From bcae81336764eb6c4cdf0f91e2fe632b625dd8b2 Mon Sep 17 00:00:00 2001 From: Prefetch Date: Sun, 23 Oct 2022 22:18:11 +0200 Subject: Optimize and improve naming of all images in knowledge base --- source/_includes/image.html | 34 +++++++ .../bernstein-vazirani-circuit.avif | Bin 0 -> 3710 bytes .../concept/bernstein-vazirani-algorithm/index.md | 4 +- source/know/concept/bloch-sphere/bloch-small.jpg | Bin 37110 -> 0 bytes source/know/concept/bloch-sphere/bloch.jpg | Bin 98023 -> 0 bytes source/know/concept/bloch-sphere/index.md | 4 +- source/know/concept/bloch-sphere/sketch-full.png | Bin 0 -> 98869 bytes source/know/concept/bloch-sphere/sketch-half.avif | Bin 0 -> 11592 bytes source/know/concept/bloch-sphere/sketch-half.jpg | Bin 0 -> 56094 bytes source/know/concept/bloch-sphere/sketch-half.png | Bin 0 -> 60457 bytes source/know/concept/bloch-sphere/sketch-half.webp | Bin 0 -> 27428 bytes .../deutsch-jozsa-algorithm/deutsch-circuit.avif | Bin 0 -> 2028 bytes 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source/know/concept/toffoli-gate/xor.avif diff --git a/source/_includes/image.html b/source/_includes/image.html new file mode 100644 index 0000000..a9bc3fd --- /dev/null +++ b/source/_includes/image.html @@ -0,0 +1,34 @@ +{% assign name_dot_format = include.file | split: "." %} +{% assign name = name_dot_format | first %} +{% assign format = name_dot_format | last %} + +{% comment %} Let 'suffix' = last 4 chars of 'name', 'prefix' = the rest {% endcomment %} +{% assign suffix = name | slice: -4, 4 %} +{% assign rname = name | split: "" | reverse | join: "" %} +{% assign rsuffix = suffix | split: "" | reverse | join: "" %} +{% assign rprefix = rname | remove_first: rsuffix %} +{% assign prefix = rprefix | split: "" | reverse | join: "" %} + +{% comment %} If 'name' ends in "full", half-size image must exist {% endcomment %} +{% assign name_full = name %} +{% if suffix == "full" %} + {% assign name_half = prefix | append: "half" %} +{% else %} + {% assign name_half = name_full %} +{% endif %} + +{% comment %} Insert the image, linking to the full-size version {% endcomment %} +

+ + {% assign set_width = "width:" | append: include.width %} + + + {% if name_full == name_half %} + {{ include.alt }} + {% else %} + + {{ include.alt }} + {% endif %} + + +

diff --git a/source/know/concept/bernstein-vazirani-algorithm/bernstein-vazirani-circuit.avif b/source/know/concept/bernstein-vazirani-algorithm/bernstein-vazirani-circuit.avif new file mode 100644 index 0000000..7bfd114 Binary files /dev/null and b/source/know/concept/bernstein-vazirani-algorithm/bernstein-vazirani-circuit.avif differ diff --git a/source/know/concept/bernstein-vazirani-algorithm/index.md b/source/know/concept/bernstein-vazirani-algorithm/index.md index f91c0ba..85017dc 100644 --- a/source/know/concept/bernstein-vazirani-algorithm/index.md +++ b/source/know/concept/bernstein-vazirani-algorithm/index.md @@ -36,9 +36,7 @@ However, the Bernstein-Vazirani algorithm allows a quantum computer to do it with only a single query. It uses the following circuit: - - - +{% include image.html file="bernstein-vazirani-circuit.png" width="52%" alt="Bernstein-Vazirani circuit" %} Where $$U_f$$ is a phase oracle, whose action is defined as follows, diff --git a/source/know/concept/bloch-sphere/bloch-small.jpg b/source/know/concept/bloch-sphere/bloch-small.jpg deleted file mode 100644 index e99c0e1..0000000 Binary files a/source/know/concept/bloch-sphere/bloch-small.jpg and /dev/null differ diff --git a/source/know/concept/bloch-sphere/bloch.jpg b/source/know/concept/bloch-sphere/bloch.jpg deleted file mode 100644 index 9515d84..0000000 Binary files a/source/know/concept/bloch-sphere/bloch.jpg and /dev/null differ diff --git a/source/know/concept/bloch-sphere/index.md b/source/know/concept/bloch-sphere/index.md index 2cb7742..0ca6f1b 100644 --- a/source/know/concept/bloch-sphere/index.md +++ b/source/know/concept/bloch-sphere/index.md @@ -13,9 +13,7 @@ In quantum mechanics, particularly quantum information, the **Bloch sphere** is an invaluable tool to visualize qubits. All pure qubit states are represented by a point on the sphere's surface: - - - +{% include image.html file="sketch-full.png" width="67%" alt="Bloch sphere" %} The $$x$$, $$y$$ and $$z$$-axes represent the components of a spin-1/2-alike system, and their extremes are the eigenstates of the Pauli matrices: diff --git a/source/know/concept/bloch-sphere/sketch-full.png