaled square grid topology. The rotated layout reduces the number of physical qubits required compared to the standard surface code construction.
Multi-level encoding for applications with the highest error-tolerance requirements, where each logical qubit is itself encoded inside a surface code. Concatenation provides exponentially improving protection at the cost of more physical qubits per logical qubit.
A decoder that uses the Fibonacci structure of the codes to weight error-detection measurements appropriately, producing more accurate identification of which physical qubits have failed compared to decoders that treat all measurements as equally informative.
A rotated planar surface code of distance d is self-dual — meaning its X-type and Z-type parity check matrices are transposes of each other — if and only if d is odd. The φCoherent code library exposes this condition directly on every surface code, and provides a dedicated code family, SelfDualFibonacciSurfaceQEC, that selects only odd N-nacci distances by construction. The Fibonacci parity period is 3 (pattern [1,1,0], self-dual fraction 2/3); the tribonacci period is 4 (pattern [1,1,0,0], fraction 1/2). At order 2 with 4 levels, the self-dual family uses distances {3, 5, 13, 21} for a total of 1,284 physical qubits, compared to 530 qubits for the standard ensemble — a 2.4× overhead in exchange for the structural symmetry guarantee.
Reliability layer — makes logical qubits out of noisy physical qubits. The fault-tolerant executor depends on this package to define how errors are corrected during live execution. The error budget allocator uses the code structure to inform how error tolerance is distributed across a circuit.
Runs fault-tolerant circuits using these codes, acting on corrections in real time to keep execution progressing through error events.
Allocates error tolerance across a circuit's components, informed by the code structure and its distance properties.
Published under the GNU AGPLv3 with whitepaper and reference implementation. Commercial licensing is available for closed-source deployments.