Fix --loopsum for amplitudes with an imaginary part (#22)

src/loop_summarization.cc

@@ -239,7 +239,11 @@ Symbol eval_symbol( const AUTOQ::Symbol::Symbolic& symbol,
             for(auto& [term, complex] : sym.complex){
                 for(auto& [string, cppint] : term){
                     if(string.back() == 'I'){
-                        mapping[term] = conc.complex.imag();
+                        // A variable v is encoded as vR + i·vI, so vI must be
+                        // bound to the real number Im(x). imag() returns
+                        // i·Im(x); rotating it by a quarter turn clockwise
+                        // (multiplying by -i) gives Im(x).
+                        mapping[term] = conc.complex.imag().clockwise(boost::rational<boost::multiprecision::cpp_int>(1, 4));
                     }
                     else if(string.back() == 'R'){
                         mapping[term] = conc.complex.real();

unit_tests/explicit_tree_aut_test.cc

@@ -13,6 +13,7 @@
 #include <filesystem>
 #include <fstream>
 #include <functional>
+#include <sstream>
 
 #include "autoq/error.hh"
 #include "autoq/inclusion.hh"
@@ -290,6 +291,39 @@ BOOST_AUTO_TEST_CASE(for_loop_summarization){
     BOOST_REQUIRE_MESSAGE(verify, folder + " failed!");
 }
 
+// Runs the circuit on the precondition and returns the printed set of states.
+static std::string execute_and_print(const std::string& pre, const std::string& circuit, const std::string& loop) {
+    auto [autVec, qp] = AUTOQ::Parsing::TimbukParser<AUTOQ::Symbol::Concrete>::ReadTwoAutomata(pre, pre, circuit);
+    auto aut = autVec.at(0);
+    autVec.erase(autVec.begin(), autVec.begin() + 2);
+    ParameterMap params;
+    params["loop"] = loop;
+    aut.execute(circuit, qp, autVec, params);
+    std::ostringstream out;
+    auto* old = std::cout.rdbuf(out.rdbuf());
+    aut.print_language();
+    std::cout.rdbuf(old);
+    return out.str();
+}
+
+// Loop summarization must give exactly the states that unrolling gives, also
+// when an iteration receives an amplitude with a nonzero imaginary part (#22).
+BOOST_AUTO_TEST_CASE(for_loop_summarization_complex_amplitudes){
+    std::string folder = test_dir_from_file(__FILE__, "testcase/ForLoopComplex/");
+    const std::vector<std::pair<std::string, std::string>> cases = {
+        {"complex_pre.hsl", "h_once.qasm"},
+        {"zero_pre.hsl", "ht_three_times.qasm"},
+        {"one_pre.hsl", "s_twice.qasm"},
+        {"two_qubit_pre.hsl", "two_qubit.qasm"},
+    };
+    for (const auto& [pre, circuit] : cases) {
+        auto unrolled = execute_and_print(folder + pre, folder + circuit, "manual");
+        auto summarized = execute_and_print(folder + pre, folder + circuit, "symbolic");
+        BOOST_CHECK_MESSAGE(unrolled == summarized,
+            pre + " + " + circuit + ": unrolled " + unrolled + " but summarized " + summarized);
+    }
+}
+
 
 static void grover_oracle(AUTOQ::ConcreteAutomata& aut, unsigned ans, int n) {
     for (int i=1; i<=n; i++) {

unit_tests/testcase/ForLoopComplex/complex_pre.hsl

@@ -0,0 +1,2 @@
+Extended Dirac
+{1/sqrt2 |0> + ei2pi(1/4)/sqrt2 |1>}

unit_tests/testcase/ForLoopComplex/h_once.qasm

@@ -0,0 +1,7 @@
+OPENQASM 3;
+include "stdgates.inc";
+qubit[1] q;
+
+for int i in [1:1] {
+    h q[0];
+}

unit_tests/testcase/ForLoopComplex/ht_three_times.qasm

@@ -0,0 +1,8 @@
+OPENQASM 3;
+include "stdgates.inc";
+qubit[1] q;
+
+for int i in [1:3] {
+    h q[0];
+    t q[0];
+}

unit_tests/testcase/ForLoopComplex/one_pre.hsl

@@ -0,0 +1,2 @@
+Extended Dirac
+{|1>}

unit_tests/testcase/ForLoopComplex/s_twice.qasm

@@ -0,0 +1,7 @@
+OPENQASM 3;
+include "stdgates.inc";
+qubit[1] q;
+
+for int i in [1:2] {
+    s q[0];
+}

unit_tests/testcase/ForLoopComplex/two_qubit.qasm

@@ -0,0 +1,10 @@
+OPENQASM 3;
+include "stdgates.inc";
+qubit[2] q;
+
+for int i in [1:3] {
+    y q[0];
+    h q[1];
+    cz q[0], q[1];
+    tdg q[0];
+}

unit_tests/testcase/ForLoopComplex/two_qubit_pre.hsl

@@ -0,0 +1,2 @@
+Extended Dirac
+{1/sqrt2 |00> + ei2pi(1/8)/sqrt2 |11>}

unit_tests/testcase/ForLoopComplex/zero_pre.hsl

@@ -0,0 +1,2 @@
+Extended Dirac
+{|0>}