From c74fab7a19351a63ab9590840379d9bf89fcc65a Mon Sep 17 00:00:00 2001 From: Guillermo Alonso-Linaje <65235481+KetpuntoG@users.noreply.github.com> Date: Wed, 18 Sep 2024 08:24:45 -0400 Subject: [PATCH] QROM demo to master (#1213) MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit New PR pointing to master Some discussions were made in the [other PR](https://github.com/PennyLaneAI/qml/pull/1123) --------- Co-authored-by: ixfoduap <40441298+ixfoduap@users.noreply.github.com> Co-authored-by: Ivana Kurečić --- .../thumbnail_large_qrom.png | Bin 0 -> 87929 bytes .../OGthumbnail_qrom.png | Bin 0 -> 85690 bytes .../thumbnail_qrom.png | Bin 0 -> 21436 bytes .../qrom/clean_version_2.jpeg | Bin 0 -> 254216 bytes .../qrom/example_selectswap.jpeg | Bin 0 -> 391201 bytes .../qrom/indixes_qrom.jpeg | Bin 0 -> 128880 bytes .../qrom/select_swap.jpeg | Bin 0 -> 379093 bytes .../qrom/select_swap_4.jpeg | Bin 0 -> 425611 bytes .../tutorial_intro_qrom.metadata.json | 82 ++++ demonstrations/tutorial_intro_qrom.py | 354 ++++++++++++++++++ 10 files changed, 436 insertions(+) create mode 100644 _static/demo_thumbnails/large_demo_thumbnails/thumbnail_large_qrom.png create mode 100644 _static/demo_thumbnails/opengraph_demo_thumbnails/OGthumbnail_qrom.png create mode 100644 _static/demo_thumbnails/regular_demo_thumbnails/thumbnail_qrom.png create mode 100644 _static/demonstration_assets/qrom/clean_version_2.jpeg create mode 100644 _static/demonstration_assets/qrom/example_selectswap.jpeg create mode 100644 _static/demonstration_assets/qrom/indixes_qrom.jpeg create mode 100644 _static/demonstration_assets/qrom/select_swap.jpeg create mode 100644 _static/demonstration_assets/qrom/select_swap_4.jpeg create mode 100644 demonstrations/tutorial_intro_qrom.metadata.json create mode 100644 demonstrations/tutorial_intro_qrom.py diff --git a/_static/demo_thumbnails/large_demo_thumbnails/thumbnail_large_qrom.png 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index 0000000000..f004331990 --- /dev/null +++ b/demonstrations/tutorial_intro_qrom.metadata.json @@ -0,0 +1,82 @@ +{ + "title": "Intro to quantum read-only memory (QROM)", + "authors": [ + { + "username": "KetPuntoG" + }, + { + "username": "ixfoduap" + } + ], + "dateOfPublication": "2024-09-18T00:00:00+00:00", + "dateOfLastModification": "2024-09-18T00:00:00+00:00", + "categories": [ + "Algorithms", + "Quantum Computing" + ], + "tags": [], + "previewImages": [ + { + "type": "thumbnail", + "uri": "/_static/demo_thumbnails/regular_demo_thumbnails/thumbnail_qrom.png" + }, + { + "type": "large_thumbnail", + "uri": "/_static/demo_thumbnails/large_demo_thumbnails/thumbnail_large_qrom.png" + } + ], + "seoDescription": "Learn how to enter data into a quantum computer with a quantum read-only memory (QROM) approach.", + "doi": "", + "canonicalURL": "/qml/demos/tutorial_intro_qrom", + "references": [ + { + "id": "unary", + "type": "article", + "title": "Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity", + "authors": "Ryan Babbush, Craig Gidney, Dominic W. Berry, Nathan Wiebe, Jarrod McClean, Alexandru Paler, Austin Fowler, Hartmut Neven", + "year": "2018", + "publisher": "", + "journal": "Physical Review X", + "url": "http://dx.doi.org/10.1103/PhysRevX.8.041015" + }, + { + "id": "selectSwap", + "type": "article", + "title": "Trading T-gates for dirty qubits in state preparation and unitary synthesis", + "authors": "Guang Hao Low, Vadym Kliuchnikov, Luke Schaeffer", + "year": "2018", + "publisher": "", + "journal": "arXiv", + "url": "https://arxiv.org/abs/1812.00954" + }, + { + "id": "cleanQROM", + "type": "article", + "title": "Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization", + "authors": "Dominic W. Berry, Craig Gidney, Mario Motta, Jarrod R. McClean, Ryan Babbush", + "year": "2019", + "publisher": "", + "journal": "Quantum", + "url": "http://dx.doi.org/10.22331/q-2019-12-02-208" + }, + { + "id": "StatePrep", + "type": "article", + "title": "Creating