Is there anything practical that can be done with a single qubit? And by "practical," I mean a problem that can be solved or information that can be stored.

I realize that one practical thing that you can do with a single qubit is to write a grant application to build a computer that has 9 qubits, but that is a bit too meta for this question.

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    $\begingroup$ generate random numbers $\endgroup$ – kludg Jan 20 at 15:31
  • $\begingroup$ You can't clone a single qubit. $\endgroup$ – Mark S Jan 21 at 0:11

Some select examples of single qubit technology that has been used for decades:

  • Atomic clocks are single qubit quantum information processors. (In fact, the natural transition frequency between the states of a specific qubit defines what humans mean by time.)
  • NMR Spectroscopy is typically applied to single qubits. (Well, ensembles of single qubits, but there is no entanglement between qubits in the ensemble. This actually less powerful than processing them one at a time.)
  • Quantum Random Number Generators use measurement of single qubits in superposition. (You can by machines that use polarisation of light to do this, for example.)
  • Interferometers are essentially dual-rail qubits. (Again, laser light in an interferometer is just an ensemble of such qubits and would be equivalent to waiting for the same number of single photons to traverse it one at a time.)

Possible future uses (nowhere near exhaustive or unbiased):

  • Coherent measurement for binary classification (see, e.g., Quantum Data Gathering)
  • Quantum metrology for estimating phases (see, e.g., Quantum metrology with full and fast control)
  • Pedagogy (We'll never stop learning quantum starting with qubits. Having access to precision controlled single qubits would be useful in teaching.)
  • Test-beds for control (Even a large scale quantum computer will be run with single qubit gates at the physical level. Research in control and noise mitigation techniques on single qubits with remain relevant for quite some time.)
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  • $\begingroup$ A couple other examples would be: quantum sensors or for quantum communication ( I'm thinking nitrogen vacancy centers with these two examples) $\endgroup$ – user245427 Jan 22 at 0:16
  • $\begingroup$ Do you have a good ref for NMR using bunch of non-interacting qubits? $\endgroup$ – user185597 Jan 23 at 7:42
  • $\begingroup$ Every NMR system works this way. The sample is always at least mesoscopic. $\endgroup$ – Chris Ferrie Jan 29 at 1:42

I particularly like this example of a single qubit quantum classifier. The idea is to use a variational approach to do ‘data reuploading’ and create a non-linear classifier, which has similarities to a single hidden layer neural network.

There’s an example implementation from Xanadu in Python along with a basic overview.

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Elitzur and Vaidman showed in 1993 that a single qubit in superposition can be used to detect the presence or absence of a bomb without the bomb necessarily going off!

I also really like O'Donnell's lecture on the Elitzur-Vaidman bomb tester here. With the naive experiment, there is a 50% chance that the bomb will still go off; O'Donnell describes a nice improvement where the same qubit is rotated by $\epsilon$ degrees for $n$ times - the probability that the bomb is present and yet still goes off decreases as $\epsilon^2$ .

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