# What is the longest quantum circuit?

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.

• Do classical computations count? They are a special case of quantum computations. – Norbert Schuch Nov 13 '18 at 10:17
• 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. – psitae Nov 15 '18 at 12:09
• 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. – Norbert Schuch Nov 15 '18 at 12:37

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.