24

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.


14

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 ...


11

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


11

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 ...


8

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 ...


6

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 "...


6

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 ...


6

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 ...


6

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

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 ...


5

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 ...


5

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


5

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 $2\times 2^n$ ...


5

If $\tilde{\lambda_{k}} < C$, the controlled rotation becomes non-physical since you have coeffecient greater than 1 on your $|1\rangle$ state. As a result $C < \lambda_{min}$ is a safer choice, and that is $O(1/\kappa)$ according to the 4th paragraph in the intro.


5

PennyLane supports measurements of tensor products of observable via the @ operator, like so: @qml.qnode(dev) def my_quantum_function(x, y): qml.RZ(x, wires=0) qml.CNOT(wires=[0, 1]) qml.RY(y, wires=1) return qml.expval(qml.PauliZ(0) @ qml.PauliZ(1)) This should return the same result as the solution by KAJ226 above, but will be slightly ...


5

There are two different ancillas floating around, one used in $|\psi\rangle$ and another to conduct the swap test later on: In the above picture with subsystems explicitly labeled we have \begin{align} |\psi \rangle_{A_2 B} &= \frac{1}{2} \left( |0\rangle_{A_2} |u\rangle_B + \frac{1}{\sqrt{M}} \sum_{j=1}^M |j\rangle_{A_2} |v_j\rangle_B\right) \\ |\phi\...


5

"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 ...


5

At the start of the circuit you're right that you only need two parameters. This is actually easy to show if you decompose into a sequence of rotations starting with a Z rotation, because Z rotations have no effect on $|0\rangle$, so clearly that Z rotation angle would be irrelevant. But in the middle of a circuit, a gate is likely operating on a state that ...


5

Just to add a little more context to your answer: TensorFlow-Quantum 0.4.0 has an explicit version dependency on sympy==1.5.0 in the setup.py module here, which should have been installed when you first installed TFQ. It's possible that other python pip packages may have overriden or upgraded the sympy version since then. Using something like pip list | grep ...


4

First: The paper references [37] for Levy's Lemma, but you will find no mention of "Levy's Lemma" in [37]. You will find it called "Levy's Inequality", which is called Levy's Lemma in this, which is not cited in the paper you mention. Second: There is an easy proof that this claim is false for VQE. In quantum chemistry we optimize the parameters of a ...


4

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 ...


4

I'm the engineer who looks after TensorFlow Quantum. Serializing custom gates is not supported. There is an active issue on the GitHub here: https://github.com/tensorflow/quantum/issues/354 . A quick workaround would be to try and determine the gate decomposition for your custom gate in terms of tfq.util.get_supported_gates gate instances. A good place to ...


4

A lot of focus in quantum machine learning in the near term revolves around variational quantum algorithms (you'll also see them called variational quantum circuits or parameterized quantum circuits), as well as their extensions to hybrid classical-quantum models. Though the field is evolving pretty fast, this recent review article gives a fairly good ...


4

The basic idea of how the quantum feature map works is that you're using a quantum computer to map each input datapoint $x$ from your training domain $\mathcal{X}$ into a quantum state $|\phi(x)\rangle = U(x)|0\rangle$ in the (presumably) high dimensional quantum state space, and then evaluating a set of kernel functions: $$ k_Q(x_i, x_j) = |\langle 0|U(x_j)^...


4

I think the following should work: n_qubits = 2 Z = [ [1,0], [0,-1]] ZZ = np.kron(Z,Z) @qml.qnode(dev) def circuit(params): qml.RY(params[0], wires=0) qml.CNOT(wires=[0, 1]) qml.RY(params[1], wires=1) return qml.expval(qml.Hermitian(ZZ, wires=[0, 1]))


4

Practically, it can be (quite often) a limitation of number of qubits/hardware, but also it is a hyperparameter to play with. So it may be that using more qubits gives you better results or worse. Also, in the QSVM, there is or may be a parameterized part you have to optimize over. So increasing the number of qubits results in more optimization (more ...


4

There are a couple of ways reversibility might be coming into play in this context. The first is that the measurement at the end of the circuit will be typically be an irreversible step. For example one scheme for training a quantum circuit to classify classical data is by encoding each data point $x_i$ (with a corresponding $0,1$ label $y_i$ for the binary ...


4

I am the first author of the paper and I have been asked this question more than once, so it’s worth answering here for further reference. Keep in mind that the goal of the paper is to describe a variational construction of GANs such that it is compatible with NISQ devices. Hence the procedure must be differentiable and start from an expectation value ...


3

Here is a good resource: Quantum machine learning for data scientists Here is another one that discusses different techniques people are proposing for QML in the literature and etc. Quantum machine learning:a classical perspective


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