b/source/know/concept/bloch-sphere/sketch-full.png new file mode 100644 index 0000000..709aceb Binary files /dev/null and b/source/know/concept/bloch-sphere/sketch-full.png differ diff --git a/source/know/concept/bloch-sphere/sketch-half.avif b/source/know/concept/bloch-sphere/sketch-half.avif new file mode 100644 index 0000000..1752c9d Binary files /dev/null and b/source/know/concept/bloch-sphere/sketch-half.avif differ diff --git a/source/know/concept/bloch-sphere/sketch-half.jpg b/source/know/concept/bloch-sphere/sketch-half.jpg new file mode 100644 index 0000000..28b97d7 Binary files /dev/null and b/source/know/concept/bloch-sphere/sketch-half.jpg differ diff --git a/source/know/concept/bloch-sphere/sketch-half.png b/source/know/concept/bloch-sphere/sketch-half.png new file mode 100644 index 0000000..d48102d Binary files /dev/null and b/source/know/concept/bloch-sphere/sketch-half.png differ diff --git a/source/know/concept/bloch-sphere/sketch-half.webp b/source/know/concept/bloch-sphere/sketch-half.webp new file mode 100644 index 0000000..257145b Binary files /dev/null and b/source/know/concept/bloch-sphere/sketch-half.webp differ diff --git a/source/know/concept/deutsch-jozsa-algorithm/deutsch-circuit.avif b/source/know/concept/deutsch-jozsa-algorithm/deutsch-circuit.avif new file mode 100644 index 0000000..c498cd9 Binary files /dev/null and b/source/know/concept/deutsch-jozsa-algorithm/deutsch-circuit.avif differ diff --git a/source/know/concept/deutsch-jozsa-algorithm/deutsch-jozsa-circuit.avif b/source/know/concept/deutsch-jozsa-algorithm/deutsch-jozsa-circuit.avif new file mode 100644 index 0000000..2312ff3 Binary files /dev/null and b/source/know/concept/deutsch-jozsa-algorithm/deutsch-jozsa-circuit.avif differ diff --git a/source/know/concept/deutsch-jozsa-algorithm/index.md b/source/know/concept/deutsch-jozsa-algorithm/index.md index bbdd58d..5f2f268 100644 --- a/source/know/concept/deutsch-jozsa-algorithm/index.md +++ b/source/know/concept/deutsch-jozsa-algorithm/index.md @@ -27,6 +27,7 @@ while classical computers need up to $$2^{N - 1} + 1$$ queries for an $$N$$-bit $$x$$. + ## Deutsch algorithm The Deutsch algorithm handles the simplest case, @@ -40,9 +41,7 @@ In other words, we only need to determine if $$f(0) = f(1)$$ or $$f(0) \neq f(1) To do this, we use the following quantum circuit, where $$U_f$$ is the oracle we query: - - - +{% include image.html file="deutsch-circuit.png" width="48%" alt="Deutsch circuit" %} Due to unitarity constraints, the action of $$U_f$$ is defined to be as follows, @@ -134,16 +133,15 @@ A classical computer would need to query it twice, once with input $$x = 0$$, and again with $$x = 1$$. -## Full Deutsch-Jozsa algorithm + +## Deutsch-Jozsa algorithm The Deutsch-Jozsa algorithm generalizes the above to $$N$$-bit inputs $$x$$. We are promised that $$f(x)$$ is either constant or balanced; other possibilities are assumed to be impossible. This algorithm is then implemented by the following quantum circuit: - - - +{% include image.html file="deutsch-jozsa-circuit.png" width="52%" alt="Deutsch-Jozsa circuit" %} There are $$N$$ qubits in initial state $$\Ket{0}$$, and one in $$\Ket{1}$$. For clarity, the oracle $$U_f$$ works like so: diff --git a/source/know/concept/dispersive-broadening/index.md b/source/know/concept/dispersive-broadening/index.md index 4e4cf82..746eb6d 100644 --- a/source/know/concept/dispersive-broadening/index.md +++ b/source/know/concept/dispersive-broadening/index.md @@ -59,9 +59,7 @@ This phenomenon is illustrated below for our example of a Gaussian pulse with parameter values $$T_0 = 1\:\mathrm{ps}$$, $$P_0 = 1\:\mathrm{kW}$$, $$\beta_2 = -10 \:\mathrm{ps}^2/\mathrm{m}$$ and $$\gamma = 0$$: - - - +{% include image.html file="simulation-full.png" width="100%" alt="Dispersive broadening simulation results" %} The **instantaneous frequency** $$\omega_\mathrm{GVD}(z, t)$$, which describes the dominant angular frequency at a given point in the time domain, diff --git a/source/know/concept/dispersive-broadening/pheno-disp-small.jpg b/source/know/concept/dispersive-broadening/pheno-disp-small.jpg deleted file mode 100644 index 8c70eac..0000000 Binary files a/source/know/concept/dispersive-broadening/pheno-disp-small.jpg and /dev/null differ diff --git a/source/know/concept/dispersive-broadening/pheno-disp.jpg b/source/know/concept/dispersive-broadening/pheno-disp.jpg deleted file mode 100644 