Add w state implementation (#391)

## Description

Implement WState from
[this](https://github.com/cda-tum/mqt-bench/blob/main/src/mqt/bench/benchmarks/wstate.py)
`mqt-bench` script in light of the DD benchmarking in [this
PR](tyi1025/dd_eval#12).

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Lukas Burgholzer <[email protected]>

include/algorithms/WState.hpp

@@ -0,0 +1,10 @@
+#pragma once
+
+#include <QuantumComputation.hpp>
+
+namespace qc {
+class WState : public QuantumComputation {
+public:
+  explicit WState(Qubit nq);
+};
+} // namespace qc

src/CMakeLists.txt

@@ -28,6 +28,7 @@ if(NOT TARGET ${PROJECT_NAME})
     ${PROJECT_SOURCE_DIR}/include/algorithms/QFT.hpp
     ${PROJECT_SOURCE_DIR}/include/algorithms/QPE.hpp
     ${PROJECT_SOURCE_DIR}/include/algorithms/RandomCliffordCircuit.hpp
+    ${PROJECT_SOURCE_DIR}/include/algorithms/WState.hpp
     ${PROJECT_SOURCE_DIR}/include/CircuitOptimizer.hpp
     ${PROJECT_SOURCE_DIR}/include/Definitions.hpp
     ${PROJECT_SOURCE_DIR}/include/operations/Expression.hpp
@@ -50,6 +51,7 @@ if(NOT TARGET ${PROJECT_NAME})
     algorithms/QFT.cpp
     algorithms/QPE.cpp
     algorithms/RandomCliffordCircuit.cpp
+    algorithms/WState.cpp
     CircuitOptimizer.cpp
     operations/Expression.cpp
     operations/NonUnitaryOperation.cpp

src/algorithms/WState.cpp

@@ -0,0 +1,25 @@
+#include "algorithms/WState.hpp"
+
+namespace qc {
+void fGate(QuantumComputation& qc, const Qubit i, const Qubit j, const Qubit k,
+           const Qubit n) {
+  const auto theta = std::acos(std::sqrt(1.0 / static_cast<double>(k - n + 1)));
+  qc.ry(j, -theta);
+  qc.z(j, qc::Control{i});
+  qc.ry(j, theta);
+}
+
+WState::WState(const Qubit nq) : QuantumComputation(nq) {
+  name = "wstate_" + std::to_string(nq);
+
+  x(nq - 1);
+
+  for (Qubit m = 1; m < nq; m++) {
+    fGate(*this, nq - m, nq - m - 1, nq, m);
+  }
+
+  for (Qubit k = nq - 1; k > 0; k--) {
+    x(k, qc::Control{k - 1});
+  }
+}
+} // namespace qc

test/CMakeLists.txt

@@ -25,7 +25,8 @@ package_add_test(
   algorithms/test_entanglement.cpp
   algorithms/test_grcs.cpp
   algorithms/test_random_clifford.cpp
-  algorithms/test_qpe.cpp)
+  algorithms/test_qpe.cpp
+  algorithms/test_wstate.cpp)
 
 package_add_test(
   ${PROJECT_NAME}-test-zx

test/algorithms/test_wstate.cpp

@@ -0,0 +1,42 @@
+#include "algorithms/WState.hpp"
+#include "dd/Simulation.hpp"
+
+#include "gtest/gtest.h"
+#include <iostream>
+#include <vector>
+
+class WState : public testing::TestWithParam<qc::Qubit> {};
+
+std::vector<std::string> generateWStateStrings(const std::size_t length) {
+  std::vector<std::string> result;
+  result.reserve(length);
+  for (std::size_t i = 0U; i < length; ++i) {
+    auto binaryString = std::string(length, '0');
+    binaryString[i] = '1';
+    result.emplace_back(binaryString);
+  }
+  return result;
+}
+
+INSTANTIATE_TEST_SUITE_P(
+    WState, WState, testing::Range<qc::Qubit>(1U, 128U, 7U),
+    [](const testing::TestParamInfo<WState::ParamType>& inf) {
+      // Generate names for test cases
+      const auto nqubits = inf.param;
+      std::stringstream ss{};
+      ss << nqubits << "_qubits";
+      return ss.str();
+    });
+
+TEST_P(WState, FunctionTest) {
+  const auto nq = GetParam();
+
+  auto qc = qc::WState(nq);
+  auto dd = std::make_unique<dd::Package<>>(qc.getNqubits());
+  const std::size_t shots = 1024;
+  const auto measurements =
+      simulate(&qc, dd->makeZeroState(qc.getNqubits()), dd, shots);
+  for (const auto& result : generateWStateStrings(nq)) {
+    EXPECT_TRUE(measurements.find(result) != measurements.end());
+  }
+}