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arXiv:quant-ph/9602019

Perfect Quantum Error Correction Code

Raymond Laflamme, César Miquel, Juan Pablo Paz, Wojciech Hubert Zurek

Published Feb 27, 1996• 34 citations
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Abstract

We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. To accomplish this, we encode the original state by distributing quantum information over five qubits, the minimal number required for this task. We give a simple circuit which takes the initial state with four extra qubits in the state |0> to the encoded state. The circuit can be converted into a decoding one by simply running it backward. Reading the extra four qubits at the decoder's output we learn which one of the sixteen alternatives (no error plus all fifteen possible 1-bit errors) was realized. The original state of the encoded qubit can then be restored by a simple unitary transformation.

DOI
10.48550/arxiv.quant-ph/9602019

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We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. To accomplish this, we encode the original state by distributing quantum information over five qubits, the minimal number required for this task. We give a simple circuit which takes the initial state with four extra qubits in the state |0> to the encoded state. The circuit can be converted into a decoding one by simply running it backward. Reading the extra four qubits at the decoder's output we learn which one of the sixteen alternatives (no error plus all fifteen possible 1-bit errors) was realized. The original state of the encoded qubit can then be restored by a simple unitary transformation.
We present a quantum error correction code which protects a qubit of information against general one qubit errors. To accomplish this, we encode the original state by distributing quantum information over five qubits, the minimal number required for this task. We describe a circuit which takes the initial state with four extra qubits in the state ∣0〉|0〉∣0〉 to the encoded state. It can also be converted into a decoder by running it backward. The original state of the encoded qubit can then be restored by a simple unitary transformation.
We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. To accomplish this, we encode the original state by distributing quantum information over six qubits which is the minimal number for the present task (see reference [1]). The encoding and error recovery operations for such a code are presented. It is noted that the present code is also a three-qubit quantum hidded information code over each qubit. In addition, an encoding scheme for hiding nnn-qubit quantum information over each qubit is proposed.
We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. To accomplish this, we encode the original state by distributing quantum information over six qubits. The encoding and error recovery operations for such a code are presented. We also show that the present code is a three-qubit quantum hidded information code over each qubit. In addition, hiding nnn-qubit quantum information over each qubit is considered.
We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. The present code has a high encoding efficiency, since only one auxiliary qubit is needed for one message qubit on average. In addition, we note that the code can also work even in a worse case that the interaction with the environment causes a leakage out of the qubit space. The code may have some applications in the storage of quantum information for small-scale quantum computing, quantum information processing, and quantum communication.