diff --git a/src/stim/stabilizers/pauli_string.h b/src/stim/stabilizers/pauli_string.h
index b27009f09..8ba6435c9 100644
--- a/src/stim/stabilizers/pauli_string.h
+++ b/src/stim/stabilizers/pauli_string.h
@@ -131,6 +131,8 @@ struct PauliString {
     ///          many times the number of requested qubits. Use this to
     ///          avoid quadratic overheads from constant slight expansions.
     void ensure_num_qubits(size_t min_num_qubits, double resize_pad_factor);
+
+    void safe_accumulate_pauli_term(GateTarget t, bool *imag);
 };
 
 /// Writes a string describing the given Pauli string to an output stream.
diff --git a/src/stim/stabilizers/pauli_string.inl b/src/stim/stabilizers/pauli_string.inl
index 112bc28f3..a07b184f0 100644
--- a/src/stim/stabilizers/pauli_string.inl
+++ b/src/stim/stabilizers/pauli_string.inl
@@ -165,6 +165,31 @@ void PauliString<W>::ensure_num_qubits(size_t min_num_qubits, double resize_pad_
     num_qubits = min_num_qubits;
 }
 
+template <size_t W>
+void PauliString<W>::safe_accumulate_pauli_term(GateTarget t, bool *imag) {
+    auto q = t.qubit_value();
+    ensure_num_qubits(q + 1, 1.25);
+    bool x2 = (bool)(t.data & TARGET_PAULI_X_BIT);
+    bool z2 = (bool)(t.data & TARGET_PAULI_Z_BIT);
+    if (!(x2 | z2)) {
+        throw std::invalid_argument("Not a pauli target: " + t.str());
+    }
+
+    bit_ref x1 = xs[q];
+    bit_ref z1 = zs[q];
+    bool old_x1 = x1;
+    bool old_z1 = z1;
+    x1 ^= x2;
+    z1 ^= z2;
+
+    // At each bit position: accumulate anti-commutation (+i or -i) counts.
+    bool x1z2 = x1 & z2;
+    bool anti_commutes = (x2 & z1) ^ x1z2;
+    sign ^= (*imag ^ old_x1 ^ old_z1 ^ x1z2) & anti_commutes;
+    sign ^= (bool)(t.data & TARGET_INVERTED_BIT);
+    *imag ^= anti_commutes;
+}
+
 template <size_t W>
 uint8_t PauliString<W>::py_get_item(int64_t index) const {
     if (index < 0) {
diff --git a/src/stim/stabilizers/pauli_string.test.cc b/src/stim/stabilizers/pauli_string.test.cc
index b58bbe151..3467a387d 100644
--- a/src/stim/stabilizers/pauli_string.test.cc
+++ b/src/stim/stabilizers/pauli_string.test.cc
@@ -633,25 +633,117 @@ TEST_EACH_WORD_SIZE_W(pauli_string, before_tableau, {
         std::invalid_argument);
 })
 