superpositions that correspond to efficiently integrable probability distributions", + "authors": "Lov Grover, Terry Rudolph", + "year": "2002", + "publisher": "", + "journal": "arXiv", + "url": "https://arxiv.org/abs/quant-ph/0208112" + } + ], + "basedOnPapers": [], + "referencedByPapers": [], + "relatedContent": [ + { + "type": "demonstration", + "id": "tutorial_initial_state_preparation", + "weight": 1.0 + } + ] +} \ No newline at end of file diff --git a/demonstrations/tutorial_intro_qrom.py b/demonstrations/tutorial_intro_qrom.py new file mode 100644 index 0000000000..ce93275f4e --- /dev/null +++ b/demonstrations/tutorial_intro_qrom.py @@ -0,0 +1,354 @@ +r"""Intro to quantum read-only memory (QROM) +============================================================= + +Managing data is a crucial task, and quantum computers are no exception: efficient data management is vital in `quantum machine learning `__, search algorithms, and :doc:`state preparation `. +In this demonstration, we will discuss the concept of a quantum read-only memory (QROM), a data structure designed to load classical data into a quantum computer. +This is a valuable tool in quantum machine learning or for preparing quantum states among others. +We also explain how to use this operator in PennyLane using the :class:`~.pennylane.QROM` template. + + +.. figure:: ../_static/demo_thumbnails/opengraph_demo_thumbnails/OGthumbnail_qrom.png + :align: center + :width: 70% + :target: javascript:void(0) + +QROM +----- + +Quantum read-only memory (QROM) is an operator that allows us to load classical data into a quantum computer. Data are represented as a collection of bitstrings (lists composed of 0s and 1s) that we denote by :math:`b_0, b_1, \ldots, b_{N-1}`. The QROM operator is then defined as: + +.. math:: + + \text{QROM}|i\rangle|0^{\otimes m}\rangle = |i\rangle|b_i\rangle, + +where :math:`|b_i\rangle` is the bitstring associated with the :math:`i`-th computational basis state, and :math:`m` is the length of the bitstrings. We have assumed all the bitstrings are of equal length. + +For example, suppose our data consists of eight bitstrings, each with two bits: :math:`[01, 11, 11, 00, 01, 11, 11, 00]`. Then, the index register will consist of three +qubits (:math:`3 = \log_2 8`) and the target register of two qubits (:math:`m = 2`). For instance, for the +first four indices, the QROM operator acts as: + +.. math:: + \begin{align} + \text{QROM}|000\rangle|00\rangle &= |000\rangle|01\rangle \\ + \text{QROM}|001\rangle|00\rangle &= |001\rangle|11\rangle \\ + \text{QROM}|010\rangle|00\rangle &= |010\rangle|11\rangle \\ + \text{QROM}|011\rangle|00\rangle &= |011\rangle|00\rangle. + \end{align} + +We will now explain three different implementations of QROM: *Select*, *SelectSwap*, and an extension of *SelectSwap*. + +Select +~~~~~~~ + +:class:`~.pennylane.Select` is an operator that prepares quantum states associated with indices. It is defined as: + +.. math:: + + \text{Select}|i\rangle|0\rangle = |i\rangle U_i|0\rangle =|i\rangle|\phi_i\rangle, + +where :math:`|\phi_i\rangle` is the :math:`i`-th state we want to encode, generated by a known unitary :math:`U_i`. +QROM can be considered a special case of the *Select* operator where the encoded states are computational basis states. +Then the unitaries :math:`U_i` can be simply products of :math:`X` gates satisfying: + +.. math:: + + U_i|0\rangle =|b_i\rangle. + +We use :class:`~.pennylane.BasisState` as a useful template for implementing the gates :math:`U_i`. Let's see how it could be written in code: + +""" + +import pennylane as qml +import numpy as np +from functools import partial +import matplotlib.pyplot as plt + + +bitstrings = ["01", "11", "11", "00", "01", "11", "11", "00"] + +control_wires = [0, 1, 2] +target_wires = [3, 4] + +Ui = [qml.BasisState(int(bitstring, 2), target_wires) for bitstring in