#Tree quantum error correction code#

Similarly, an error on the first bit will be revealed by the pattern Q1=“No”, Q2=“Yes”. From this response, the recipient can infer the existence of an error and its location. If there were no errors, the answer to both of these questions would be “yes”, regardless of whether the message was 000 or 111.īut if the last bit suffered an error (receiving 001 or 110), the answer to Q1 would be “yes” but Q2 would be “no”. Q2: is the second bit the same as the third bit? Q1: is the first bit the same as the second bit? Instead of looking at the bit values, the receiver could instead ask the following two questions:

#Tree quantum error correction code#

To resolve this we return to the repetition code for guidance. So a quantum receiver isn’t allowed to measure the qubits directly, but she still needs to figure out whether errors have occurred, and where. Simply measuring quantum bits (qubits) changes the message. The receiver knows exactly what physical bits she received (001 in the example, above), which implies that she had to measure them (that is, look at them).īut quantum mechanics tells us that the act of measurement fundamentally changes the state of a quantum system. One quantum wrinkle in this picture is that it involves a “measurement”. The Conversation, CC BY-ND Known unknowns As long as errors are rare, the repetition code will allow logical data to be transmitted reliably over a noisy, error-prone channel.Įrror detection and error correction if the data is sent in threes.

The recipient would immediately see that an error had corrupted the data.įurther, by taking a majority vote, she would guess that an error affected the third physical bit, and correctly decode the logical bit: “0”. Suppose during data transmission of “0”, the last physical bit was accidentally flipped, so that the received message is 001. But if they disagree, which is right? With three clocks, a majority vote allows the timekeeper to detect and reset a wayward timepiece.įor binary data, represented by 0s and 1s, repetition protects information: a logical bit “0” is represented in three physical bits as 000, while “1” is represented as 111. Ideally, one clock would be sufficient, but what if something went wrong? Two clocks are better, so long as they both agree. They knew that longitude could be calculated from the elevation of the Sun so long as the time at home port was known - hence the naval imperative to build accurate, stable clocks. To see how this works for classical coding, consider the solution used by early navigators. And these can be adapted for quantum computing. This is because these devices use error correcting codes: even if errors corrupt the raw data stream, the important logical information can still be reconstructed.