Partition the Pauli group into qubit-wise commuting terms #2185
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Hello. You may have forgotten to update the changelog!
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[sc-14640] |
trbromley
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## master #2185 +/- ##
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Coverage 99.21% 99.21%
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Files 231 231
Lines 17873 17901 +28
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+ Hits 17732 17760 +28
Misses 141 141
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Looks awesome, thanks @trbromley !
I've left a minor Q and suggestion. Approved ✔️
| @@ -250,3 +253,80 @@ def pauli_mult_with_phase(pauli_1, pauli_2, wire_map=None): | |||
| phase *= -1j | |||
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| return pauli_product, phase | |||
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| @lru_cache() | |||
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how did you know to use this decorator here? I don't really understand how caching works and when to take advantage of it!
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There's probably better explanations out there, but from my perspective partition_pauli_group fits the criteria nicely of:
- simple inputs that can be hashed
- function takes a long time to compute
- restricted set of inputs that may be called multiple times (e.g., in circuit cutting we might have a few fragments with 3-wire measure nodes)
| # We know that I and Z always commute on a given qubit. The following generates all product | ||
| # sequences of len(n_qubits) over "FXYZ", with F indicating a free slot that can be swapped for | ||
| # the product over I and Z, and all other terms fixed to the given X/Y/Z. For example, if | ||
| # ``n_qubits = 3`` our first value for ``string`` will be ``('F', 'F', 'F')``. We then expand | ||
| # the product of I and Z over the three free slots, giving | ||
| # ``['III', 'IIZ', 'IZI', 'IZZ', 'ZII', 'ZIZ', 'ZZI', 'ZZZ']``, which is our first group. The | ||
| # next element of ``string`` will be ``('F', 'F', 'X')`` which we use to generate our second | ||
| # group ``['IIX', 'IZX', 'ZIX', 'ZZX']``. |
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Nice explanation! Makes sense and useful to have it here 👌
| @@ -250,3 +253,80 @@ def pauli_mult_with_phase(pauli_1, pauli_2, wire_map=None): | |||
| phase *= -1j | |||
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| return pauli_product, phase | |||
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| @lru_cache() | |||
There was a problem hiding this comment.
There's probably better explanations out there, but from my perspective partition_pauli_group fits the criteria nicely of:
- simple inputs that can be hashed
- function takes a long time to compute
- restricted set of inputs that may be called multiple times (e.g., in circuit cutting we might have a few fragments with 3-wire measure nodes)
Context:
As part of the QCut module, we need to efficiently measure over the full N-qubit Pauli group. Although there are
4^Nterms, we can measure only3^Ngroups.Description of the Change:
Added the
partition_pauli_groupfunction to thegroupingmodule.Possible Drawbacks:
The function returns Pauli words expressed as simple strings. This is sufficient for the QCut module's needs but some users may prefer the Pauli words as PL observables/tensors. Since the current implementation is sufficient for now, I propose to leave returning PL observables/tensors as a follow up addition.
Example:
>>> qml.grouping.partition_pauli_group(3) [['III', 'IIZ', 'IZI', 'IZZ', 'ZII', 'ZIZ', 'ZZI', 'ZZZ'], ['IIX', 'IZX', 'ZIX', 'ZZX'], ['IIY', 'IZY', 'ZIY', 'ZZY'], ['IXI', 'IXZ', 'ZXI', 'ZXZ'], ['IXX', 'ZXX'], ['IXY', 'ZXY'], ['IYI', 'IYZ', 'ZYI', 'ZYZ'], ['IYX', 'ZYX'], ['IYY', 'ZYY'], ['XII', 'XIZ', 'XZI', 'XZZ'], ['XIX', 'XZX'], ['XIY', 'XZY'], ['XXI', 'XXZ'], ['XXX'], ['XXY'], ['XYI', 'XYZ'], ['XYX'], ['XYY'], ['YII', 'YIZ', 'YZI', 'YZZ'], ['YIX', 'YZX'], ['YIY', 'YZY'], ['YXI', 'YXZ'], ['YXX'], ['YXY'], ['YYI', 'YYZ'], ['YYX'], ['YYY']]