To realize correct quantum computing it seems that both quantum error correction and quantum tomography would be necessary. Is this true? What is the relationship between these two fields?

  • $\begingroup$ Yes, this is probably true. And you also have to realize quantum fault-tolerance. Quantum error correction is storing or transmitting quantum information in a manner that lets you correct errors in it. Quantum tomography is figuring out what a quantum process is actually doing. And even if in theory you know what your quantum gates do, you probably need to check them using quantum tomography. Quantum fault tolerance is correcting errors on a quantum computer faster than they occur. These are connected in a several ways—e.g., similar techniques. $\endgroup$ – Peter Shor Nov 3 '15 at 4:07
  • $\begingroup$ If I understand correctly, Wiki on quantum tomography claims that for more than a few quantum bits quantum tomography is impossible in practice owing to exponential increase of work. Wouldn't that imply that the chance of having a practical quantum computer is extremely low from the very beginning? $\endgroup$ – Mok-Kong Shen Nov 3 '15 at 15:00
  • $\begingroup$ @PeterShor: I should very much appreciate it, if you would with your expertise also kindly help in the question I raised in my last comment. $\endgroup$ – Mok-Kong Shen Nov 6 '15 at 9:01
  • $\begingroup$ The reason fault tolerance works on a quantum computer is that the effect of quantum gates is confined to only a few qubits. Thus, you only need to use quantum tomography on a few qubits to figure out what your gates are doing and what the error model for them should be. $\endgroup$ – Peter Shor Nov 6 '15 at 10:47
  • $\begingroup$ @PeterShor: But a practical quantum computer has presumably a fairly sizeable number of gates and, while design is mostly a onetime work, the work involved in manufacture and maintenance might constitute a formidable issue in practice, I would as layman surmise. $\endgroup$ – Mok-Kong Shen Nov 7 '15 at 9:02

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