Fix interleaved feedback being removed incorrectly (#731)

- When a pure-feedback instruction was between two instructions of the
same type, they were fused when partially reversed when the feedback
instruction was removed
- Fixed by turning off fusion while the circuit is only partially
reversed
- Fixes #730

src/stim/circuit/circuit.cc

@@ -404,8 +404,8 @@ void Circuit::append_from_text(const char *text) {
         READ_CONDITION::READ_UNTIL_END_OF_FILE);
 }
 
-void Circuit::safe_append(const CircuitInstruction &operation) {
-    safe_append(operation.gate_type, operation.targets, operation.args);
+void Circuit::safe_append(const CircuitInstruction &operation, bool block_fusion) {
+    safe_append(operation.gate_type, operation.targets, operation.args, block_fusion);
 }
 
 void Circuit::safe_append_ua(const std::string &gate_name, const std::vector<uint32_t> &targets, double singleton_arg) {
@@ -433,7 +433,7 @@ void Circuit::safe_append_u(
     safe_append(gate.id, converted, args);
 }
 
-void Circuit::safe_append(GateType gate_type, SpanRef<const GateTarget> targets, SpanRef<const double> args) {
+void Circuit::safe_append(GateType gate_type, SpanRef<const GateTarget> targets, SpanRef<const double> args, bool block_fusion) {
     auto flags = GATE_DATA[gate_type].flags;
     if (flags & GATE_IS_BLOCK) {
         throw std::invalid_argument("Can't append a block like a normal operation.");
@@ -446,7 +446,7 @@ void Circuit::safe_append(GateType gate_type, SpanRef<const GateTarget> targets,
     to_add.args = arg_buf.take_copy(to_add.args);
     to_add.targets = target_buf.take_copy(to_add.targets);
 
-    if (!operations.empty() && operations.back().can_fuse(to_add)) {
+    if (!block_fusion && !operations.empty() && operations.back().can_fuse(to_add)) {
         // Extend targets of last gate.
         fuse_data(operations.back().targets, to_add.targets, target_buf);
     } else {

src/stim/circuit/circuit.h

@@ -105,14 +105,14 @@ struct Circuit {
     Circuit &operator*=(uint64_t repetitions);
 
     /// Safely adds an operation at the end of the circuit, copying its data into the circuit's jagged data as needed.
-    void safe_append(const CircuitInstruction &operation);
+    void safe_append(const CircuitInstruction &operation, bool block_fusion = false);
     /// Safely adds an operation at the end of the circuit, copying its data into the circuit's jagged data as needed.
     void safe_append_ua(const std::string &gate_name, const std::vector<uint32_t> &targets, double singleton_arg);
     /// Safely adds an operation at the end of the circuit, copying its data into the circuit's jagged data as needed.
     void safe_append_u(
         const std::string &gate_name, const std::vector<uint32_t> &targets, const std::vector<double> &args = {});
     /// Safely adds an operation at the end of the circuit, copying its data into the circuit's jagged data as needed.
-    void safe_append(GateType gate_type, SpanRef<const GateTarget> targets, SpanRef<const double> args);
+    void safe_append(GateType gate_type, SpanRef<const GateTarget> targets, SpanRef<const double> args, bool block_fusion = false);
     /// Safely copies a repeat block to the end of the circuit.
     void append_repeat_block(uint64_t repeat_count, const Circuit &body);
     /// Safely moves a repeat block to the end of the circuit.

src/stim/simulators/transform_without_feedback.cc

@@ -127,7 +127,7 @@ struct WithoutFeedbackHelper {
         if (GATE_DATA[op.gate_type].flags & GATE_CAN_TARGET_BITS) {
             undo_feedback_capable_pcp_operation(op);
         } else {
-            reversed_semi_flattened_output.safe_append(op);
+            reversed_semi_flattened_output.safe_append(op, true);
             tracker.undo_gate(op);
         }
     }

src/stim/simulators/transform_without_feedback.test.cc

@@ -144,3 +144,33 @@ TEST(circuit_with_inlined_feedback, mpp) {
         DETECTOR rec[-3] rec[-1]
     )CIRCUIT"));
 }
+
+TEST(circuit_with_inlined_feedback, interleaved_feedback_does_not_reorder_operations) {
+    ASSERT_EQ(circuit_with_inlined_feedback(Circuit(R"CIRCUIT(
+        H 0
+        CZ
+        H 1
+    )CIRCUIT")), Circuit(R"CIRCUIT(
+        H 0 1
+    )CIRCUIT"));
+
+    ASSERT_EQ(circuit_with_inlined_feedback(Circuit(R"CIRCUIT(
+        M 0
+        CX
+        M 1
+    )CIRCUIT")), Circuit(R"CIRCUIT(
+        M 0 1
+    )CIRCUIT"));
+
+    ASSERT_EQ(circuit_with_inlined_feedback(Circuit(R"CIRCUIT(
+        M 0 1
+        CX
+        M 2
+        CX rec[-1] 3
+        M 3
+        DETECTOR rec[-1]
+    )CIRCUIT")), Circuit(R"CIRCUIT(
+        M 0 1 2 3
+        DETECTOR rec[-2] rec[-1]
+    )CIRCUIT"));
+}