bitstrings] + +dev = qml.device("default.qubit", shots=1) + + +# This line is included for drawing purposes only. +@partial(qml.devices.preprocess.decompose, stopping_condition=lambda obj: False, max_expansion=1) + +@qml.qnode(dev) +def circuit(index): + qml.BasisState(index, wires=control_wires) + qml.Select(Ui, control=control_wires) + return qml.sample(wires=target_wires) + + +qml.draw_mpl(circuit, style="pennylane")(3) +plt.show() + +############################################################################## +# Now we can check that all the outputs are as expected: + +for i in range(8): + print(f"The bitstring stored in index {i} is: {circuit(i)}") + + +############################################################################## +# The outputs match the elements of our initial data list: :math:`[01, 11, 11, 00, 01, 11, 11, 00]`. Nice! +# +# The :class:`~.pennylane.QROM` template can be used to implement the previous circuit using directly the bitstring +# without having to calculate the :math:`U_i` gates: + +import warnings +# This line will suppress ComplexWarnings for output visibility +warnings.filterwarnings(action="ignore", category=np.ComplexWarning) + +bitstrings = ["01", "11", "11", "00", "01", "11", "11", "00"] + +control_wires = [0, 1, 2] +target_wires = [3, 4] + + +@partial(qml.compile, basis_set="CNOT") # Line added for resource estimation purposes only. +@qml.qnode(dev) +def circuit(index): + qml.BasisState(index, wires=control_wires) + qml.QROM(bitstrings, control_wires, target_wires, work_wires=None) + return qml.sample(wires=target_wires) + + +for i in range(8): + print(f"The bitstring stored in index {i} is: {circuit(i)}") + +############################################################################## +# Although this approach works correctly, the number of multicontrol gates is high — gates with a costly decomposition. +# Here we show the number of 1 and 2 qubit gates we use when decomposing the circuit: + +print("Number of qubits: ", len(control_wires + target_wires)) +print("One-qubit gates: ", qml.specs(circuit)(0)["resources"].gate_sizes[1]) +print("Two-qubit gates: ", qml.specs(circuit)(0)["resources"].gate_sizes[2]) + +############################################################################## +# You can learn more about these resource estimation methods in +# the `PennyLane documentation `__. +# There are numerous works that attempt to simplify this, of which +# we highlight reference [#unary]_, which introduces an efficient technique using measurements in the middle +# of the circuit. Another clever approach was introduced in [#selectSwap]_ , with a smart structure known as *SelectSwap*, +# which we describe below. +# +# SelectSwap +# ~~~~~~~~~~ +# The goal of the *SelectSwap* construction is to trade depth of the circuit for width. That is, using multiple auxiliary qubits, +# we reduce the circuit depth required to build the QROM. Before we get into how it works, let's show you how easy it is to use: +# we simply add ``work_wires`` to the code we had previously. +# + +bitstrings = ["01", "11", "11", "00", "01", "11", "11", "00"] + +control_wires = [0, 1, 2] +target_wires = [3, 4] +work_wires = [5, 6] + + +@partial(qml.compile, basis_set="CNOT") +@qml.qnode(dev) +def circuit(index): + qml.BasisState(index, wires=control_wires) + # added work wires below + qml.QROM(bitstrings, control_wires, target_wires, work_wires, clean=False) + return qml.sample(wires=control_wires + target_wires + work_wires) + +print("Number of qubits: ", len(control_wires + target_wires + work_wires)) +print("One-qubit gates: ", qml.specs(circuit)(0)["resources"].gate_sizes[1]) +print("Two-qubit gates: ", qml.specs(circuit)(0)["resources"].gate_sizes[2]) + +############################################################################## +# The number of 1 and 2 qubit gates is significantly reduced! +# +# Internally, the main idea of this approach is to