add Quantum Shannon Decomposition #7907
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Overall this LGTM, I'll have to read the paper again to check the algorithm against this. But other than that the only other thing I'm wondering is around our plugin structure now. Specifically, I'm wondering if we should just make isometry a separate plugin now move it out of the default plugin. Or if we want to make this a standalone plugin with min_qubits=3, but I'm guess the performance of this method is good enough that it just makes sense to leave it in the default.
| nqubits = int(np.log2(dim)) | ||
| if opt_a2: | ||
| raise NotImplementedError("Optimization A.2 is not currently implemented.") | ||
| if np.allclose(np.identity(dim), mat): |
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Do you think there is value in having an option to tweak the tolerances here (and anywhere we're doing float comparisons)?
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Maybe, but I'm not sure how to do that sensibly at the moment.
| if dim == 2: | ||
| if decomposer_1q is None: | ||
| decomposer_1q = one_qubit_decompose.OneQubitEulerDecomposer() | ||
| circ = decomposer_1q(mat) | ||
| elif dim == 4: | ||
| if decomposer_2q is None: | ||
| decomposer_2q = two_qubit_decompose.TwoQubitBasisDecomposer(CXGate()) | ||
| circ = decomposer_2q(mat) | ||
| else: |
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I'm wondering if it makes more sense here to just raise if we expect people to use other decomposition techniques for 1 and 2 qubit matricies. For example, if this were a separate unitary synthesis plugin we'd just set min qubits to 3 and it would fallback to the default plugin for smaller matrices.
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Actually this decomposition method will go down to single qubit unitaries but it's just that the known 3-cnot decomposition will yield lower cnot counts. If we let it go down to single qubits, this would correspond to the "QSD, l=1" column of the table above. I wouldn't raise, however; since you'd raise every time you tried to do this decomposition due to the recursion. I could see, however allowing it to use this the QSD all the way down to 1q but I wasn't sure how best to implement that or if anyone would actually prefer the higher CX cost.
mtreinish
added
the
Changelog: New Feature
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Oh, the other thing I just noticed this could use a release note. Probably a feature note about the new function and a upgrade note about the change in the behavior of the unitary synthesis pass. (this is where having a dedicated isometry synthesis plugin would be useful because we could document calling transpile(unitary_synthesis_method='isometry") as a way to preserve the previous decompositions for >2q unitaries).
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This looks good to me, thanks for implementing it. There are some potential duplicates of some inner bits and pieces, mainly around uniformly-controlled (multiplexed) gates with those existing under qiskit/extensions/quantum_initializer/ (which isometry is built on). It would be good to unify these.
Co-authored-by: Ali Javadi-Abhari <[email protected]>
Co-authored-by: Ali Javadi-Abhari <[email protected]>
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@ajavadia The duplication was an attempt to make the code more efficient as suggested by Matthew (#7907 (comment)). Another alternative would be to let the code in UCPauliRotGate take keyword options to replace CX with CZ and remove the final CZ but that seemed somewhat specific to this decomposition method. |
Summary
Currently, general unitary decomposition yields CX gate counts which are about double one of the best currently known algorithms, the Quantum Shannon Decomposition, which is itself within a factor of two from the theoretical lower bound. This PR adds this decomposition as described in arXiv:quant-ph/0406176.
Details and comments
In this implementation recursive decomposition proceeds down to two qubit operators which it hands off to the
TwoQubitBasisDecomposer.Only, one of the two optimizations mentioned in the paper is currently implemented. When option
a1_optis set, the default, the CX gate count is9/16 * 4^(n) - 3/2 * 2^n - 1/3 * 4^(n-1) - 1
The table shows a comparison of CX gates counts before and after this PR along with the methods described in the paper,