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Description
Is your feature request related to a use case or problem? Please explain
Product state mode (controlled by the simulator flag split_untangled_states, defaults to True for all circuits. This likely isn't optimal.
Describe the solution you would prefer
While in theory, product state mode should always be faster, there are caveats
- It substitutes 2N*2N matrix multiplication with N 2*2 multiplications (in the simplest case) for N qubits when they're not entangled. This seems nice, but for smallish N, a single large matrix multiplication in numpy could be much faster than jumping back and forth from C to Python N times. For qubits<N, where N needs to be determined by testing, it should default to False.
- For nonterminal measurements, when the measured qubits immediately get entangled again, it causes an unnecessary factorization and re-kronning of the substates, that can be an expensive and useless operation.
- For terminal measurements, there's no need to factor the substate after measuring because it's terminal.
- The factorization and kronning of substates during simulation likely increases rounding error. (I would guess kronning-only has little to no effect, or plausibly even decrease error, but factorization would likely have a significant effect).
- Perhaps the boolean flag should be replaced by an enum: None, KronOnly, and Full, where KronOnly starts in product state mode but doesn't try to factor after each measurement, whereas Full does both.
- For real-world quantum circuits, the first step in many algorithms is "entangle all qubits". Perhaps the default setting should be Off.
I think the first bullet point could be done easily without tradeoffs; just run some simulations, figure out where the breakeven N is, and update the code to turn it off if N <= breakeven. The remainder may need more analysis in terms of real-world circuits we'd like to optimize for vs artificial examples that highlight a single characteristic.
How urgent is this for you? Is it blocking important work?
P3 – I'm not really blocked by it; it's an idea I'm proposing based on principle