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No qudit Y gate #5814

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Merged
viathor merged 2 commits into from
Aug 1, 2022
Merged

No qudit Y gate #5814

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No qudit Y gate
viathor Aug 1, 2022
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viathor Aug 1, 2022
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10 changes: 10 additions & 0 deletions cirq-core/cirq/ops/common_gates.py
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Expand Up @@ -389,6 +389,16 @@ class YPowGate(eigen_gate.EigenGate):
parameter when initializing.

`cirq.Y`, the Pauli Y gate, is an instance of this gate at `exponent=1`.

Unlike `cirq.XPowGate` and `cirq.ZPowGate`, this gate has no generalization
to qudits and hence does not take the dimension argument. Ignoring the
global phase all generalized Pauli operators on a d-level system may be
written as X**a Z**b for a,b=0,1,...,d-1. For a qubit, there is only one
"mixed" operator: XZ, conventionally denoted -iY. However, when d > 2 there
are (d-1)*(d-1) > 1 such "mixed" operators (still ignoring the global phase).
Due to this ambiguity, qudit Y gate is not well defined. The "mixed" operators
for qudits are generally not referred to by name, but instead are specified in
terms of X and Z.
"""

def _num_qubits_(self) -> int:
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