[WIP] QROM demo #1123
[WIP] QROM demo #1123
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| { | ||
| "title": "Intro to QSVT", | ||
| "authors": [ | ||
| { | ||
| "id": "guillermo_alonso" | ||
| } | ||
| ], | ||
| "dateOfPublication": "2023-05-23T00:00:00+00:00", | ||
| "dateOfLastModification": "2024-03-04T00:00:00+00:00", | ||
| "categories": [ | ||
| "Algorithms", |
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The metadata I usually updated at the end when we already have the thumbnails
| Managing data is a crucial task on any computer, and quantum computers are no exception. Efficient data management is vital in Quantum Machine Learning (QML), search algorithms or state preparation. | ||
| In this demonstration, we will introduce the concept of Quantum Read-Only Memory (QROM), a data structure designed to facilitate these tasks. |
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| Managing data is a crucial task on any computer, and quantum computers are no exception. Efficient data management is vital in Quantum Machine Learning (QML), search algorithms or state preparation. | |
| In this demonstration, we will introduce the concept of Quantum Read-Only Memory (QROM), a data structure designed to facilitate these tasks. | |
| Managing data is a crucial task on any computer, and quantum computers are no exception. Efficient data management is vital in quantum machine learning, search algorithms, and state preparation. | |
| In this demonstration, we will introduce the concept of a Quantum Read-Only Memory (QROM), a data structure designed to load classical data on a quantum computer. |
No need for acronyms (QML) if you are not using them again
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You should also mention in the introduction that we are going to explain how to implement it using PennyLane
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In particular, we should probably mention that we have a specific QROM operation that implements it directly, and link to it already at the beginning for easy access
| The QROM is an operator that allows us to load classical data into a quantum computer | ||
| associated with indices. This data is represented as a bitstring (list of 0s and 1s) and the operator can be defined as: |
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| The QROM is an operator that allows us to load classical data into a quantum computer | |
| associated with indices. This data is represented as a bitstring (list of 0s and 1s) and the operator can be defined as: | |
| The QROM is an operator that allows us to load classical data into a quantum computer. Data is represented as a collection of bitstrings (list of 0s and 1s) that we denote by :math:`b_1, b_2, \ldots, b_N`. The QROM operator is then defined as: |
| Suppose our data consists of eight bit-strings :math:`[11, 01, 11, 00, 10, 10, 11, 00]`. Then, the index register will consist of three | ||
| qubits (:math:`\log_2 8`) and the target register of two qubits (length of the bit-strings). Following the same example, | ||
| :math:`\text{QROM}|010\rangle|00\rangle = |010\rangle|11\rangle`, since the bit-string associated with index :math:`2` is :math:`11`. | ||
| We will show three different implementations of this operator: Select, SelectSwap and an extension of the | ||
| last one. |
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| Suppose our data consists of eight bit-strings :math:`[11, 01, 11, 00, 10, 10, 11, 00]`. Then, the index register will consist of three | |
| qubits (:math:`\log_2 8`) and the target register of two qubits (length of the bit-strings). Following the same example, | |
| :math:`\text{QROM}|010\rangle|00\rangle = |010\rangle|11\rangle`, since the bit-string associated with index :math:`2` is :math:`11`. | |
| We will show three different implementations of this operator: Select, SelectSwap and an extension of the | |
| last one. | |
| For example, suppose our data consists of eight bit-strings, each with two bits: :math:`[11, 01, 11, 00, 10, 10, 11, 00]`. Then, the index register will consist of three | |
| qubits (:math:`3 = \log_2 8`) and the target register of two qubits (length of the bit-strings). In this case, the QROM operator acts as | |
| :math:`\text{QROM}|010\rangle|00\rangle = |010\rangle|11\rangle`, since the bit-string associated with index :math:`2` is :math:`11`. | |
| We will now explain three different implementations of a QROM: Select, SelectSwap, and an extension of SelectSwap. |
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Actually, here I think it may be better to have a simple dataset of 4 strings of 2 bits, then show the complete action of QROM on all of them. If we pick the first 4 in your example it would be
QROM |00> |00> = |00>|11>
QROM |01> |00> = |01>|01>
QROM |10> |00> = |10>|11>
QROM |11> |00> = |11>|00>
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You can use one example with 4 bitstrings here, then have another example with 8 bitstrings to be used later throughout
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| .. math:: | ||
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| \text{Sel}|i\rangle|0\rangle = |i\rangle|\phi_i\rangle, |
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| \text{Sel}|i\rangle|0\rangle = |i\rangle|\phi_i\rangle, | |
| \text{Sel}|i\rangle|0\rangle = |i\rangleU_i|0\rangle =|i\rangle|\phi_i\rangle, |
| Since the bitstrings can be seen as a particular quantum state, we particularize this operator to the QROM case. | ||
| For the following example we are going to use :class:`~.pennylane.BasisEmbedding` as :math:`U_i`, and | ||
| the :class:`~.pennylane.Select` template provided by PennyLane. |
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| Since the bitstrings can be seen as a particular quantum state, we particularize this operator to the QROM case. | |
| For the following example we are going to use :class:`~.pennylane.BasisEmbedding` as :math:`U_i`, and | |
| the :class:`~.pennylane.Select` template provided by PennyLane. | |
| Since the bitstrings are encoded in computational basis states, we can view QROM as a special case of a Select operator. | |
| For the following example we are going to use :class:`~.pennylane.BasisEmbedding` as :math:`U_i`, and | |
| the :class:`~.pennylane.Select` template provided by PennyLane. |
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I don't understand what you mean by "use :class:~.pennylane.BasisEmbedding as :math:U_i". Please clarify in the text.
| # | ||
| # QROM in PennyLane | ||
| # ----------------- | ||
| # Coding these ideas from scratch can be painful but with the help of PennyLane you can use it in just one line. |
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| # Coding these ideas from scratch can be painful but with the help of PennyLane you can use it in just one line. | |
| # Coding a QROM circuit from scratch can be painful, but with the help of PennyLane you can do it in just one line. |
| # QROM in PennyLane | ||
| # ----------------- | ||
| # Coding these ideas from scratch can be painful but with the help of PennyLane you can use it in just one line. | ||
| # We are going to encode the same bitstrings, using the first SelectSwap approach. In this example we use two work wires |
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| # We are going to encode the same bitstrings, using the first SelectSwap approach. In this example we use two work wires | |
| # We are going to encode the same bitstrings, using the SelectSwap approach. In this example we use two work wires |
| return True | ||
| return False | ||
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| @partial(qml.devices.preprocess.decompose, stopping_condition = my_stop, max_expansion=2) |
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What's the purpose of this @partial?
| qml.PauliX(control_wires[-3]) | ||
| qml.Hadamard(control_wires[-1]) | ||
| qml.Hadamard(control_wires[-2]) |
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I find this confusing, like you're trying to do too much. I suggest instead creating a more complicated QROM circuit and drawing it to show that it's correct and easy to implement with PL
| # | ||
| # By implementing various versions of the QROM operator, such as Select and SelectSwap, we optimize quantum circuits | ||
| # for enhanced performance and scalability. Numerous studies demonstrate the efficacy of these methods in improving | ||
| # State Preparation [#StatePrep]_ techniques by reducing the number of required gates, which I recommend you explore. |
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| # State Preparation [#StatePrep]_ techniques by reducing the number of required gates, which I recommend you explore. | |
| # state preparation [#StatePrep]_ techniques by reducing the number of required gates, which we recommend you explore. |
Use "we", not "I"
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