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| ############################################################################## | ||
| # Here the :class:`~.pennylane.estimator.compact_hamiltonian.PauliHamiltonian` class is used to |
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I would like to know why this are the resources, something like: note that by default we decompose the target get_set [...]. There is probably another demo you can link for the basics of the resource estimation functionality
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| # Polynomial Approximations of the Inverse Function | ||
| # ------------------------------------------------- | ||
| # The cost of QSVT is directly proportional to the degree of the polynomial transformation. More |
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I'd recommend to link the matrix inversion demo for more details
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I think that could clarify a bit better the concept of kappa, right now it is not very clear
| # | ||
| # Diagonal Matrices & the Walsh-Hadamard Transform | ||
| # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ | ||
| # Let's start with the :math:`D_{k}` operators. These are a list of diagonal operators where |
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The operator D_k is not diagonal, it is a block encoding of a diagonal matrix
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It becomes block diagonal when we include the multiplexer. But I guess my point is that each individual D_i is a diagonal operator no?
Co-authored-by: ANT0N <39093564+AntonNI8@users.noreply.github.com> Co-authored-by: Guillermo Alonso-Linaje <65235481+KetpuntoG@users.noreply.github.com>
drdren
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The initial Python code block does not execute
| print(resources) | ||
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| ############################################################################## | ||
| # With one line, we can see that that the estimated T gate cost of naive block encoding this matrix is :math:`1 \times 10^{12}`. This block encoding is called many times within an instance of the QSVT algorithm, and can be the dominant cost. Now that we have established a baseline of the `standard' cost, we ask: Can we do better? |
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| print(resources) | |
| ############################################################################## | |
| # With one line, we can see that that the estimated T gate cost of naive block encoding this matrix is :math:`1 \times 10^{12}`. This block encoding is called many times within an instance of the QSVT algorithm, and can be the dominant cost. Now that we have established a baseline of the `standard' cost, we ask: Can we do better? | |
| print(resources) | |
| ############################################################################## | |
| # With one line, we can see that that the estimated T gate cost of naive block encoding this matrix is :math:`1 \times 10^{12}`. This block encoding is called many times within an instance of the QSVT algorithm, and can be the dominant cost. Now that we have established a baseline of the `standard' cost, we ask: Can we do better? |
| # Each :math:`D_{k}` is a block-diagonal operator that contains the normalised entries from the :math:`k^{\text{th}}` | ||
| # diagonal of our d-diagonal matrix :math:`A`. By multiplexing over the :math:`D_{k}` operators, we can load all of | ||
| # the diagonals in *parallel*. | ||
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5 participants
Title:
A new demo using the resource estimation functionality for CFD example using QSVT.
Summary:
Relevant references:
Possible Drawbacks:
Related GitHub Issues:
estimatormodule)Algo Researcher:
Algo Software Dev:
QSVT, Resource Estimation, Matrix Inversion, CFD, Linear systems of equations,
(more details here)