According to Gottesman's paper https://arxiv.org/abs/quant-ph/0406196, the maximally mixed state is also simulable by stabilizers. Is there any way to include this kind of state in Stim?
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$\begingroup$ What are you trying to get as the output of the simulation? If all you want is samples of measurement outputs then the easiest way to do mixed states is to include noise processes in the circuit. $\endgroup$– Craig GidneyCommented Aug 7, 2022 at 0:22
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$\begingroup$ I wish to estimate the von Neumann entropy on a large scale. $\endgroup$– Yucheng HeCommented Aug 7, 2022 at 0:34
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$\begingroup$ By the way, there is a typo in that paper. In the second equation the exponent of $2$ should be $n$ not $r$ as in $2^n$, otherwise the state is not normalized. $\endgroup$– lcvCommented Mar 5 at 21:11
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1 Answer
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The underlying answer is that Stim doesn't directly support this use case, but it provides tools that can be used to implement it.
For example, the expected output of a circuit that contains noise is a mixed state. If you can decompose your mixed state into a noisy stim.Circuit that produces the mixed state, then stim can give you boatloads of samples from that circuit.
If you want to get a bit fancier you can create a mixed state by entangling with ancilla qubits ("purifying the mixed state"). Then, by using stim.TableauSimulator, you can answer more abstract questions like the existence of a stabilizer.
The specific strategy proposed in the paper you linked is a constant factor optimization of the purification based approach. It's unlikely that you're doing circuits large enough (think >10K qubits, >10M operations) that you'll need this optimization on top of what stim already does.
answered Aug 7, 2022 at 8:04