From 2a4c7f744156775af0173f2a4ba4c206c5328b93 Mon Sep 17 00:00:00 2001
From: michael <65613226+michaelontiveros@users.noreply.github.com>
Date: Wed, 9 Nov 2022 16:11:19 -0700
Subject: [PATCH 1/2] fixed XPowGate matrix description

Let t = 1.
Then the XPowGate matrix should be a phase factor times the Pauli X-matrix,
which means that the first coefficient should equal 0.
As written, the first coefficient is equal to a phase factor times \cos(\pi t),
which does not equal 0.
---
 cirq-core/cirq/ops/common_gates.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/cirq-core/cirq/ops/common_gates.py b/cirq-core/cirq/ops/common_gates.py
index a8131613942..9dfd43fc9ae 100644
--- a/cirq-core/cirq/ops/common_gates.py
+++ b/cirq-core/cirq/ops/common_gates.py
@@ -74,8 +74,8 @@ class XPowGate(eigen_gate.EigenGate):
     $$
     e^{i \pi s t}
     \begin{bmatrix}
-      e^{i \pi t /2} \cos(\pi t) & -i e^{i \pi t /2} \sin(\pi t) \\
-      -i e^{i \pi t /2} \sin(\pi t) & e^{i \pi t /2} \cos(\pi t)
+      e^{i \pi t /2} \cos(\pi t /2) & -i e^{i \pi t /2} \sin(\pi t /2) \\
+      -i e^{i \pi t /2} \sin(\pi t /2) & e^{i \pi t /2} \cos(\pi t /2)
     \end{bmatrix}
     $$
 

From 084af174f8a761a90f7806373e79e31df9388430 Mon Sep 17 00:00:00 2001
From: michael <65613226+michaelontiveros@users.noreply.github.com>
Date: Thu, 10 Nov 2022 15:06:41 -0700
Subject: [PATCH 2/2] combined and moved phase factors to the front

---
 cirq-core/cirq/ops/common_gates.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/cirq-core/cirq/ops/common_gates.py b/cirq-core/cirq/ops/common_gates.py
index 9dfd43fc9ae..7efc8139f70 100644
--- a/cirq-core/cirq/ops/common_gates.py
+++ b/cirq-core/cirq/ops/common_gates.py
@@ -72,10 +72,10 @@ class XPowGate(eigen_gate.EigenGate):
 
     The unitary matrix of `cirq.XPowGate(exponent=t, global_shift=s)` is:
     $$
-    e^{i \pi s t}
+    e^{i \pi t (s + 1/2)}
     \begin{bmatrix}
-      e^{i \pi t /2} \cos(\pi t /2) & -i e^{i \pi t /2} \sin(\pi t /2) \\
-      -i e^{i \pi t /2} \sin(\pi t /2) & e^{i \pi t /2} \cos(\pi t /2)
+      \cos(\pi t /2) & -i \sin(\pi t /2) \\
+      -i \sin(\pi t /2) & \cos(\pi t /2)
     \end{bmatrix}
     $$