-TEST_EACH_WORD_SIZE_W(pauli_string, weight, {
-    ASSERT_EQ(PauliString<W>::from_str("+").ref().weight(), 0);
-    ASSERT_EQ(PauliString<W>::from_str("+I").ref().weight(), 0);
-    ASSERT_EQ(PauliString<W>::from_str("+X").ref().weight(), 1);
-    ASSERT_EQ(PauliString<W>::from_str("+Y").ref().weight(), 1);
-    ASSERT_EQ(PauliString<W>::from_str("+Z").ref().weight(), 1);
-
-    ASSERT_EQ(PauliString<W>::from_str("+IX").ref().weight(), 1);
-    ASSERT_EQ(PauliString<W>::from_str("+XZ").ref().weight(), 2);
-    ASSERT_EQ(PauliString<W>::from_str("+YY").ref().weight(), 2);
-    ASSERT_EQ(PauliString<W>::from_str("+XI").ref().weight(), 1);
-
-    PauliString<W> p(1000);
-    ASSERT_EQ(p.ref().weight(), 0);
-    for (size_t k = 0; k < 1000; k++) {
-        p.xs[k] = k % 3 == 1;
-        p.zs[k] = k % 5 == 1;
-    }
-    ASSERT_EQ(p.ref().weight(), 333 + 199 - 66);
-    p.sign = true;
-    ASSERT_EQ(p.ref().weight(), 333 + 199 - 66);
+TEST_EACH_WORD_SIZE_W(pauli_string, safe_accumulate_pauli_term, {
+    PauliString<W> p(0);
+    bool imag = false;
+
+    p.safe_accumulate_pauli_term(GateTarget::x(5), &imag);
+    ASSERT_EQ(imag, 0);
+    ASSERT_EQ(p, PauliString<W>("_____X"));
+
+    p.safe_accumulate_pauli_term(GateTarget::x(5), &imag);
+    ASSERT_EQ(imag, 0);
+    ASSERT_EQ(p, PauliString<W>("______"));
+
+    p.safe_accumulate_pauli_term(GateTarget::x(5), &imag);
+    ASSERT_EQ(imag, 0);
+    ASSERT_EQ(p, PauliString<W>("_____X"));
+
+    p.safe_accumulate_pauli_term(GateTarget::z(5), &imag);
+    ASSERT_EQ(imag, 1);
+    ASSERT_EQ(p, PauliString<W>("_____Y"));
+
+    p.safe_accumulate_pauli_term(GateTarget::z(5), &imag);
+    ASSERT_EQ(imag, 0);
+    ASSERT_EQ(p, PauliString<W>("_____X"));
+
+    p.safe_accumulate_pauli_term(GateTarget::y(5), &imag);
+    ASSERT_EQ(imag, 1);
+    ASSERT_EQ(p, PauliString<W>("-_____Z"));
+
+    p.safe_accumulate_pauli_term(GateTarget::y(15), &imag);
+    ASSERT_EQ(imag, 1);
+    ASSERT_EQ(p, PauliString<W>("-_____Z_________Y"));
+
+    p.safe_accumulate_pauli_term(GateTarget::y(15, true), &imag);
+    ASSERT_EQ(imag, 1);
+    ASSERT_EQ(p, PauliString<W>("_____Z__________"));
+})
+
+TEST_EACH_WORD_SIZE_W(pauli_string, safe_accumulate_pauli_term_mul_table, {
+    PauliString<W> p(1);
+    bool imag = false;
+
+    p = PauliString<W>(1);
+    imag = false;
+    p.safe_accumulate_pauli_term(GateTarget::x(0), &imag);
+    p.safe_accumulate_pauli_term(GateTarget::y(0), &imag);
+    p.safe_accumulate_pauli_term(GateTarget::z(0), &imag);
+    ASSERT_EQ(imag, 1);
+    ASSERT_EQ(p, PauliString<W>("-I"));
+
+    p = PauliString<W>(1);
+    imag = false;
+    p.safe_accumulate_pauli_term(GateTarget::z(0), &imag);
+    p.safe_accumulate_pauli_term(GateTarget::y(0), &imag);
+    p.safe_accumulate_pauli_term(GateTarget::x(0), &imag);
+    ASSERT_EQ(imag, 1);
+    ASSERT_EQ(p, PauliString<W>("I"));
+
+    p = PauliString<W>(1);
+    imag = false;
+    p.safe_accumulate_pauli_term(GateTarget::x(0), &imag);
+    p.safe_accumulate_pauli_term(GateTarget::x(0), &imag);
+    ASSERT_EQ(imag, 0);
+    ASSERT_EQ(p, PauliString<W>("I"));
+    p = PauliString<W>(1);
+    imag = false;
+    p.safe_accumulate_pauli_term(GateTarget::x(0), &imag);
+    p.safe_accumulate_pauli_term(GateTarget::y(0), &imag);
+    ASSERT_EQ(imag, 1);
+    ASSERT_EQ(p, PauliString<W>("-Z"));
+    p = PauliString<W>(1);
+    imag = false;
+    p.safe_accumulate_pauli_term(GateTarget::x(0), &imag);
+    p.safe_accumulate_pauli_term(GateTarget::z(0), &imag);
+    ASSERT_EQ(imag, 1);
+    ASSERT_EQ(p, PauliString<W>("Y"));
+
+    p = PauliString<W>(1);
+    imag = false;
+    p.safe_accumulate_pauli_term(GateTarget::y(0), &imag);
+    p.safe_accumulate_pauli_term(GateTarget::x(0), &imag);
+    ASSERT_EQ(imag, 1);
+    ASSERT_EQ(p, PauliString<W>("Z"));
+    p = PauliString<W>(1);
+    imag = false;
+    p.safe_accumulate_pauli_term(GateTarget::y(0), &imag);
+    p.safe_accumulate_pauli_term(GateTarget::y(0), &imag);
+    ASSERT_EQ(imag, 0);
+    ASSERT_EQ(p, PauliString<W>("I"));
+    p = PauliString<W>(1);
+    imag = false;
+    p.safe_accumulate_pauli_term(GateTarget::y(0), &imag);
+    p.safe_accumulate_pauli_term(GateTarget::z(0), &imag);
+    ASSERT_EQ(imag, 1);
+    ASSERT_EQ(p, PauliString<W>("-X"));
+
+    p = PauliString<W>(1);
+    imag = false;
+    p.safe_accumulate_pauli_term(GateTarget::z(0), &imag);
+    p.safe_accumulate_pauli_term(GateTarget::x(0), &imag);
+    ASSERT_EQ(imag, 1);
+    ASSERT_EQ(p, PauliString<W>("-Y"));
+    p = PauliString<W>(1);
+    imag = false;
+    p.safe_accumulate_pauli_term(GateTarget::z(0), &imag);
+    p.safe_accumulate_pauli_term(GateTarget::y(0), &imag);
+    ASSERT_EQ(imag, 1);
+    ASSERT_EQ(p, PauliString<W>("X"));
+    p = PauliString<W>(1);
+    imag = false;
+    p.safe_accumulate_pauli_term(GateTarget::z(0), &imag);
+    p.safe_accumulate_pauli_term(GateTarget::z(0), &imag);
+    ASSERT_EQ(imag, 0);
+    ASSERT_EQ(p, PauliString<W>("I"));
 })
diff --git a/src/stim/stabilizers/pauli_string_ref.h b/src/stim/stabilizers/pauli_string_ref.h
index dc1d7ecfd..3519e7312 100644
--- a/src/stim/stabilizers/pauli_string_ref.h
+++ b/src/stim/stabilizers/pauli_string_ref.h
@@ -139,6 +139,8 @@ struct PauliStringRef {
     PauliString<W> before(const CircuitInstruction &operation) const;
 
