Support for Projectors

Is your feature request related to a use case or problem? Please describe.

This is related to expanding functionality in TFQ here ( https://github.com/tensorflow/quantum/issues/357 )

Describe the solution you’d like

It would be nice to support projectors in cirq.PauliSum so that more complex (and still valid) expressions in cirq.PauliSum can be compressed to a reasonable length. Maybe something like:

# Normal functionality
a = 5.0 * cirq.Z(q0) - 2.0 * cirq.X(q0)

# New functionality
a = 5.0 * cirq.Z(q0) - 2.0 * cirq.X(q0) + cirq.OneProjector(q0) * cirq.ZeroProjector(q1)

Doing this right now in Cirq does not scale well:

def one_proj(q):
  return (1 - cirq.Z(q)) / 2

def zero_proj(q):
  return (1 + cirq.Z(q)) / 2

a = one_proj(q0) * one_proj(q1)
print(len(a._linear_dict.keys()))  # => 4

a = one_proj(q0) * one_proj(q1) * one_proj(q2)
print(len(a._linear_dict.keys()))  # => 8

a = one_proj(q0) * one_proj(q1) * one_proj(q2) * one_proj(q3)
print(len(a._linear_dict.keys()))  # => 16

.
.
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# Anything past 20 is already 1 million elements and not all that usable anymore.

What is the urgency from your perspective for this issue? Is it blocking important work?

P1 - I need this no later than the next release (end of quarter)

[tonybruguier]

Thanks for the feedback, new version (and new URL) of the RFC at: https://tinyurl.com/ketbra

[tonybruguier]

@MichaelBroughton With #4331 and #4364 merged, is there anything left to do? If so, happy to help of course, but otherwise, maybe this issue can be closed?