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The adiabatic model This model of quantum computation is motivated by ideas in quantum many-body theory, and differs substantially both from the circuit model (in that it is a continuous-time model) and from continuous-time quantum walks (in that it has a time-dependent evolution). Adiabatic computation usually takes the following form. Start with some ...

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Measurement-based quantum computation (MBQC) This is a way to perform quantum computation, using intermediary measurements as a way of driving the computation rather than just extracting the answers. It is a special case of "quantum circuits with intermediary measurements", and so is no more powerful. However, when it was introduced, it up-ended many people'...

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A Quantum Annealer, such as a D-Wave machine is a physical representation of the Ising model and as such has a 'problem' Hamiltonian of the form $$H_P = \sum_{J=1}^nh_j\sigma_j^z + \sum_{i, j}J_{ij}\sigma_i^z\sigma_j^z.$$ Essentially, the problem to be solved is mapped to the above Hamiltonian. The system starts with the Hamiltonian $H_I = \sum_{J=1}^nh'_j\... 17 The idea of topological quantum computing was introduced by Kitaev in this paper. The basic idea is to build a quantum computer using the properties of exotic types of particles, known as anyons. There are two main properties of anyons that would make them great for this purpose. One is what happens when you use them to create composite particles, a process ... 16 Annealing's more of an analog tactic. The gist is that you have some weird function that you want to optimize. So, you bounce around it. At first, the "temperature" is very high, such that the selected point can bounce around a lot. Then as the algorithm "cools", the temperature goes down, and the bouncing becomes less aggressive. Ultimately, it settles ... 12 The Unitary Circuit Model This is the best well-known model of quantum computation. In this model one has constraints such as the following: a set of qubits initialised to a pure state, which we denote$\lvert 0 \rangle$; a sequence of unitary transformations which one performs on them, which may depend on a classical bit-string$x\in \{0,1\}^n$; one or ... 11 Vinci and Lidar have a nice explanation in their introduction of non-stoquastic Hamiltonians in quantum annealing (which is necessary to a quantum annealing device to simulate gate model computation). https://arxiv.org/abs/1701.07494 It is well known that the solution of computational problems can be encoded into the ground state of a time-dependent quantum ... 11 Discrete-time quantum walk A "discrete-time quantum walk" is a quantum variation on a random walk, in which there is a 'walker' (or multiple 'walkers') which takes small steps in a graph (e.g. a chain of nodes, or a rectangular grid). The difference is that where a random walker takes a step in a randomly determined direction, a quantum walker takes a step ... 11 Since$U$is a normal matrix, the spectral theorem applies, i.e. we can write $$U=\sum_n\lambda_n|\lambda_n\rangle\langle\lambda_n|,$$ where$\lambda_n$are the eigenvalues, and$|\lambda_n\rangle$are the eigenvectors. Moreover, since$UU^\dagger=I$, we know that$|\lambda_n|^2=1$, and thus we can write$\lambda_n=e^{-i\theta_n}$for$\theta_n$in the ... 10 What is a qubit? And what is a quantum computer? Any claim about about which is first will depend on our definitions. One suggestion might be the 1981 experiment by Aspect, Grangier and Roger to demonstrate a violation of Bell’s inequality. My arguments for this are: It uses a physical degree of freedom (photon polarization) which has since been ... 10 Quantum circuits with intermediary measurements This is a slight variation on "unitary circuits", in which one allows measurements in the middle of the algorithm as well as the end, and where one also allows future operations to depend on the outcomes of those measurements. It represents a realistic picture of a quantum processor which interacts with a ... 9 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! 8 I would like to suggest that period finding (a subroutine, if you like, of the famous Shor algorithm) demonstrates a very intuitive, exponential speed-up: It should be intuitively clear that something on the order of (the square root of the uncertainty$\Delta p$) of the period$p$of function evaluations is required classically to find an unknown period$p$... 8 Quantum annealing Quantum annealing is a model of quantum computation which, roughly speaking, generalises the adiabatic model of computation. It has attracted popular — and commercial — attention as a result of D-WAVE's work on the subject. Precisely what quantum annealing consists of is not as well-defined as other models of computation, ... 8 Disclosure: while I am not an experimental physicist, I am part of the NQIT project, which is aiming to develop quantum hardware which is suitable to realise scalable quantum computers. The architecture that we're investing most heavily in is optically linked ion traps. Ions represent some of the physically best understood systems to experimental and ... 