[Performance] cuTN circuit2einsum slower than opt_einsum

Discussed in https://github.com/NVIDIA/cuQuantum/discussions/53

^{Originally posted by rht May 12, 2023}
I was benchmarking cuTensorNet and opt_einsum on the QFT and QAOA circuit, and I found the former to be consistently slower than the latter.
I used the same code in https://github.com/NVIDIA/cuQuantum/discussions/23 for cuTensorNet, and for opt_einsum:

bitstring = "0" * len(qubits)
# https://optimized-einsum.readthedocs.io/en/stable/autosummary/opt_einsum.contract_path.html#opt_einsum.contract_path
expression, operands = myconverter.amplitude(bitstring=bitstring)
tic = time.time()
path, path_info = oe.contract_path(expression, *operands)
elapsed1 = time.time() - tic
print("Elapsed opt_einsum path finding", elapsed1)
tic = time.time()
output = oe.contract(expression, *operands, optimize=path)
elapsed2 = time.time() - tic
print("Elapsed opt_einsum contract", elapsed2)

Plot for QFT:

I think it has something to do with cuTensorNet's path finding being closer to the global optimum. Is there a way to tweak the hyperoptimizer to either stop early, or to have a larger error tolerance, so as to minimize the overall time?