organize the :math:`U_i` operators into two dimensions, +# whose positions will be determined by a column index :math:`c` and a row index :math:`r`. +# +# .. figure:: ../_static/demonstration_assets/qrom/select_swap.jpeg +# :align: center +# :width: 70% +# :target: javascript:void(0) +# +# Following this structure, for instance, the :math:`U_5` operator (or :math:`101` in binary) is in column :math:`2` and row :math:`1` (zero-based indexing): +# +# .. figure:: ../_static/demonstration_assets/qrom/indixes_qrom.jpeg +# :align: center +# :width: 70% +# :target: javascript:void(0) +# +# In order to load the desired bitstring in the target wires, we use two building blocks in the construction: +# +# - **Select block**: Loads the :math:`c`-th column in the target and work wires. +# - **Swap block**: Swaps the :math:`r`-th row to the target wires. +# +# +# Let's look at an example by assuming we want to load in the target wires the bitstring with +# the index :math:`5`, i.e., :math:`U_5|0\rangle = |b_5\rangle`. +# +# .. figure:: ../_static/demonstration_assets/qrom/example_selectswap.jpeg +# :align: center +# :width: 85% +# :target: javascript:void(0) +# +# Now we run the circuit with our initial data list: :math:`[01, 11, 11, 00, 01, 11, 11, 00]`. + +index = 5 +output = circuit(index) +print(f"control wires: {output[:3]}") +print(f"target wires: {output[3:5]}") +print(f"work wires: {output[5:7]}") + + +############################################################################## +# As expected, :math:`|b_5\rangle = |11\rangle` is loaded in the target wires. +# Note that with more auxiliary qubits we could make larger groupings of bitstrings reducing the depth of the +# *Select* operator. Below we show an example with two columns and four rows: +# +# .. figure:: ../_static/demonstration_assets/qrom/select_swap_4.jpeg +# :align: center +# :width: 70% +# :target: javascript:void(0) +# +# The QROM template will put as many rows as possible using the ``work_wires`` we pass. +# Let's check how it looks in PennyLane: + +bitstrings = ["01", "11", "11", "00", "01", "11", "11", "00"] + +control_wires = [0, 1, 2] +target_wires = [3, 4] +work_wires = [5, 6, 7, 8, 9, 10, 11, 12] + + +# Line added for drawing purposes only +@partial(qml.devices.preprocess.decompose, stopping_condition=lambda obj: False, max_expansion=2) +@qml.qnode(qml.device("default.qubit", shots=1)) +def circuit(index): + qml.BasisState(index, wires=control_wires) + qml.QROM(bitstrings, control_wires, target_wires, work_wires, clean=False) + return qml.sample(wires=target_wires), qml.sample(wires=target_wires) + + +qml.draw_mpl(circuit, style="pennylane")(0) +plt.show() + + +############################################################################## +# The circuit matches the one described above. +# +# Reusable qubits +# ~~~~~~~~~~~~~~~~ +# +# The above approach has a drawback. The work wires have been altered, i.e., after applying the operator they have not +# been returned to state :math:`|00\rangle`. This could cause unwanted behaviors, but in PennyLane it can be easily solved +# by setting the parameter ``clean = True``. + + +bitstrings = ["01", "11", "11", "00", "01", "11", "11", "00"] + +control_wires = [0, 1, 2] +target_wires = [3, 4] +work_wires = [5, 6] + + +@qml.qnode(dev) +def circuit(index): + qml.BasisState(index, wires=control_wires) + qml.QROM(bitstrings, control_wires, target_wires, work_wires, clean=True) + return qml.sample(wires=target_wires + work_wires) + + +for i in range(8): + print(f"The bitstring stored in index {i} is: {circuit(i)[:2]}") + print(f"The work wires for that index are in the state: {circuit(i)[2:4]}\n") + + +############################################################################## +# All the work wires have been reset to the zero state. +# +# To achieve this, we follow the technique shown in [#cleanQROM]_, where the proposed circuit (with :math:`R` rows) is as follows: +# +# .. figure:: ../_static/demonstration_assets/qrom/clean_version_2.jpeg +# :align: center +# :width: 90% +# :target: javascript:void(0) +# +# To see how this circuit works, let's suppose we want to load the bitstring :math:`b_{cr}` in the target wires, where :math:`b_{cr}` +# is the bitstring whose operator :math:`U` is placed in the :math:`c`-th column and :math:`r`-th row in the two-dimensional representation shown in the *Select* block. +# We can summarize the idea in a few simple steps. +# +# 0. **Initialize the state.