Work on QITE algorithm

Added basic algorithm flow/structure.
Signed-off-by: Thien Nguyen <nguyentm@ornl.gov>

quantum/plugins/algorithms/qite/CMakeLists.txt

@@ -21,9 +21,10 @@ add_library(${LIBRARY_NAME} SHARED ${SRC})
 
 target_include_directories(
   ${LIBRARY_NAME}
-  PUBLIC .)
+  PUBLIC .
+  ${CMAKE_SOURCE_DIR}/tpls/eigen)
 
-target_link_libraries(${LIBRARY_NAME} PUBLIC xacc CppMicroServices)
+target_link_libraries(${LIBRARY_NAME} PUBLIC xacc CppMicroServices xacc-quantum-gate)
 
 set(_bundle_name xacc_algorithm_qite)
 set_target_properties(${LIBRARY_NAME}

quantum/plugins/algorithms/qite/qite.cpp

@@ -14,9 +14,11 @@
 
 #include "Observable.hpp"
 #include "xacc.hpp"
-
+#include "xacc_service.hpp"
+#include "PauliOperator.hpp"
+#include "Circuit.hpp"
 #include <memory>
-#include <iomanip>
+#include <Eigen/Dense>
 
 using namespace xacc;
 
@@ -34,9 +36,86 @@ const std::vector<std::string> QITE::requiredParameters() const
   return {};
 }
 
+std::shared_ptr<CompositeInstruction> QITE::constructPropagateCircuit() const
+{
+  auto gateRegistry = xacc::getService<xacc::IRProvider>("quantum");
+  auto propagateKernel = gateRegistry->createComposite("statePropCircuit");
+
+  // Adds ansatz if provided
+  if (m_ansatz)
+  {
+    propagateKernel->addInstructions(m_ansatz->getInstructions());
+  } 
+
+  const auto pauliTermToString = [](const std::shared_ptr<xacc::Observable>& in_term){
+    std::string pauliTermStr = in_term->toString();
+    std::stringstream s;
+    s.precision(12);
+    s << std::fixed << in_term->coefficient();
+    // Find the parenthesis
+    const auto startPosition = pauliTermStr.find("(");
+    const auto endPosition = pauliTermStr.find(")");
+
+    if (startPosition != std::string::npos && endPosition != std::string::npos)
+    {
+      const auto length = endPosition - startPosition + 1;
+      pauliTermStr.replace(startPosition, length, s.str());
+    }
+    return pauliTermStr;
+  };
+
+  // Progagates by Trotter steps
+  // Using those A operators that have been 
+  // optimized up to this point.
+  for (const auto& aObs : m_approxOps)
+  {
+    // Circuit is: exp(-idt*A),
+    // i.e. regular evolution which approximates the imaginary time evolution.
+    for (const auto& term : aObs->getNonIdentitySubTerms())
+    {
+      const auto pauliStr = pauliTermToString(term);
+      auto expCirc = std::dynamic_pointer_cast<xacc::quantum::Circuit>(xacc::getService<Instruction>("exp_i_theta"));
+      expCirc->addVariable("theta");
+      expCirc->expand({ std::make_pair("pauli", term) });
+      auto evaled = expCirc->operator()({ m_dBeta });
+      propagateKernel->addInstructions(evaled->getInstructions());
+    }
+  }
+
+  return propagateKernel;
+}
+
+
 void QITE::execute(const std::shared_ptr<AcceleratorBuffer> buffer) const 
 {
-  // TODO
+  // Calculate approximate A operator observable at each time step.
+  const auto calcAOps = [&](std::shared_ptr<CompositeInstruction>) -> std::shared_ptr<Observable> {
+    // Step 1: Observe the kernels using the various Pauli
+    // operators to calculate S and b.
+    // TODO: this requires some Pauli algebra computation.
+    // Step 2: Calculate S matrix and b vector
+    // i.e. set up the linear equation Sa = b
+    // These are expectations on the current state.
+    // i.e. set-up the observables to calculate those entries.
+    // TODO: construct circuits and evaluate to get expectation values
+    // and populate S matrix and b vector.
+    Eigen::MatrixXf S_Mat;
+    Eigen::VectorXf b_Vec; 
+    
+    // const auto a_Vec = S_Mat.bdcSvd(ComputeThinU | ComputeThinV).solve(b_Vec);
+    // TODO: construct A observable from the coefficients in a_Vec
+    return nullptr; 
+  };
+  
+  // Time stepping:
+  for (int i = 0; i < m_nbSteps; ++i)
+  {
+    // Propagates the state via Trotter steps:
+    auto kernel = constructPropagateCircuit();
+    // Optimizes/calculates next A ops
+    auto nextAOps = calcAOps(kernel);
+    m_approxOps.emplace_back(nextAOps);
+  }
 }
 
 std::vector<double> QITE::execute(const std::shared_ptr<AcceleratorBuffer> buffer, const std::vector<double>& x) 

quantum/plugins/algorithms/qite/qite.hpp

@@ -27,6 +27,24 @@ public:
   const std::string name() const override { return "qite"; }
   const std::string description() const override { return ""; }
   DEFINE_ALGORITHM_CLONE(QITE)
+private:
+  // Construct the Trotter propagate circuit up to current time step.
+  std::shared_ptr<CompositeInstruction> constructPropagateCircuit() const;
+
+private:
+  // Number of Trotter steps
+  int m_nbSteps;
+  // dBeta, i.e. step size
+  double m_dBeta;
+  // Hamiltonian Observable, i.e. H = Sum(h_i)
+  Observable* m_observable;
+  // Ansatz circuit (apply before Trotter steps)
+  CompositeInstruction* m_ansatz;
+  // List of A operators for each time step
+  // which approximates the imaginary-time step 
+  // of the Hamiltonian observable
+  // i.e. exp(-iAt) -> exp(-Ht)
+  mutable std::vector<std::shared_ptr<Observable>> m_approxOps;
 };
 } // namespace algorithm
 } // namespace xacc