State Preparation in MQT ✨

include/mqt-core/algorithms/StatePreparation.hpp

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+/*
+ * Copyright (c) 2025 Chair for Design Automation, TUM
+ * All rights reserved.
+ *
+ * SPDX-License-Identifier: MIT
+ *
+ * Licensed under the MIT License
+ */
+
+#pragma once
+
+#include "ir/QuantumComputation.hpp"
+
+#include <complex>
+#include <vector>
+
+namespace qc {
+/**
+ * Prepares a generic Quantum State from a list of normalized complex
+ amplitudes
+ * Adapted implementation of Qiskit State Preparation:
+ *
+ https://github.com/Qiskit/qiskit/blob/main/qiskit/circuit/library/data_preparation/state_preparation.py#
+ * based on paper:
+ *      Shende, Bullock, Markov. Synthesis of Quantum Logic Circuits (2004)
+        [`https://ieeexplore.ieee.org/document/1629135`]
+ * */
+
+/**
+ * @throws invalid_argument when amplitudes are not normalized or length not
+ * power of 2
+ * @param list of complex amplitudes to initialize to
+ * @return MQT Circuit that initializes a state
+ * */
+[[nodiscard]] auto
+createStatePreparationCircuit(std::vector<std::complex<double>>& amplitudes)
+    -> QuantumComputation;
+} // namespace qc

src/algorithms/StatePreparation.cpp

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+/*
+ * Copyright (c) 2025 Chair for Design Automation, TUM
+ * All rights reserved.
+ *
+ * SPDX-License-Identifier: MIT
+ *
+ * Licensed under the MIT License
+ */
+
+#include "algorithms/StatePreparation.hpp"
+
+#include "Definitions.hpp"
+#include "circuit_optimizer/CircuitOptimizer.hpp"
+#include "ir/QuantumComputation.hpp"
+#include "ir/operations/OpType.hpp"
+#include "ir/operations/Operation.hpp"
+#include "ir/operations/StandardOperation.hpp"
+
+#include <algorithm>
+#include <cmath>
+#include <complex>
+#include <cstddef>
+#include <cstdint>
+#include <iterator>
+#include <numeric>
+#include <tuple>
+#include <vector>
+
+static const double EPS = 1e-10;
+
+namespace qc {
+using Matrix = std::vector<std::vector<double>>;
+
+template <typename T> [[nodiscard]] auto twoNorm(std::vector<T> vec) -> double {
+  double norm = 0;
+  for (auto elem : vec) {
+    norm += std::norm(elem);
+  }
+  return sqrt(norm);
+}
+
+template <typename T>
+[[nodiscard]] auto isNormalized(std::vector<T> vec) -> bool {
+  return std::abs(1 - twoNorm(vec)) < EPS;
+}
+
+[[nodiscard]] auto kroneckerProduct(Matrix matrixA, Matrix matrixB) -> Matrix {
+  size_t const rowA = matrixA.size();
+  size_t const rowB = matrixB.size();
+  size_t const colA = matrixA[0].size();
+  size_t const colB = matrixB[0].size();
+  // initialize size
+  Matrix newMatrix{(rowA * rowB), std::vector<double>(colA * colB, 0)};
+  // code taken from RosettaCode slightly adapted
+  for (size_t i = 0; i < rowA; ++i) {
+    // k loops till rowB
+    for (size_t j = 0; j < colA; ++j) {
+      // j loops till colA
+      for (size_t k = 0; k < rowB; ++k) {
+        // l loops till colB
+        for (size_t l = 0; l < colB; ++l) {
+          // Each element of matrix A is
+          // multiplied by whole Matrix B
+          // resp and stored as Matrix C
+          newMatrix[i * rowB + k][j * colB + l] = matrixA[i][j] * matrixB[k][l];
+        }
+      }
+    }
+  }
+  return newMatrix;
+}
+
+[[nodiscard]] auto createIdentity(size_t size) -> Matrix {
+  Matrix identity{
+      std::vector<std::vector<double>>(size, std::vector<double>(size, 0))};
+  for (size_t i = 0; i < size; ++i) {
+    identity[i][i] = 1;
+  }
+  return identity;
+}
+
+[[nodiscard]] auto matrixVectorProd(const Matrix& matrix,
+                                    std::vector<double> vector)
+    -> std::vector<double> {
+  std::vector<double> result;
+  for (const auto& matrixVec : matrix) {
+    double sum{0};
+    for (size_t i = 0; i < matrixVec.size(); ++i) {
