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Traditional quantum error correction involves the redundant encoding of k quantum bits using n quantum bits to allow the detection and correction of any t bit error. The smallest general t=1 code requires n=5 for k=1. However, the dominant error process in a physical system is often well known, thus inviting the following question: Given a specific error model, can more efficient codes be devised? We demonstrate alternative codes that correct just amplitude damping errors that allow, for example, a t=1, k=1 code using effectively n=4. 6. Our scheme is based on using bosonic states of photons in a finite number of optical modes. We present necessary and sufficient conditions for the codes and describe construction algorithms, physical implementation, and performance bounds.
Chuang et al. (Fri,) studied this question.