Shot batching is made more efficient by executing all the shots in one go on Lightning Qubit

[maliasadi]

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---

Context:
Shot batching is made more efficient by executing all the shots in one go on LightningQubit using shots.bin.

Description of the Change:

• Update _measure_with_samples_diagonalizing_gates
• Add shots_vector tests.

Benefits:

dev = qml.device('lightning.qubit', wires=20, shots=(10_000, ) * N)
for i in range(1000):
    @qml.qnode(dev)
    def circuit():
        return qml.counts(wires=0)

dev = qml.device('lightning.qubit', wires=20, shots=(10, ) * N)
for i in range(1000):
    @qml.qnode(dev)
    def circuit():
        return qml.counts(wires=0)

Possible Drawbacks:
n/a

Related GitHub Issues:

[sc-66537]

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 93.63%. Comparing base (073395b) to head (c0fdffa).

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #814      +/-   ##
==========================================
- Coverage   98.57%   93.63%   -4.94%     
==========================================
  Files         114       17      -97     
  Lines       18069     1902   -16167     
==========================================
- Hits        17812     1781   -16031     
+ Misses        257      121     -136     

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[multiphaseCFD]

Thanks @maliasadi ! Nice work!

[vincentmr]

Thanks @maliasadi , LGTM. A few suggestions and then I'm ready to approve. Nice speed-ups for shot-vectors (thinking about it, I think I'd prefer speed-up plots instead of the time vs. XXX above; no need to change it here though).

[vincentmr]

Code reduction, good speed-ups, nice PR @maliasadi !

[multiphaseCFD]

LGTM! Thanks @maliasadi !