----------------------------------------------- Sampling the Matrix Product State (QFT Circuit) ----------------------------------------------- The following code example illustrates how to define a tensor network state for a given quantum circuit (QFT), then compute its Matrix Product State (MPS) factorization, and, finally, sample the MPS-factorized state. The full code can be found in the `NVIDIA/cuQuantum `_ repository (`here `_). -------------------------- Headers and error handling -------------------------- .. literalinclude:: ../../../../tensor_network/samples/high_level/qft_mps_sampling_example.cu :language: c++ :linenos: :lineno-match: :start-after: Sphinx: QFT MPS Sampler #1 :end-before: Sphinx: QFT MPS Sampler #2 ------------------------------------------------------------------------------------ Define the tensor network state and the desired number of output samples to generate ------------------------------------------------------------------------------------ Let's define a tensor network state for a quantum circuit with the given number of qubits and request to produce a given number of output samples for the full qubit register. .. literalinclude:: ../../../../tensor_network/samples/high_level/qft_mps_sampling_example.cu :language: c++ :linenos: :lineno-match: :start-after: Sphinx: QFT MPS Sampler #2 :end-before: Sphinx: QFT MPS Sampler #3 ----------------------------------------- Initialize the cuTensorNet library handle ----------------------------------------- .. literalinclude:: ../../../../tensor_network/samples/high_level/qft_mps_sampling_example.cu :language: c++ :linenos: :lineno-match: :start-after: Sphinx: QFT MPS Sampler #3 :end-before: Sphinx: QFT MPS Sampler #4 ---------------------------------- Define quantum gates in GPU memory ---------------------------------- .. literalinclude:: ../../../../tensor_network/samples/high_level/qft_mps_sampling_example.cu :language: c++ :linenos: :lineno-match: :start-after: Sphinx: QFT MPS Sampler #4 :end-before: Sphinx: QFT MPS Sampler #5 ---------------------------------- Allocate MPS tensors in GPU memory ---------------------------------- Here we set the shapes of MPS tensors and allocate GPU memory for their storage. .. literalinclude:: ../../../../tensor_network/samples/high_level/qft_mps_sampling_example.cu :language: c++ :linenos: :lineno-match: :start-after: Sphinx: QFT MPS Sampler #5 :end-before: Sphinx: QFT MPS Sampler #6 ---------------------------------- Allocate the scratch buffer on GPU ---------------------------------- .. literalinclude:: ../../../../tensor_network/samples/high_level/qft_mps_sampling_example.cu :language: c++ :linenos: :lineno-match: :start-after: Sphinx: QFT MPS Sampler #6 :end-before: Sphinx: QFT MPS Sampler #7 ---------------------------------- Create a pure tensor network state ---------------------------------- Now let's create a pure tensor network state for a quantum circuit with the given number of qubits. .. literalinclude:: ../../../../tensor_network/samples/high_level/qft_mps_sampling_example.cu :language: c++ :linenos: :lineno-match: :start-after: Sphinx: QFT MPS Sampler #7 :end-before: Sphinx: QFT MPS Sampler #8 ------------------- Apply quantum gates ------------------- Let's construct the QFT quantum circuit with no bit reversal by applying the corresponding quantum gates. .. literalinclude:: ../../../../tensor_network/samples/high_level/qft_mps_sampling_example.cu :language: c++ :linenos: :lineno-match: :start-after: Sphinx: QFT MPS Sampler #8 :end-before: Sphinx: QFT MPS Sampler #9 ------------------------------------------------------------- Request MPS factorization for the final quantum circuit state ------------------------------------------------------------- Here we express our intent to factorize the final quantum circuit state using MPS factorization. The provided shapes (mode extents) of the MPS tensors refer to their maximal size limit during the MPS renormalization procedure. The actually computed shapes (mode extents) of the final MPS tensors may be smaller than their limits. Note that no computation is done here