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I read in an article that in order to perform error correction on a quantum computer there can only be one error per 10.000 calculations (=unitary transformations).

This sounds pretty high but how much errors do actually occur typically? Are we close? Are we close to being close?

Article: http://www.cs.virginia.edu/~robins/Computing_with_Quantum_Knots.pdf

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  • $\begingroup$ This article is about topological quantum computation, which is believed to have very low error rate by design for some of the topologically protected gates. However the material required for such topological quantum computer is quite exotic, and largely remain elusive so far(although there has been remarkable progress recently). Error rate for more "conventional" quantum computing schemes is typically much lower by several orders of magnitude. $\endgroup$ – Meng Cheng Jul 15 '15 at 15:32
  • $\begingroup$ Lower compared to the Topological Computer or compared to the required error correction rate? $\endgroup$ – Thomas Elliot Jul 15 '15 at 15:42
  • $\begingroup$ Sorry, I meant to say the error threshold (below which error correction is possible) for conventional qubit realizations is much lower than topological quantum computers, at least in theory. We do not have a full fledged topological qubits experimentally yet, so these numbers are at best theoretical estimates. $\endgroup$ – Meng Cheng Jul 15 '15 at 15:50
  • $\begingroup$ Since we have normal qubits - do we have a error rate for those guys? How close are we to build large quantum computers (I know we are not close, but I never found a specific number - which I would like to know). $\endgroup$ – Thomas Elliot Jul 15 '15 at 17:40
  • $\begingroup$ I discuss this a bit in chapter 1 of my thesis. $\endgroup$ – DanielSank Jul 15 '15 at 22:40
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The answer depends on the implementation, as is often the case when asking practical questions about quantum computing. To give you an example of the state of the art in trapped ions, the Lucas group in Oxford can achieve less than one error in 1 million single-qubit gates, which they claim is less than the fault-tolerance threshold. Their error rate for two-qubit gates is more like one in every hundred operations, which will not be sufficient for fault-tolerance. However, it seems likely that error rates for two-qubit gates will continue to decrease as technology develops.

The key issue in all of these implementations is scalability. It is not enough to demonstrate low error rates on just a few qubits. One also needs to be able to design an architecture allowing one to manipulate and store quantum information on tens or hundreds of qubits, while keeping the error rates low, before anything remotely useful can be done with your putative quantum computer.

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    $\begingroup$ I wish I could upvote this one hundred times for emphasizing that scalability is as important as demonstrating sub-threshold 2 qubit gates. $\endgroup$ – DanielSank Jul 15 '15 at 21:51
  • $\begingroup$ Wow, how come the error rate for two qubits is so horrible compared to the one qubit rate? What makes the scalability so difficult? $\endgroup$ – Thomas Elliot Jul 19 '15 at 5:08

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