     size_t weight() const;
+    bool has_no_pauli_terms() const;
+    bool intersects(PauliStringRef<W> other) const;
 
    private:
     void check_avoids_MPP(const CircuitInstruction &inst);
diff --git a/src/stim/stabilizers/pauli_string_ref.inl b/src/stim/stabilizers/pauli_string_ref.inl
index c91794f57..6c1b743d9 100644
--- a/src/stim/stabilizers/pauli_string_ref.inl
+++ b/src/stim/stabilizers/pauli_string_ref.inl
@@ -651,6 +651,16 @@ void PauliStringRef<W>::scatter_into(PauliStringRef<W> out, SpanRef<const size_t
     out.sign ^= sign;
 }
 
+template <size_t W>
+bool PauliStringRef<W>::intersects(const PauliStringRef<W> other) const {
+    size_t n = std::min(xs.num_u64_padded(), other.xs.num_u64_padded());
+    uint64_t v = 0;
+    for (size_t k = 0; k < n; k++) {
+        v |= (xs.u64[k] | zs.u64[k]) & (other.xs.u64[k] | other.zs.u64[k]);
+    }
+    return v != 0;
+}
+
 template <size_t W>
 size_t PauliStringRef<W>::weight() const {
     size_t total = 0;
@@ -660,6 +670,16 @@ size_t PauliStringRef<W>::weight() const {
     return total;
 }
 
