To date, what is the longest quantum computation ever performed? Length is measured in number of operations.

EDIT --- I'm looking for a quantum computation with a clear ending and a clear output. Something like a quantum computation that solves a set of linear equations would count. But I consider a benchmarking experiment that measures the lifetime of the quantum information 'long' because it can be arbitrarily long and give the same output as a similar experiment which is much shorter.

  • 2
    $\begingroup$ Do classical computations count? They are a special case of quantum computations. $\endgroup$ – Norbert Schuch Nov 13 '18 at 10:17
  • $\begingroup$ I'm talking about computations performed on a quantum computer. So I guess classical computations count, but only if they are performed on a quantum computer. $\endgroup$ – psitae Nov 15 '18 at 12:09
  • $\begingroup$ I'm pretty sure that if you would run a classical computation on a quantum computer (optimized for that), you could get much longer coherence times, as decoherence usually takes place in a preferred basis (i.e., there is a "classical" basis which is much more stable). Issue is that quantum computers are not built to support a "native" gate set for that basis. $\endgroup$ – Norbert Schuch Nov 15 '18 at 12:37

The longest circuit ever performed is probably one used for benchmarking. So the point would be to run many gates, look at the associated decay in fidelity, and use that to find a measure of how good the gates are.

Here's a recent paper that I found on a fairly brief search. In Fig. 2 we see depths of 1500 single qubit gates and 130 for gates on two qubits. Given that these circuits are designed to drive states to a point of complete randomness, there's not much point in going further.

However, note that circuit depth isn't uniquely defined, especially since one circuit can be recompiled to an equivalent one with non-equal depth. This is especially true of single qubit operations. For example, should the gate sequence $H Z H$ be regarded as depth 3 or as depth 1, because it is equivalent to $X$. So a more concrete measure is perhaps the depth of cnots.

For this, the longest I know of is my own benchmarking program that I ran for 10 'rounds' in which each round has a cnot depth of 4 (except for the last, which has two). This makes a total cnot depth of 38. But, of course, I only know of this because it is my own project. There might be runs with more cnots, though current noise levels mean that there is not much reason to go too far beyond this.

| improve this answer | |
  • 1
    $\begingroup$ Hi James. Yes benchmarking experiments make sense as an answer to my question, but this is a terribly common experiment. Plus using this a longest quantum circuit record isn't very meaningful, because there's no clear place where you must stop -- you can keep making it longer and longer. The question has been edited with these thoughts in mind. Also, BTW I love you decodoku game. $\endgroup$ – psitae Nov 15 '18 at 12:23

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.