# Tag Info

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The Nielsen and Chuang of Quantum Machine Learning is this extensive review called "Quantum Machine Learning" published in Nature in 2017. The arXiv version is here and has been updated as recently as 10 May 2018.

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I will only answer to the part of the question regarding how quantum mechanics can be useful to analyse classical data with machine-learning-like techniques. There are also works related to "quantum AI", but that is a much more speculative (and less defined) kind of thing, which I do not want to go into. So, can quantum computers be used to speed-up data ...

14

This is very much an open question, but yes, there is a considerable amount of work that is being done on this front. Some clarifications It is, first of all, to be noted that there are two major ways to merge machine learning (and deep learning in particular) with quantum mechanics/quantum computing: 1) ML $\to$ QM Apply classical machine learning ...

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First we should take a step back. Is there any machine learning done a quantum computer that cannot be efficiently simulated on a classical computer? The answer currently (2020) is no. In this respect quantum machine learning (which has many variants) is at the fundamental research phase. None of this is at a stage where it is at all considered something ...

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Here's a list of other resources to learn about quantum machine learning: An introduction to quantum machine learning The quest for a Quantum Neural Network Quantum Machine Learning: What Quantum Computing Means to Data Mining Quantum Machine Learning 1.0

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Both finite differences and the parameter-shift rule can be used to compute quantum gradients on quantum hardware. However, there are several reasons that lead to the parameter-shift rule being preferred. Numerical differentiation One method to compute gradients is finite difference, a form of numerical differentiation. Here we treat the function to be ...

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I know this is not what you are asking but this paper: Quantum Algorithm Implementations for Beginners explains the implementation of some machine learning algorithms. Hope this helps!

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Yes, all classical algorithms can be run on quantum computers, moreover any classical algorithm involving searching can get a $\sqrt{\text{original time}}$ boost by the use of grovers algorithm. An example that comes to mind is treating the fine tuning of neural network parameters as a "search for coefficients" problem. For the fact there are clear ...

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We can use the SWAP test to determine the inner product of 2 states $|\phi\rangle$ and $|\psi\rangle$. The circuit is shown below The state of the system at the beginning of the protocol is $|0\rangle \otimes |\phi \rangle \otimes |\psi \rangle$. After the Hadamard gate, the state of the system is $|+\rangle \otimes |\phi \rangle \otimes |\psi \rangle$. The ...

7

You are not swapping the first register (one qubit) with the entire second register ($k$ qubits), but just with the first qubit of the second register. What you need to know is what is meant by $\langle x | y \rangle$ when $x$ is one qubit and $y$ is $k$ qubits. The resulting state is the $k-1$ qubit state you get when you project one qubit (generally the ...

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I am not an expert in the field but there are a few points that I am aware of: There are proofs that certain quantum machine learning algorithms cannot be efficiently simulated on a classical computer even if the classical computer has analagous sampling access to the data as the quantum algorithm does (i.e. they cannot be dequantized) [1-3]. However there ...

7

One can recommend PennyLane by Xanadu.AI. You can find complete examples of quantum machine learning algorithms (e.g. Iris Classification), using hybrid quantum-classical computations. Additionally, they offer built-in plugins for IBM QisKit, Pyquil etc., to enable running Pennylane QML codes on IBM and Rigetti quantum hardwares.

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In my view, if artificial general intelligence (AGI) is ever 'solved', it likely won't be because of the development of a quantum AI algorithm. Rather, it will be because of a breakthrough in the training of existing classical algorithms. That said, much like in the classical case (i.e. classical machine learning), research on quantum algorithms with ...

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As so often, and especially in young research areas, the answer depends quite a lot on how you break down the question. Let me try a few examples: Does quantum mechanics change what is theoretically learnable? A beautiful paper is this reference which states a few complex results in rather clear words. Again, it depends very much on what you define as "...

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There are arguments that our brains are quantum mechanical, and arguments against, so that's a hotly debated topic. Fisher at UCSB has some speculative thinking about how brains might still use quantum effects even though they aren't quantum mechanical in nature. While there's no direct experimental evidence there are two references you might want to read: ...

6

I've not looked at those papers specifically, but there are several different models for quantum computation (see here), including the gate model and the adiabatic model, which are polynomial time equivalent. That means if one has an exponential speedup, so does the other. The discussion should be interchangeable. The title, if not the question body, also ...