+template <size_t W>
+bool PauliStringRef<W>::has_no_pauli_terms() const {
+    size_t total = 0;
+    size_t n = xs.num_u64_padded();
+    for (size_t k = 0; k < n; k++) {
+        total |= xs.u64[k] | zs.u64[k];
+    }
+    return total == 0;
+}
+
 template <size_t W>
 std::ostream &operator<<(std::ostream &out, const PauliStringRef<W> &ps) {
     out << "+-"[ps.sign];
diff --git a/src/stim/stabilizers/pauli_string_ref.test.cc b/src/stim/stabilizers/pauli_string_ref.test.cc
index e730c82f8..35fdd091d 100644
--- a/src/stim/stabilizers/pauli_string_ref.test.cc
+++ b/src/stim/stabilizers/pauli_string_ref.test.cc
@@ -76,3 +76,80 @@ TEST_EACH_WORD_SIZE_W(pauli_string, do_instruction_agrees_with_tableau_sim, {
         }
     }
 })
+
+TEST_EACH_WORD_SIZE_W(pauli_string, intersects, {
+    ASSERT_FALSE((PauliString<W>("_").ref().intersects(PauliString<W>("_"))));
+    ASSERT_FALSE((PauliString<W>("_").ref().intersects(PauliString<W>("X"))));
+    ASSERT_FALSE((PauliString<W>("_").ref().intersects(PauliString<W>("Y"))));
+    ASSERT_FALSE((PauliString<W>("_").ref().intersects(PauliString<W>("Z"))));
+    ASSERT_FALSE((PauliString<W>("X").ref().intersects(PauliString<W>("_"))));
+    ASSERT_TRUE((PauliString<W>("X").ref().intersects(PauliString<W>("X"))));
+    ASSERT_TRUE((PauliString<W>("X").ref().intersects(PauliString<W>("Y"))));
+    ASSERT_TRUE((PauliString<W>("X").ref().intersects(PauliString<W>("Z"))));
+    ASSERT_FALSE((PauliString<W>("Y").ref().intersects(PauliString<W>("_"))));
+    ASSERT_TRUE((PauliString<W>("Y").ref().intersects(PauliString<W>("X"))));
+    ASSERT_TRUE((PauliString<W>("Y").ref().intersects(PauliString<W>("Y"))));
+    ASSERT_TRUE((PauliString<W>("Y").ref().intersects(PauliString<W>("Z"))));
+    ASSERT_FALSE((PauliString<W>("Z").ref().intersects(PauliString<W>("_"))));
+    ASSERT_TRUE((PauliString<W>("Z").ref().intersects(PauliString<W>("X"))));
+    ASSERT_TRUE((PauliString<W>("Z").ref().intersects(PauliString<W>("Y"))));
+    ASSERT_TRUE((PauliString<W>("Z").ref().intersects(PauliString<W>("Z"))));
+
+    ASSERT_TRUE((PauliString<W>("_Z").ref().intersects(PauliString<W>("ZZ"))));
+    ASSERT_TRUE((PauliString<W>("Z_").ref().intersects(PauliString<W>("ZZ"))));
+    ASSERT_TRUE((PauliString<W>("ZZ").ref().intersects(PauliString<W>("ZZ"))));
+    ASSERT_FALSE((PauliString<W>("ZZ").ref().intersects(PauliString<W>("__"))));
+    ASSERT_FALSE((PauliString<W>("__").ref().intersects(PauliString<W>("XZ"))));
+    ASSERT_FALSE((PauliString<W>("________________________________________________")
+                      .ref()
+                      .intersects(PauliString<W>("________________________________________________"))));
+    ASSERT_TRUE((PauliString<W>("_______________________________________X________")
+                     .ref()
+                     .intersects(PauliString<W>("_______________________________________X________"))));
+})
+
+TEST_EACH_WORD_SIZE_W(pauli_string, weight, {
+    ASSERT_EQ(PauliString<W>::from_str("+").ref().weight(), 0);
+    ASSERT_EQ(PauliString<W>::from_str("+I").ref().weight(), 0);
+    ASSERT_EQ(PauliString<W>::from_str("+X").ref().weight(), 1);
+    ASSERT_EQ(PauliString<W>::from_str("+Y").ref().weight(), 1);
+    ASSERT_EQ(PauliString<W>::from_str("+Z").ref().weight(), 1);
+
+    ASSERT_EQ(PauliString<W>::from_str("+IX").ref().weight(), 1);
+    ASSERT_EQ(PauliString<W>::from_str("+XZ").ref().weight(), 2);
+    ASSERT_EQ(PauliString<W>::from_str("+YY").ref().weight(), 2);
+    ASSERT_EQ(PauliString<W>::from_str("+XI").ref().weight(), 1);
+
+    PauliString<W> p(1000);
+    ASSERT_EQ(p.ref().weight(), 0);
+    for (size_t k = 0; k < 1000; k++) {
+        p.xs[k] = k % 3 == 1;
+        p.zs[k] = k % 5 == 1;
+    }
+    ASSERT_EQ(p.ref().weight(), 333 + 199 - 66);
+    p.sign = true;
+    ASSERT_EQ(p.ref().weight(), 333 + 199 - 66);
+})
+
+TEST_EACH_WORD_SIZE_W(pauli_string, has_no_pauli_terms, {
+    ASSERT_EQ((PauliString<W>::from_str("+").ref().has_no_pauli_terms()), true);
+    ASSERT_EQ((PauliString<W>::from_str("+I").ref().has_no_pauli_terms()), true);
+    ASSERT_EQ((PauliString<W>::from_str("+X").ref().has_no_pauli_terms()), false);
+    ASSERT_EQ((PauliString<W>::from_str("+Y").ref().has_no_pauli_terms()), false);
+    ASSERT_EQ((PauliString<W>::from_str("+Z").ref().has_no_pauli_terms()), false);
+
+    ASSERT_EQ((PauliString<W>::from_str("+II").ref().has_no_pauli_terms()), true);
+    ASSERT_EQ((PauliString<W>::from_str("+IX").ref().has_no_pauli_terms()), false);
+    ASSERT_EQ((PauliString<W>::from_str("+XZ").ref().has_no_pauli_terms()), false);
+    ASSERT_EQ((PauliString<W>::from_str("+YY").ref().has_no_pauli_terms()), false);
+    ASSERT_EQ((PauliString<W>::from_str("+XI").ref().has_no_pauli_terms()), false);
+
+    PauliString<W> p(1000);
+    ASSERT_TRUE(p.ref().has_no_pauli_terms());
+    p.xs[700] = true;
+    ASSERT_FALSE(p.ref().has_no_pauli_terms());
+    p.zs[700] = true;
+    ASSERT_FALSE(p.ref().has_no_pauli_terms());
+    p.xs[700] = false;
+    ASSERT_FALSE(p.ref().has_no_pauli_terms());
+})