Hawkynt

Cat Code

Bosonic quantum error correction using superpositions of coherent states (cat states) in cavity modes. Encodes qubit as

0⟩ = (

α⟩+

-α⟩)/N and

1⟩ = (

α⟩-

-α⟩)/N. Protects against photon loss with exponential bit-flip suppression scaling as e^(-2α²). Developed by Mirrahimi, Leghtas, and Albert (2014). Experimentally implemented in superconducting circuits by Alice&Bob quantum computing.

Properties

Property	Value
Category	Error Correction
Sub-category	Bosonic Quantum Code
Security status	🧪 Experimental
Complexity	Expert
Inventor	Mazyar Mirrahimi, Zaki Leghtas, Victor Albert
Year	2014
Origin	🇫🇷 France
Source	algorithms/ecc/cat-code.js

Security

Status: 🧪 Experimental

Known vulnerabilities

Issue	Description	Mitigation
Phase-Flip Vulnerability	Cat codes suppress bit-flip errors exponentially with |α|² but phase-flip errors increase linearly. Requires concatenation with outer codes (e.g., surface code) for full protection. Typical approach: cat code suppresses bit-flips, outer code corrects phase-flips.	—
Coherent State Approximation	Classical simulation uses truncated Fock basis representation. Real quantum implementation requires cavity QED hardware with strong dispersive coupling and multi-photon driven dissipation for autonomous error correction.	—
Limited Distance	Two-component cat code (S=1) can detect single photon loss. Higher-component codes (S>1) required for correcting multiple losses, increasing hardware complexity.	—
Decoherence Time	Cat state coherence requires cavity quality factor Q > 10⁶ and temperatures T < 50 mK. Experimental lifetimes reach 1-10ms for |α|=2, limiting gate operation speeds.	—

Documentation

• Error Correction Zoo - Cat Code
• Error Correction Zoo - Two-Component Cat Code
• Mirrahimi et al. - Dynamically Protected Cat-Qubits (2014)
• Grimm et al. - Stabilization of Cat Qubits (2020)
• Alice&Bob - Cat Qubit Explained
• Microsoft Azure - Cat Qubits Resource Estimator

References

• Leghtas et al. - Hardware-Efficient Autonomous QEC (2015)
• Albert et al. - Performance and Structure of Cat Codes (2019)
• Campagne-Ibarcq et al. - Quantum Error Correction of Cat Qubit (2020)
• Puri et al. - Stabilized Cat in Driven Nonlinear Cavity (2017)

Test vectors

9 vectors ship with this algorithm and run in the test suite. Byte values are hexadecimal.

Vector 1 — [Encode logical

0⟩ as even cat state with α=2.0](https://errorcorrectionzoo.org/c/two-legged-cat)

Field	Value
alpha	2
input	00
expected	00

Vector 2 — [Encode logical

1⟩ as odd cat state with α=2.0](https://errorcorrectionzoo.org/c/two-legged-cat)

Field	Value
alpha	2
input	01
expected	01

Vector 3 — Photon parity measurement on even cat state (no errors)

Field	Value
alpha	2
parityMeasurement	Yes
input	00
expected	00

Vector 4 — Photon parity measurement on odd cat state (no errors)

Field	Value
alpha	2
parityMeasurement	Yes
input	01
expected	01

Vector 5 — Encode with smaller coherent amplitude α=1.0

Field	Value
alpha	1
input	00
expected	00

Vector 6 — Encode with larger coherent amplitude α=3.0 (enhanced bit-flip suppression)

Field	Value
alpha	3
input	01
expected	01

Vector 7 — Single photon loss error detection and recovery

Field	Value
alpha	2
simulatePhotonLoss	Yes
input	00
expected	00

Vector 8 — Encode two logical qubits in separate cavity modes

Field	Value
alpha	2
input	0001
expected	0001

Vector 9 — Verify cat state fidelity remains high (F > 0.99) for α=2

Field	Value
alpha	2
checkFidelity	Yes
minFidelity	0.99
input	00
expected	00

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