+      sum += matrixVec[i] * vector[i];
+    }
+    result.push_back(sum);
+  }
+  return result;
+}
+
+// recursive implementation that returns multiplexer circuit
+/**
+ * @param target_gate : Ry or Rz gate to apply to target qubit, multiplexed
+ * over all other "select" qubits
+ * @param angles : list of rotation angles to apply Ry and Rz
+ * @param lastCnot : add last cnot if true
+ * @return multiplexer circuit as QuantumComputation
+ */
+[[nodiscard]] auto multiplex(OpType targetGate, std::vector<double> angles,
+                             bool lastCnot) -> QuantumComputation {
+  size_t const listLen = angles.size();
+  double const localNumQubits =
+      std::floor(std::log2(static_cast<double>(listLen))) + 1;
+  QuantumComputation multiplexer{static_cast<size_t>(localNumQubits)};
+  // recursion base case
+  if (localNumQubits == 1) {
+    multiplexer.emplace_back<StandardOperation>(Controls{}, 0, targetGate,
+                                                std::vector{angles[0]});
+    return multiplexer;
+  }
+
+  Matrix const matrix{std::vector<double>{0.5, 0.5},
+                      std::vector<double>{0.5, -0.5}};
+  Matrix const identity =
+      createIdentity(static_cast<size_t>(pow(2., localNumQubits - 2.)));
+  Matrix const angleWeights = kroneckerProduct(matrix, identity);
+
+  angles = matrixVectorProd(angleWeights, angles);
+
+  std::vector<double> const angles1{
+      std::make_move_iterator(angles.begin()),
+      std::make_move_iterator(angles.begin() +
+                              static_cast<int64_t>(listLen) / 2)};
+  QuantumComputation multiplex1 = multiplex(targetGate, angles1, false);
+
+  // append multiplex1 to multiplexer
+  multiplexer.emplace_back<Operation>(multiplex1.asOperation());
+  // flips the LSB qubit, control on MSB
+  multiplexer.cx(0, static_cast<Qubit>(localNumQubits - 1));
+
+  std::vector<double> const angles2{std::make_move_iterator(angles.begin()) +
+                                        static_cast<int64_t>(listLen) / 2,
+                                    std::make_move_iterator(angles.end())};
+  QuantumComputation multiplex2 = multiplex(targetGate, angles2, false);
+
+  // extra efficiency by reversing (!= inverting) second multiplex
+  if (listLen > 1) {
+    multiplex2.reverse();
+    multiplexer.emplace_back<Operation>(multiplex2.asOperation());
+  } else {
+    multiplexer.emplace_back<Operation>(multiplex2.asOperation());
+  }
+
+  if (lastCnot) {
+    multiplexer.cx(0, static_cast<Qubit>(localNumQubits - 1));
+  }
+
+  CircuitOptimizer::flattenOperations(multiplexer);
+  return multiplexer;
+}
+
+[[nodiscard]] auto blochAngles(std::complex<double> const complexA,
+                               std::complex<double> const complexB)
+    -> std::tuple<std::complex<double>, double, double> {
+  double theta{0};
+  double phi{0};
+  double finalT{0};
+  double const magA = std::abs(complexA);
+  double const magB = std::abs(complexB);
+  double const finalR = sqrt(pow(magA, 2) + pow(magB, 2));
+  if (finalR > EPS) {
+    theta = 2 * acos(magA / finalR);
+    double const aAngle = std::arg(complexA);
+    double const bAngle = std::arg(complexB);
+    finalT = aAngle + bAngle;
+    phi = bAngle - aAngle;
+  }
+  return {finalR * exp(std::complex<double>{0, 1} * finalT / 2.), theta, phi};
+}
+
+// works out Ry and Rz rotation angles used to disentangle LSB qubit
+// rotations make up block diagonal matrix U
+[[nodiscard]] auto
+rotationsToDisentangle(std::vector<std::complex<double>> amplitudes)
+    -> std::tuple<std::vector<std::complex<double>>, std::vector<double>,
+                  std::vector<double>> {
+  std::vector<std::complex<double>> remainingVector;
+  std::vector<double> thetas;
+  std::vector<double> phis;
+  for (size_t i = 0; i < (amplitudes.size() / 2); ++i) {