** We create the state: +# +# .. math:: +# |c\rangle |r\rangle |0\rangle |0\rangle \dots |0\rangle. +# +# 1. **A uniform superposition is created in the r-th register of the work wires**. To do this, we put the Hadamards in the target wires and move it to the :math:`r`-th row with the *Swap* block: +# +# .. math:: +# |c\rangle |r\rangle |0\rangle |0\rangle \dots |+\rangle_r \dots |0\rangle. +# +# 2. **The Select block is applied.** This loads the whole :math:`c`-th column in the registers. Note that in the :math:`r`-th position, the *Select* has no effect since the state :math:`|+\rangle` is not modified by :math:`X` gates: +# +# .. math:: +# |c\rangle |r\rangle |b_{c0}\rangle |b_{c1}\rangle \dots |+\rangle_r \dots |b_{c(R-1)}\rangle. +# +# +# 3. **The Hadamard gate is applied to the r-th register of the work wires.** This returns that register to the zero state. The two *Swap* blocks and the Hadamard gate applied to the target wires achieve this: +# +# .. math:: +# |c\rangle |r\rangle |b_{c0}\rangle |b_{c1}\rangle \dots |0\rangle_r \dots |b_{c(R-1)}\rangle. +# +# 4. **Select block is applied.** Thanks to this, we clean the used registers. That is because loading the bitstring twice in the same register leaves the state as :math:`|0\rangle` since :math:`X^2 = \mathbb{I}`. On the other hand, the bitstring :math:`|b_{cr}\rangle` is loaded in the :math:`r` register: +# +# .. math:: +# |c\rangle |r\rangle |0\rangle |0\rangle \dots |b_{cr}\rangle_r \dots |0\rangle. +# +# 5. **Swap block is applied.** With this, we move :math:`|b_{cr}\rangle` that is encoded in the r-th row to the target wires: +# +# .. math:: +# |c\rangle |r\rangle |b_{cr}\rangle |0\rangle \dots |0\rangle_r \dots |0\rangle. +# +# The desired bitstring has been encoded in the target wires and the rest of the qubits have been left in the zero state. +# +# Conclusion +# ---------- +# +# By implementing various versions of the QROM operator, such as *Select* and *SelectSwap*, we can optimize quantum circuits +# for enhanced performance and scalability. These methods improve the efficiency of +# state preparation [#StatePrep]_ techniques. After all, state preparation is a special case of data encoding, where the data are the coefficients that define the state. +# QROM methods are particularly attractive for large-scale quantum computing due to their superior asymptotic efficiency. +# This makes them an indispensable tool for developing new algorithms. +# +# References +# ---------- +# +# .. [#unary] +# +# Ryan Babbush, Craig Gidney, Dominic W. Berry, Nathan Wiebe, Jarrod McClean, Alexandru Paler, Austin Fowler, and Hartmut Neven, +# "Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity," +# `Physical Review X, 8(4), 041015 (2018). `__, 2018 +# +# .. [#selectSwap] +# +# Guang Hao Low, Vadym Kliuchnikov, and Luke Schaeffer, +# "Trading T-gates for dirty qubits in state preparation and unitary synthesis", +# `arXiv:1812.00954 `__, 2018 +# +# .. [#cleanQROM] +# +# Dominic W. Berry, Craig Gidney, Mario Motta, Jarrod R. McClean, and Ryan Babbush, +# "Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization", +# `Quantum 3, 208 `__, 2019 +# +# .. [#StatePrep] +# +# Lov Grover and Terry Rudolph, +# "Creating superpositions that correspond to efficiently integrable probability distributions", +# `arXiv:quant-ph/0208112 `__, 2002 +# +# About the authors +# -----------------