Let’s say you have a state ( |0> + |1> ) / √2 and want to rotate it by 45 degrees and measure it, expecting to get “1” with certainty. But a bug in your equipment affects some other unrelated qubit, which was |0> before and becomes |0 xor your qubit> afterward. So now you have ( |00> + |11> ) / √2. Now rotating your qubit leads to ( |00> + |10> + |11> - |01> ) / 2, and measuring gives “0″ or “1” with probability 1⁄2 each. Some unrelated qubit being xor’ed with yours caused your qubit to become mixed.
In theory, this is recoverable: find the stray qubit and xor it with yours again. But what if you accidentally measured it? Then you’d have to xor your memory with the qubit, which sounds impractical. Worse, what if you measured it and learned about the problem only in case of “1”? This is why quantum computation is so fragile.
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Decoherence.
Let’s say you have a state ( |0> + |1> ) / √2 and want to rotate it by 45 degrees and measure it, expecting to get “1” with certainty. But a bug in your equipment affects some other unrelated qubit, which was |0> before and becomes |0 xor your qubit> afterward. So now you have ( |00> + |11> ) / √2. Now rotating your qubit leads to ( |00> + |10> + |11> - |01> ) / 2, and measuring gives “0″ or “1” with probability 1⁄2 each. Some unrelated qubit being xor’ed with yours caused your qubit to become mixed.
In theory, this is recoverable: find the stray qubit and xor it with yours again. But what if you accidentally measured it? Then you’d have to xor your memory with the qubit, which sounds impractical. Worse, what if you measured it and learned about the problem only in case of “1”? This is why quantum computation is so fragile.