13

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 ...


12

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 ...


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

Again, this is still an open question. There are two lines of work that come to mind when you talk of "hardware-based neural networks" which try/claim to use photonics as a mean to speed-up processing, and make direct reference to speeding up machine learning tasks. Shen et al. 2016 (1610.02365) propose a method to implement "fully-optical neural networks" ...


5

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 ...


5

Taking the density matrix $$\rho=W+\frac{I_d}{d}=\frac 1M \sum_{m=1}^M\left|x^{\left(m\right)}\rangle\langle x^{\left(m\right)}\right|,$$ many of the details are all contained in the following paragraph on page 2: Crucial for quantum adaptations of neural networks is the classical-to-quantum read-in of activation patterns. In our setting, ...


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 ...


3

Short, sort-of right answer: you can't This is in essence due to the superconducting qubits that e.g. IBM use being, well, qubits, while continuous variable (CV) operations don't act on qubits. Well, sort of. These are two fundamentally different ways of going about making a quantum computer, so let's start from first principles: When you take a state $\...


3

First, they reduce the size from 28*28 to 4*4 images (by downsampling), then convert into binary values for pixels by just comparing to a value. Then, they encode the data in a quantum uniform superposition (with computational basis representing a bitstring data image with its label).


3

All of the answers here seem to be ignoring a fundamental practical limitation: Deep Learning specifically works best with big data. MNIST is 60000 images, ImageNet is 14 Million images. Meanwhile, the largest quantum computers right now have 50~72 Qbits. Even in the most optimistic scenarios, quantum computers that can handle the volumes of data that ...


3

I am not an expert but I read a few papers and here is what I have found. Similarly to NN, people found strategies to avoid this issue with the gradients. Basically, for some problems, you can use ansatzes that are inspired by the physics of the problem itself. For example, in quantum chemistry, people use something called unitary coupled clusters. See ...


2

On page 2, the authors of the paper write "We continue to use the word 'neural' to describe our network since the term has been adopted by the machine learning community recognizing that the connection to neuroscience is now only historical". As for the question about subset parity, you implement subset parity with controlled unitary gates. However, ...


2

A QNN is a "quantum implementation of a NN" that actually runs on a quantum device. Look for example at this paper by Tacchino et al. A QINN instead is a complex model that runs on traditional hardware (maybe special-purpose, but still classical). For quantum vs. quantum inspired computing, look at this white paper.


2

Here is a latest development from Xanadu, a photonic quantum circuit which mimics a neural network. This is an example of a neural network running on a quantum computer. This photonic circuit contains interferometers and squeezing gates which mimic the weighing functions of a NN, a displacement gate acting as bias and a non-linear transformation similar to ...


2

As of now we can properly simulate only ~50 qubits. You are talking about a full quantum simulation of a vector containing $2^{50}$ elements. In quantum neural networks and quantum annealing, we usually only need something close to the ground state (optimal value) rather than the absolute global minimum. Here is another example from 2017 where 1000 ...


2

I will assume you are asking about D-Wave's quantum annealer. If there is a part of the learning process that can fit the QUBO (Quadratic Unconstrained Binary Optimization) formulation, then yes. The problem however is what to consider as binary variables of your problem. In CNN, we have in general real-valued parameters that we tweak for training (using ...


2

Calculation of the inverse of an $N\times N$ matrix can be done by applying HHL with $N$ different $\vec{b}_i$ (specifically, HHL is applied $N$ times, once for each computational basis vector used as the $\vec{b}_i$). In each case, phase estimation has to be done for an $N \times N$ matrix. The number of qubits required for phase estimation is written on ...


1

How is back-propagation done through the classical weights feeding into the quantum unitaries? In this particular case, the gradient of the quantum variational circuit is computed using the parameter-shift rule. The parameter-shift rule allows us to compute the gradient by simply evaluating linear combinations of the variational circuit under study, so ...


1

As far as I understand from the paper, eq. (13) gives $U_l$ as a product of two qubit unitaries, independently of $l(z)$. Then the authors present two cases, subset parity and subset majority, and derive their specific $U_l$. Thus I guess your classification problem will need its own specialization of eq. (13). If you get an acceptable accuracy with the ...


1

$\newcommand{\ket}[1]{|{#1}\rangle}$ $\newcommand{\bra}[1]{\langle{#1}|}$ Applying $H$ to the auxiliary qubit results in: $\frac{1}{2}(\ket{z,1}(\ket{0}+\ket{1}) + iU\ket{z,1}(\ket{0}-\ket{1}))$ $= \frac{1}{2}(\ket{z,1} + iU\ket{z,1})\ket{0} + \frac{1}{2}(\ket{z,1} - iU\ket{z,1})\ket{1}$ Then the probability of having one on the auxiliary qubit is $p(...


1

I don't think a hello world really exists here. You can have different points of view or goals here. I will give references. The first one is speeding up parts of the algorithm with a quantum version (here is an example reference). But here, we assume a perfect hardware. Another one is to apply it to quantum many-body systems. The interesting point here is ...


1

What are some other proposed applications of quantum neural networks? Absolutely any application of classical neural networks can be an application of quantum neural networks. There's a lot of examples beyond the two you listed. Also, have any of those proposed solutions been programmed/simulated? Yes, for example Ed Farhi of MIT and Hartmut Neven of ...


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