+    auto [remains, theta, phi] =
+        blochAngles(amplitudes[2 * i], amplitudes[2 * i + 1]);
+    remainingVector.push_back(remains);
+    // minus sign because we move it to zero
+    thetas.push_back(-theta);
+    phis.push_back(-phi);
+  }
+  return {remainingVector, thetas, phis};
+}
+
+// creates circuit that takes desired vector to zero
+[[nodiscard]] auto
+gatesToUncompute(std::vector<std::complex<double>> amplitudes, size_t numQubits)
+    -> QuantumComputation {
+  QuantumComputation disentangler{numQubits};
+  for (size_t i = 0; i < numQubits; ++i) {
+    // rotations to disentangle LSB
+    auto [remainingParams, thetas, phis] = rotationsToDisentangle(amplitudes);
+    amplitudes = remainingParams;
+    // perform required rotations
+    bool addLastCnot = true;
+    double const phisNorm = twoNorm(phis);
+    double const thetasNorm = twoNorm(thetas);
+    if (phisNorm != 0 && thetasNorm != 0) {
+      addLastCnot = false;
+    }
+    if (phisNorm != 0) {
+      // call multiplex with RZGate
+      QuantumComputation rzMultiplexer =
+          multiplex(OpType{RZ}, phis, addLastCnot);
+      // append rzMultiplexer to disentangler, but it should only attach on
+      // qubits i-numQubits, thus "i" is added to the local qubit indices
+      for (auto& op : rzMultiplexer) {
+        for (auto& target : op->getTargets()) {
+          target += static_cast<unsigned int>(i);
+        }
+        for (auto control : op->getControls()) {
+          // there were some errors when accessing the qubit directly and
+          // adding to it
+          op->setControls(
+              Controls{Control{control.qubit + static_cast<unsigned int>(i)}});
+        }
+      }
+      disentangler.emplace_back<Operation>(rzMultiplexer.asOperation());
+    }
+    if (thetasNorm != 0) {
+      // call multiplex with RYGate
+      QuantumComputation ryMultiplexer =
+          multiplex(OpType{RY}, thetas, addLastCnot);
+      // append reversed ry_multiplexer to disentangler, but it should only
+      // attach on qubits i-numQubits, thus "i" is added to the local qubit
+      // indices
+      std::reverse(ryMultiplexer.begin(), ryMultiplexer.end());
+      for (auto& op : ryMultiplexer) {
+        for (auto& target : op->getTargets()) {
+          target += static_cast<unsigned int>(i);
+        }
+        for (auto control : op->getControls()) {
+          // there were some errors when accessing the qubit directly and
+          // adding to it
+          op->setControls(
+              Controls{Control{control.qubit + static_cast<unsigned int>(i)}});
+        }
+      }
+      disentangler.emplace_back<Operation>(ryMultiplexer.asOperation());
+    }
+  }
+  // adjust global phase according to the last e^(it)
+  double const arg = -std::arg(std::accumulate(
+      amplitudes.begin(), amplitudes.end(), std::complex<double>(0, 0)));
+  if (arg != 0) {
+    disentangler.gphase(arg);
+  }
+  return disentangler;
+}
+
+auto createStatePreparationCircuit(
+    std::vector<std::complex<double>>& amplitudes) -> QuantumComputation {
+
+  if (!isNormalized(amplitudes)) {
+    throw std::invalid_argument{
+        "Using State Preparation with Amplitudes that are not normalized"};
+  }
+
+  // get number of qubits needed
+  double const numQubits = std::log2(amplitudes.size());
+
+  if (numQubits == 0 || std::floor(numQubits) != numQubits) {
+    throw std::invalid_argument{
+        "Using State Preparation with vector size that is not a power of 2"};
+  }
+
+  QuantumComputation toZeroCircuit =
+      gatesToUncompute(amplitudes, static_cast<size_t>(numQubits));
+
+  // invert circuit
+  CircuitOptimizer::flattenOperations(toZeroCircuit);
+  toZeroCircuit.invert();
+
+  return toZeroCircuit;
+}
+} // namespace qc