AGE-TGI-2S3/IDS + QEC
High-order symmetric composition of operators combined with quantum error correction codes to achieve fault-tolerant quantum computing on integrated photonic platforms.
Key Results
Reference parameters obtained with a representative silicon photonic platform
What is the AGE gate control?
AGE-TGI-2S3/IDS is an high-order symmetric composition of operators, notation S₂(h/3)³, which approximates the target unitary operator U_target = e^{h(A+B)} through 7 physical segments with an alternating sequence of operators A and B:
A(h/6) · B(h/3) · A(h/3) · B(h/3) · A(h/3) · B(h/3) · A(h/6)
In the SU(2) model, the elementary operators correspond to Pauli‑like rotations. This decomposition achieves a high‑order Trotter error cancellation, providing excellent fidelity with a reduced number of physical segments.
Method details →Dual-Rail Photonic Qubit Model
In the photonic implementation, each physical qubit is encoded in 2 optical modes (dual-rail encoding). Operator A is implemented via directional couplers and operator B via thermal or electro-optic phase shifters. Optical loss per segment is the critical parameter determining gate fidelity.
QEC Code
An erasure/repetition binomial code with distance d is employed. The mini-QEC d=5 fails if 3 or more out of 5 physical qubits fail. The strong QEC d=13 fails if 7 or more out of 13 fail. The parameter ηdet (detection efficiency) is the critical bottleneck: increasing from typical values to near‑unity improves εlogical by several orders of magnitude.
Integrated Photonic PDKs
We have analyzed and optimized AGE-TGI-2S3/IDS + QEC across 4 state-of-the-art photonic platforms
CORNERSTONE
Silicon 220nm Active 1310nm platform. Competitive loss per segment. Supports dozens of logical qubits for d=5 and d=13.
See detailsIMEC iSiPP50G
The best platform: hundreds of logical qubits (d=5) and over two hundred (d=13). Very low optical losses among the best available.
See detailsVTT SiN
Silicon nitride with low losses in the visible-near IR band. Ideal for long-distance interconnects.
See detailsLuxtelligence GF
University of Glasgow platform with Foundry Service for custom photonic circuits.
See detailsηdet: The Critical Parameter
Photon detection efficiency ηdet is the most important limiting factor for quantum error correction in photonic systems. Our analyses demonstrate that improving ηdet from typical values to near‑unity reduces εlogical by several orders of magnitude, a qualitative leap that determines the viability of fault-tolerant quantum computing.
With moderate ηdet and d = 13, the logical error is in the 10⁻⁶ range. With ηdet = 0.99, this value drops to the 10⁻⁹ range, opening the door to deep quantum algorithms with thousands of logical gates before decoherence.
| ηdet | εlogical (d=5) | εlogical (d=13) | Improvement factor |
|---|---|---|---|
| 0.90 | 2.3×10-2 | 5.8×10-4 | 1× |
| 0.95 | 7.18×10-3 | 1.4×10-6 | ~400× |
| 0.99 | ~10-4 | ~10-9 | ~105× |
Meet the Innovator
Kerym Makraini
Photonic Quantum Computing Researcher
Kerym Makraini is a quantum computing researcher and inventor specializing in photonic quantum gate control and error correction. His groundbreaking work on the AGE Framework represents a fundamental advance in high-fidelity quantum gate design.
With deep expertise in mathematical physics, numerical methods, and silicon photonics, Makraini identified and solved the critical fidelity bottleneck that has constrained the entire photonic quantum computing industry.
Based in Melilla, Spain, he is the author of the fundamental methodology behind the AGE Framework.
Frequently Asked Questions
What does AGE-TGI-2S3/IDS mean?
AGE-TGI-2S3/IDS denotes a high‑order symmetric composition of operators with multiple partitions. It is a high‑order formula for approximating the exponential of a sum of non‑commuting operators, using 7 physical segments with an optimized sequence of weights.
What is an erasure QEC code?
In photonics, the dominant error is photon loss (erasure), not phase flip. An erasure code exploits the fact that we know which qubit was lost, unlike Pauli errors where the location is unknown. This allows more efficient codes such as the binomial/repetition code with distances d=5 and d=13.
How many logical qubits can be obtained?
It depends on the platform. Some commercial silicon photonic platforms offer dozens of logical qubits for d=5 and d=13. Our best‑in‑class platform, based on low‑loss silicon photonics, yields hundreds of logical qubits (d=5) and over two hundred (d=13), representing the highest reported capacity.
Why is ηdet so important?
Detection efficiency ηdet determines the fraction of erasures that can be detected and corrected. An increase from typical values to near‑unity improves the logical error by several orders of magnitude, making it the main bottleneck for photonic quantum scalability.