Add Harrow-Hassidim-Lloyd (HHL) algorithm

README.md

@@ -33,6 +33,7 @@ Running notebooks locally requires additional dependencies located in [notebooks
 | Quantum PCA | [Quantum_Principal_Component_Analysis.ipynb](notebooks/advanced_algorithms/Quantum_Principal_Component_Analysis.ipynb) | [He2022](https://ieeexplore.ieee.org/document/9669030) |
 | QMC | [Quantum_Computing_Quantum_Monte_Carlo.ipynb](notebooks/advanced_algorithms/Quantum_Computing_Quantum_Monte_Carlo.ipynb) | [Motta2018](https://wires.onlinelibrary.wiley.com/doi/10.1002/wcms.1364), [Peruzzo2014](https://www.nature.com/articles/ncomms5213) |
 | Adaptive Shot Allocation | [2_Adaptive_Shot_Allocation.ipynb](notebooks/advanced_algorithms/adaptive_shot_allocation/2_Adaptive_Shot_Allocation.ipynb) | [Shlosberg2023](https://doi.org/10.22331/q-2023-01-26-906) |
+| HHL Algorithm | [HHL_Algorithm.ipynb](notebooks/advanced_algorithms/HHL_Algorithm.ipynb) | [Harrow2009](https://arxiv.org/abs/0811.3171) |
 
 
 | Auxiliary functions | Notebook |

setup.py

@@ -34,6 +34,7 @@
         "scipy>=1.5.2",
         # Sympy 1.13 produces different results for Simon's algorithm
         "sympy<1.13",
+        "qiskit-braket-provider",
     ],
     extras_require={
         "test": [

src/braket/experimental/algorithms/hhl/__init__.py

@@ -0,0 +1,5 @@
+from braket.experimental.algorithms.hhl.hhl import (  # noqa: F401,E501
+    get_hhl_results,
+    hhl_circuit,
+    run_hhl,
+)

src/braket/experimental/algorithms/hhl/hhl.md

@@ -0,0 +1,7 @@
+The Harrow-Hassidim-Lloyd (HHL) algorithm is a quantum algorithm for solving systems of linear equations of the form Ax = b. Given an N×N Hermitian matrix A and a unit vector b, the algorithm produces a quantum state |x⟩ whose amplitudes encode the solution vector x = A⁻¹b. For sparse, well-conditioned matrices, HHL runs in O(log(N) κ²) time versus O(Nκ) classically, where κ is the condition number of A. However, the overall speedup depends on the efficiency of state preparation and readout, which can be problem-dependent. Applications include machine learning, computational finance, solving differential equations, and quantum chemistry.
+
+<!-- 
+[metadata-name]: HHL Algorithm
+[metadata-tags]: Advanced
+[metadata-url]: https://github.com/amazon-braket/amazon-braket-algorithm-library/blob/main/src/braket/experimental/algorithms/hhl
+-->