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There are many possible ways to encode data into a quantum neural network (QNN). In one of the first papers to suggest the use of variational circuits to classify data [1], the authors suggest the following general architecture for a QNN: The circuit starts with the $|0\rangle$ state, encodes a data point $\textbf{x}$ using a circuit $S_\textbf{x}$, and ...

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Besides number of qubits, the devices can have other differences as well. The architecture of the device can be different, meaning that each device could have different connectivity maps. This would affect the mapping of valid multiqubit gates. They also can have different error rates at any given time. Calibrations are run on each device daily. These error ...

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Consider a simple implementation of a Support Vector Machine (SVM) that finds a hyperplane (defined by its normal vector $w$) that maximally separates vectors $\{v_1, \dots, v_m\}$ according to their labels $\{y_1, \dots, y_m\}$, where each $y$ is either $-1$ or $1$. For simplicity we'll assume that such a $w$ exists (i.e. the vectors $\{v_k\}$ are linearly ...

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Thanks for the answers from @forky40. I accept it as the right answer, but do want to provide a complete derivation as follows. (Same as in the original question) First, initialize per DistCalc: $$|\psi\rangle = \frac{1}{\sqrt{2}} (|0,a\rangle + |1,b\rangle)$$ $$|\phi\rangle = \frac{1}{\sqrt{Z}} (|a||0\rangle - |b||1\rangle)$$ Also let:  |\psi'\...

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In general, the efficiency of Quantum Machine Learning Techniques will be calibrated and measured more in terms of the energy efficiency, ability to handle complex computational problems, NP-hard problems and the ability to ensemble different domain algorithms than the speed and learning rate. However, there could be exceptionally faster quantum algorithms ...

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The most recent quantum machine learning textbook is Schuld and Petruccione (2018). Supervised Learning with Quantum Computers while a nice companion to Nielsen and Chuang for introductory quantum maths is Marinescu and Marinescu (2011). Classical and Quantum Information, Chapter 1: Preliminaries

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I don't understand their notion of a $2^n$ dimensional complex vector. If each of the components of their classical data array has two floating point numbers, wouldn't encoding that into a $n$-qubit quantum state be equivalent to storing a $2\times 2^{n}$ size classical array in a $n$-qubit system? You are absolutely correct that a $2\times 2^n$ ...

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Much of the work done so far with quantum computers has been focused on solving combinatorial optimization problems. Both D-Wave style Quantum Annealers and the more recent Gate Model machines from Rigetti, IBM, and Google have been solving combinatorial optimization problems. One promising approach to connecting machine learning and quantum computing ...

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As far as I know, there are four possibilities for having a quantum advantage in Bayesian machine learning: Gaussian processes: there is a known quantum speed-up for Gaussian processes that you can easily test on IBM Q [1,2]. The idea is to use HHL (quantum algorithm for matrix inversion) in order to compute the inverse of the kernel matrix, which is used ...

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First of all, the name of backends (devices) have nothing to do with their location! They are all located in US. Back to your question, as others already mentioned the difference is in the architecture (topology), number of qubits, connectivity, and performance (influenced by various types of errors). If you click the name of any backend (device) in your ...

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"IonQ is claiming to have a potential application in machine learning by 2023. What applications could they have in mind?" None. The plot you showed has no units on the y-axis. It doesn't even have numbers. The choice of 2023, 2025, and 2027 for "inflection points" (which they didn't define, and based on their graph has nothing to do ...

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Gaussian Processes are a key component of the model-building procedure at the core of Bayesian Optimization. Therefore speeding up the training of Gaussian processes directly enhances Bayesian Optimization. The recent paper by Zhao et. al on Quantum algorithms for training Gaussian Processes does exactly this.

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I was not able to find references specifically in quantum biology. I found however a review called Quantum Assisted biomolecular modeling. You may find it interesting but this is from 2010. The field has evolved since but I guess the ideas remain similar. The authors focus more on the idea of the ability of a quantum computer to try every classical paths ...

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There are different review overviews about Quantum Machine Learning (see the question referenced in comments to find a few) but it is an evolving field so you will have to keep updated. There is also an EDX online course about the subject made by Wittek recently released if you would like a little more hands-on format. I would advise to start with basics ...

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