Will We Ever Have a Quantum Computer? by Mikhail I. Dyakonov

Author:Mikhail I. Dyakonov
Language: eng
Format: epub
ISBN: 9783030420192
Publisher: Springer International Publishing

However, this proposed method assumed that the additional (ancilla) qubits, the measurements, and the unitary transformations to be applied, remain ideal. It is said that this type of error correction is not fault-tolerant, whatever this may mean. (If the ancilla qubits are flawless, why not use them in the first place?) The ultimate solution, the fault-tolerant quantum computation, was advanced by Shor [44] and further developed by other mathematicians, see [45–49] and references therein.

Now, nothing is ideal: all the qubits are subject to noise, measurements may contain errors, and our quantum gates are not perfect. Nevertheless, the threshold theorem says that arbitrarily long quantum computations are possible, so long as the errors are not correlated in space and time and the noise level remains below a certain threshold. In particular, with error correction a single qubit may be stored in memory, i.e. it can be maintained arbitrarily close to its initial state during an indefinitely long time. (See Chap. 6 for a discussion of this issue).

This contradicts all our experience in physics. Imagine a pointer, which can freely rotate in a plane around a fixed axis. Fluctuating external fields cause random rotations of the pointer, so that after a certain relaxation time the initial position gets completely forgotten. (For electron spins the corresponding relaxation time is typically on the scale of nanoseconds).

How is it possible that by using only other identical pointers (also subject to random rotations) and some external fields (which cannot be controlled perfectly), it might be possible to maintain indefinitely a given pointer close to its initial position? The answer we get from experts in the field, is that it can work because of quantum mechanics: “We fight entanglement with entanglement” or, in the words of the Quantum Error Correction Sonnet by Gottesman [46],With group and eigenstate, we’ve learned to fix

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