# What is the longest time a qubit has survived with 0.9999 fidelity?

I am pretty intrigued by the record time that a qubit has survived.

• I guess it's the one I mentioned in this answer, from the decoherence time you should be able to calculate the time until the fidelity drops below some value Apr 12, 2018 at 19:44
• The number seems a bit arbitrary. Why not 0.999 or 0.99999? Apr 12, 2018 at 20:05
• From Figure 4b in Zhong et al Nature 2015 linked above, it seems that (a) yes, as suggested by @M.Stern the number can be estimated (is it about less than 1 second?) but (b) it was in fact not experimentally measured, so as far as we know it could be any time between arbitrarily close to zero and up to 10 minutes, depending on the details of the spin dynamics. Apr 12, 2018 at 20:26
• Do you mean longest time that a 'memory' qubit has survived (i.e. sitting there, not actually doing anything) or the longest time a 'computational' qubit has survived (i.e. one that's actively having gates performed on it)? Apr 12, 2018 at 21:38

Well, for the longest coherence time ever, I'm finding this Science from 2013 entitled Room-Temperature Quantum Bit Storage Exceeding 39 Minutes Using Ionized Donors in Silicon-28, which indicates qubits that lasted for over 39 minutes; these, however, only had an 81% fidelity rate. (This is for qubits used in computation, not memory storage. For memory storage, see M. Stern's link.)

But you're looking for qubits with a high fidelity rate. In that case, I found a Nature Nanotechnology from 2014 entitled Storing quantum information for 30 seconds in a nanoelectronic device(alternate link to arXiv) which was coherent for 30 seconds - but had a greater than 99.99% fidelity rate, which is exactly what you're looking for. Most other papers I'm finding with a 99.99% fidelity rate or greater measure their coherence times in nano or microseconds.

I will keep looking.

• Thanks a lot for the answer! Indeed this second paper covers exactly what I needed and it is pretty pretty impressive! Apr 15, 2018 at 9:39
• Unfortunately this answer is wrong for the fidelity of both the 2013 paper, and the 2014 paper. The 81% for the first paper was low because they were just trying to show they could disturb the system and maintain coherence (they were successful up to 81%). The second paper maintains 0.9999 fidelity for only 0.000 seconds !!! (see Fig S2c in the supplement). As the authors admit (see my last comment to my answer), "Despite the record coherence times discussed above, our results do not match those obtained in bulk ensembles[6–8]". Reference 8 is the 2013 paper, where it lasts far far longer. May 3, 2018 at 23:17
• I'm not sure why I can't edit comments, but 0.000 seconds should say 0.0002 seconds. Also the fidelity for the first experiment is higher than 81% for the case where they don't try disturbing the system. See my answer. May 4, 2018 at 19:21
• I think you can't edit comments @user1271772 after some fixed period of time. Mar 9, 2020 at 9:11

More details: The $T_2$ was 180 minutes, or 3 hours.

What about the 81% that Heather mentioned?: The fidelity of 81% that Heather quotes, was actually referring to something else. In the same paper they wanted to show that they could change the temperature of the sample while still maintaining the spins in a coherent superposition. The sample was increased in temperature from 4.2K to 300K gradually over 6 minutes, held there for 2 minutes, then reduced back to 4.2K gradually over 4 minutes. After doing all that, the spins had impressively maintained a fidelity of 81% with respect to the starting state.

But that 12 minute experiment where they wanted to show that they can maintain coherence even when majorly disturbing the thermal equilibrium of the sample, was far less than the 3 hours $T_2$ they measured in an experiment where the coherence survived for 300 minutes (5 hours) with temperature kept constant at 1.2K.

What about the 2014 paper with 0.9999 fidelity?: This comes from Figure S2c in the Supplement, which is only up to 0.0002 seconds. If you want to get the fidelity at 30 seconds, or at 180 minutes, look at the $T_2$ times in Fig S1 of the supplement, and you will see that all of these are orders of magnitude smaller than what it was in the 2013 paper.

The authors admit this 3 times:
1) "Despite the record coherence times discussed above, our results do not match those obtained in bulk ensembles[6–8]" Reference 8 is the 2013 paper.
2) "This currently represents the record coherence for any single qubit in the solid state." Note they say "single" qubit and "solid state".
3) "which reach here a new record for solid-state single qubits with $T_2$ > 30 s in the $^{31}$P$^+$spin" Note the 30s is a T2!! This is much smaller than the $T_2$ = 180 minutes mentioned above.

• Note, however, the fundamental difference between characterizing a decay by a (mono)exponential function with a T2 (and inerpolating from that function) and experimentally obtaining a datapoint worth 0.9999 fidelity. May 3, 2018 at 4:51
• @agaitaarino: Where in the 2014 paper do they say that they obtained a single datapoint with 0.9999 fidelity after 30 seconds? They obtained their fidelities from the Rabi Oscillation data in Figure S2 of the Supplement, where lots and lots of points are used for each fidelity. May 3, 2018 at 23:08
• @agaitaarino The 0.9999 you refer to comes from Figures S2b and S2c in the Supplement, which goes up to 0.0002 seconds at most most, not 30 seconds! We have no idea what these fidelities will be at 30 seconds (or 180 minutes), because of the exact reason you mentioned: fitting to a curve and extrapolating over 6 orders of magnitude is questionable. If you want to compare this paper to the one I mentioned, see the summary of T2 times in Fig S1 of the supplement. None of these come close to the T2 of 180 minutes in the 2013 paper. Unfortunately they have only achieved 0.9999 fidelity for 0.0002s May 3, 2018 at 23:08
• @agaitaarino: If you want to know the amount of time that the coherence lasted with fidelity 0.9999 in my paper, it is 1.08 seconds, which is 4 orders of magnitude larger than anything in the 2014 paper, which is at most 0.0002 seconds. May 3, 2018 at 23:09
• @agaitaarino: The 2014 paper admits that they do not reach the coherence times achieved in the 2013 paper, and are very careful to say they only set the record for a SINGLE spin in the solid state. "Despite the record coherence times discussed above, our results do not match those obtained in bulk ensembles[6–8]" Reference 8 is the 2013 paper. "This currently represents the record coherence for any single qubit in the solid state." Note they say "single" qubit and "solid state". "which reach here a new record for solid-state single qubits with T2 > 30 s in the 31P+spin" Note the 30s is a T2!! May 3, 2018 at 23:12