@tonybruguier @balopat I just want to mention that this diagonal Hamiltonian representation is highly related with diagonal gate decomposition #3890. One main application of diagonal gate is to simulate the Hamiltonian (Ref. Sec 4. in (https://iopscience.iop.org/article/10.1088/1367-2630/16/3/033040/pdf).

@tonybruguier @balopat I just want to mention that this diagonal Hamiltonian representation is highly related with diagonal gate decomposition #3890. One main application of diagonal gate is to simulate the Hamiltonian (Ref. Sec 4. in (https://iopscience.iop.org/article/10.1088/1367-2630/16/3/033040/pdf).

Ohhhh, nice! Thanks for the reference.

I will need more time to digest the paper and your PR. I took a little time to study both, and my temporary understanding is that the approach you just linked is that it approximates a function defined by its enumerated values while the present PR is an exact representation of a function defined by its formula.

Also, do you suggest a refactoring (now or later)? I'm open to suggestions, I just could use some more advice on how to proceed (if you have the time). I will read the paper more carefully later no matter what.

@tonybruguier I don't suggest any refactoring at all. Just mention the connection. For example, here this Hamiltonian representation exploited the special format of QAOA \sum(1-s_is_j), which is not considered in the diagonal gate at all. But I am interested to have a deep look and check more differences and connections here.

@tonybruguier I don't suggest any refactoring at all. Just mention the connection. For example, here this Hamiltonian representation exploited the special format of QAOA \sum(1-s_is_j), which is not considered in the diagonal gate at all. But I am interested to have a deep look and check more differences and connections here.

Thanks. I think I understand a little bit more now. I think it is indeed the case that the diagonal gates uses the values directly to construct an approximate circuit, while the present PR uses the formula to construct an exact circuit.

It seems the circuit could be a bit different though:
https://github.com/tonybruguier/sandbox/blob/master/try_out_diagonal_gate.py#L29

The main difference and the biggest advantage of this work, I think, is it does not evaluate the whole truth table of boolean function directly to construct the circuit. Meanwhile, the diagonal gate has to know all values (not limited to boolean function through).
I want to correct that diagonal gates give the exact circuit instead of the approximate one if the function is f:[0,1]^n -> R. It gives an approximation for f: R -> R.

It seems the circuit could be a bit different though:
https://github.com/tonybruguier/sandbox/blob/master/try_out_diagonal_gate.py#L29

Yes, they will give different circuits. As for this particular circuit example you showed, they are exactly the same actually (if you ignore the identical operatorRz(0)). You can try print(cirq.Circuit(cirq.decompose(circuit2))) to see. (cirq.decompose will further decompose the CNOT gates)

Since the connection, I am reviewing this PR. (so me again :) ) Will send more comments after I understand this better.

Thanks. PTAL. I am thinking about what you said, and trying to see whether I can improve the number of gates.

Thanks @balopat . I think this is what you had suggested. PTAL?

@MichaelBroughton
Would you be interested in taking this over from Balint?

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@MichaelBroughton
Friendly ping. Not super urgent and I can withdraw it if you have objections.

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