yet. .. literalinclude:: ../../../../tensor_network/samples/high_level/qft_mps_sampling_example.cu :language: c++ :linenos: :lineno-match: :start-after: Sphinx: QFT MPS Sampler #9 :end-before: Sphinx: QFT MPS Sampler #10 ------------------------------------- Configure MPS factorization procedure ------------------------------------- After expressing our intent to perform MPS factorization of the final quantum circuit state, we can also configure the MPS factorization procedure by resetting different options, for example, the SVD algorithm. .. literalinclude:: ../../../../tensor_network/samples/high_level/qft_mps_sampling_example.cu :language: c++ :linenos: :lineno-match: :start-after: Sphinx: QFT MPS Sampler #10 :end-before: Sphinx: QFT MPS Sampler #11 -------------------------------------------- Prepare the computation of MPS factorization -------------------------------------------- Let's create a workspace descriptor and prepare the computation of the MPS factorization of the final quantum circuit state. .. literalinclude:: ../../../../tensor_network/samples/high_level/qft_mps_sampling_example.cu :language: c++ :linenos: :lineno-match: :start-after: Sphinx: QFT MPS Sampler #11 :end-before: Sphinx: QFT MPS Sampler #12 ------------------------- Compute MPS factorization ------------------------- Once the MPS factorization procedure has been configured and prepared, let's compute the MPS factorization of the final quantum circuit state. .. literalinclude:: ../../../../tensor_network/samples/high_level/qft_mps_sampling_example.cu :language: c++ :linenos: :lineno-match: :start-after: Sphinx: QFT MPS Sampler #12 :end-before: Sphinx: QFT MPS Sampler #13 --------------------------------------- Create the tensor network state sampler --------------------------------------- Once the quantum circuit state has been constructed and factorized using the MPS representation, let's create the tensor network state sampler for the full qubit register (all qubits). .. literalinclude:: ../../../../tensor_network/samples/high_level/qft_mps_sampling_example.cu :language: c++ :linenos: :lineno-match: :start-after: Sphinx: QFT MPS Sampler #13 :end-before: Sphinx: QFT MPS Sampler #14 ------------------------------------------ Configure the tensor network state sampler ------------------------------------------ Optionally, we can configure the tensor network state sampler by setting the number of hyper-samples to be used by the tensor network contraction path finder. .. literalinclude:: ../../../../tensor_network/samples/high_level/qft_mps_sampling_example.cu :language: c++ :linenos: :lineno-match: :start-after: Sphinx: QFT MPS Sampler #14 :end-before: Sphinx: QFT MPS Sampler #15 ---------------------------------------- Prepare the tensor network state sampler ---------------------------------------- Now let's prepare the tensor network state sampler. .. literalinclude:: ../../../../tensor_network/samples/high_level/qft_mps_sampling_example.cu :language: c++ :linenos: :lineno-match: :start-after: Sphinx: QFT MPS Sampler #15 :end-before: Sphinx: QFT MPS Sampler #16 -------------------- Set up the workspace -------------------- Now we can set up the required workspace buffer. .. literalinclude:: ../../../../tensor_network/samples/high_level/qft_mps_sampling_example.cu :language: c++ :linenos: :lineno-match: :start-after: Sphinx: QFT MPS Sampler #16 :end-before: Sphinx: QFT MPS Sampler #17 --------------------------------------------------- Perform sampling of the final quantum circuit state --------------------------------------------------- Once everything had been set up, we perform sampling of the quantum circuit state and print the output samples. .. literalinclude:: ../../../../tensor_network/samples/high_level/qft_mps_sampling_example.cu :language: c++ :linenos: :lineno-match: :start-after: Sphinx: QFT MPS Sampler #17 :end-before: Sphinx: QFT MPS Sampler #18 -------------- Free resources -------------- .. literalinclude:: ../../../../tensor_network/samples/high_level/qft_mps_sampling_example.cu :language: c++ :linenos: :lineno-match: :start-after: Sphinx: QFT MPS Sampler #18