8 One of the best places to learn about the continuous-variable (CV) model is the documentation of the Strawberry Fields software for photonic quantum computing. It also includes several numerical examples. You can also read the white paper here, which contains a dedicated section to explaining the CV model. Additionally, this review paper by Braunstein and ... 7 If we have a QTM with state set$Q$and a tape alphabet$\Sigma = \{0,1\}$, we cannot say that the qubit being scanned by the tape head "holds" a vector$a|0\rangle + b|1\rangle$or that the (internal) state is a vector with basis states corresponding to$Q$. The qubits on the tape can be correlated with one another and with the internal state, as well as ... 7 Virtual reality in a classical computer is just a fancy front-end on top of a classical simulation. A classical computer can simulate all of the quantum physics happening inside a quantum computer, including all the phenomena referred to in the question, but only for a limited number of qubits. A 45-qubit circuit was simulated using 0.5PB of RAM in 2017. ... 7 It's difficult to define the point where an experimental setup is a quantum computer. But the crucial feature of a quantum computer is that it's able to perform a quantum computation. The first experimental realization of an algorithm was indeed Jones' and Mosca's implementation of the Deutsch algorithm in 1998 using an NMR setup. Of course previous ... 7 Are there other instances of topological QC that do not use anyons? No, that's basically by definition. That said, there are different ways that one could use topological systems in order to achieve quantum computation. In the version you're talking about, you use these anyon pairs to define qubits, and braid them around each other to create quantum gates. ... 6 Here's a paper comparing Trapped Ion and Superconducting (the main competitors right now) from the group at UMD which compares their trapped ion system with IBM's transmon (superconducting) system. If you want to look at a more algorithm-focused line of thought. If you are looking for a more general summary of the strengths and weaknesses this paper seems ... 6 It think the (very) short answer is that there is not a preferred platform yet. This is why there are very active research communities around each of these technologies. Often if someone says otherwise they are probably working on one of the platforms :) 6 The difficulty with the question is the word intuitive. Intuition basically reflects our understanding of the world around us, which is described by classical physics. Quantum mechanics is exactly the regime where our intuition breaks down because it functions very differently from the world of our everyday experience. As Terry Pratchett said : It’s very ... 6 The point is that free parallel computation or cloning of your existence is a wholesale misinterpretation of the concept of quantum superposition. Quantum states are analogous to probability distributions. If you might wash the dishes or you might wash the floor and you flip a coin to decide which one, then no one takes that to mean that you will wash ... 5 Virtual reality is just a pretty front-end on top of a computer program. So, anything the computer program can do can be given a VR interface. As I see it, what is really being asked for is nice, yet 'authentic' ways of visualising quantum mechanics. One thing that immediately springs to mind is a book I read as an undergraduate, Mr. Tompkins in Paperback. ... 5 Quantum rotor models are quantum systems based on the quantization of systems with rotational configuration spaces. For example, a particle moving on a ring or a pendulum are rotors whose configuration spaces are circular$S^1$, while a rigid body a system whose configuration space is the three-dimensional sphere$S^3$(or equivalently, the group manifold$...

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A non-exhaustive list of theoretical models of quantum computation are provided as answers to another question: "What are the methods of quantum computation?". As to which models are polynomial-time equivalent — the following is an incomplete list of models which are provably universal for polynomial-time quantum computation, assuming perfect control: ...

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The quantum Turing machine can move into a superposition of moving left and right. This is different from the classical Turing machine which can only move either left or right.

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As others have said, VR is just a way of visualizing an output from a computer. If the computer producing the output is classical, it will struggle to visualize a universal set of gates on a many qubit system. Even so, there are ways to visualize systems of few qubits with a classical computer (though not with VR). The Bloch sphere is the well known example ...

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Problems to be solved by a quantum computer can be programmed by creating a set of qubit input registers and connecting them to a set of output registers through an assemblage of quantum logic gates that define the problem to be solved or computation to be done. There are always exactly as many input registers (usually just called qubits) as output ...

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