Cannot add identity to PauliSum

[95-martin-orion]

Description of the issue

Identities cannot be added to PauliSums. This might be related to cirq.IdentityGate not being a cirq.Pauli.

How to reproduce the issue

ps = cirq.PauliSum()
ps += cirq.I(cirq.LineQubit(0))

# Generates the error:
# TypeError: unsupported operand type(s) for +=: 'PauliSum' and 'GateOperation'

Cirq version
0.11.0.dev

[95-martin-orion]

In lieu of a fix, users can wrap identity gates in cirq.PauliStrings before mixing them into PauliSums to avoid this issue.

psum = cirq.PauliSum()
pstr = cirq.PauliString(cirq.I(cirq.LineQubit(0)))
# does not fail
psum += pstr

[BichengYing]

Another shorter workaround is

ps = cirq.PauliSum()
ps += 1*cirq.I(cirq.LineQubit(0))

but I was also wondering if cirq.XPowerGate(exponent=0) acts same as IdentifyGate or not. (Seems no except global phase difference).

[viathor]

The PauliString class maps sets of qubits to Pauli gates. This representation makes an implicit assumption that the operator corresponding to any given key-value pair in the dictionary acts as a scalar multiple of the identity on qubits which are not members of its key. This has a special case for scalars: scalar is an operator that acts as a scalar multiple of the identity on all qubits, hence the empty key.

This gives us another workaround for the issue:

ps = cirq.PauliSum()
ps += 1

which actually works fine at the moment. I think that the above code snippet and

ps = cirq.PauliSum()
ps += cirq.I(cirq.LineQubit(0))

should have the same effect once the issue is fixed.