index a97312b..0000000 Binary files a/source/know/concept/dispersive-broadening/pheno-disp.jpg and /dev/null differ diff --git a/source/know/concept/dispersive-broadening/simulation-full.png b/source/know/concept/dispersive-broadening/simulation-full.png new file mode 100644 index 0000000..5ff78dc Binary files /dev/null and b/source/know/concept/dispersive-broadening/simulation-full.png differ diff --git a/source/know/concept/dispersive-broadening/simulation-half.avif b/source/know/concept/dispersive-broadening/simulation-half.avif new file mode 100644 index 0000000..7f5d2ad Binary files /dev/null and b/source/know/concept/dispersive-broadening/simulation-half.avif differ diff --git a/source/know/concept/dispersive-broadening/simulation-half.jpg b/source/know/concept/dispersive-broadening/simulation-half.jpg new file mode 100644 index 0000000..3d9a53a Binary files /dev/null and b/source/know/concept/dispersive-broadening/simulation-half.jpg differ diff --git a/source/know/concept/dispersive-broadening/simulation-half.png b/source/know/concept/dispersive-broadening/simulation-half.png new file mode 100644 index 0000000..a7b4aac Binary files /dev/null and b/source/know/concept/dispersive-broadening/simulation-half.png differ diff --git a/source/know/concept/dispersive-broadening/simulation-half.webp b/source/know/concept/dispersive-broadening/simulation-half.webp new file mode 100644 index 0000000..a781bc4 Binary files /dev/null and b/source/know/concept/dispersive-broadening/simulation-half.webp differ diff --git a/source/know/concept/fabry-perot-cavity/cavity.png b/source/know/concept/fabry-perot-cavity/cavity.png deleted file mode 100644 index f7b0c2a..0000000 Binary files a/source/know/concept/fabry-perot-cavity/cavity.png and /dev/null differ diff --git a/source/know/concept/fabry-perot-cavity/index.md b/source/know/concept/fabry-perot-cavity/index.md index 980fa54..6eefc6e 100644 --- a/source/know/concept/fabry-perot-cavity/index.md +++ b/source/know/concept/fabry-perot-cavity/index.md @@ -19,9 +19,8 @@ We divide the $$x$$-axis into three domains: left $$L$$, center $$C$$, and right The cavity $$C$$ has length $$\ell$$ and is centered on $$x = 0$$. Let $$n_L$$, $$n_C$$ and $$n_R$$ be the respective domains' refractive indices: - - - +{% include image.html file="sketch-full.png" width="70%" alt="Cavity structure" %} + ## Microscopic cavity @@ -129,6 +128,7 @@ $$A_1$$, $$A_2$$, $$A_3$$ or $$A_4$$ freely, and then the others are determined by $$k_m$$ and the field's continuity. + ## Macroscopic cavity Next, consider a "macroscopic" Fabry-Pérot cavity diff --git a/source/know/concept/fabry-perot-cavity/sketch-full.png b/source/know/concept/fabry-perot-cavity/sketch-full.png new file mode 100644 index 0000000..0568fd2 Binary files /dev/null and b/source/know/concept/fabry-perot-cavity/sketch-full.png differ diff --git a/source/know/concept/fabry-perot-cavity/sketch-half.avif b/source/know/concept/fabry-perot-cavity/sketch-half.avif new file mode 100644 index 0000000..e980a70 Binary files /dev/null and b/source/know/concept/fabry-perot-cavity/sketch-half.avif differ diff --git a/source/know/concept/fabry-perot-cavity/sketch-half.jpg 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b/source/know/concept/feynman-diagram/impurity.png differ diff --git a/source/know/concept/feynman-diagram/index.md b/source/know/concept/feynman-diagram/index.md index c36e7df..ace8dbc 100644 --- a/source/know/concept/feynman-diagram/index.md +++ b/source/know/concept/feynman-diagram/index.md @@ -25,6 +25,7 @@ Below, we go through the most notable components of Feynman diagrams and how to translate them into a mathematical expression. + ## Real space The most common component is a **fermion line**, which represents @@ -37,9 +38,7 @@ Let the subscript $$I$$ refer to the and $$\mathcal{T}\{\}$$ denote the [time-ordered product](/know/concept/time-ordered-product/): - - - +{% include image.html file="fermion-light.png" width="60%" alt="Fermion line diagram" %} $$\begin{aligned} = i \hbar G_{s_2 s_1}^0(\vb{r}_2, t_2; \vb{r}_1, t_1) @@ -59,9 +58,7 @@ Less common is a **heavy fermion line**, representing a causal Green's function $$G$$ for the entire Hamiltonian $$\hat{H}$$, where the subscript $$H$$ refers to the [Heisenberg picture](/know/concept/heisenberg-picture/): - - - +{% include image.html file="fermion-heavy.png" width="60%" alt="Heavy fermion line diagram" %} $$\begin{aligned} = i \hbar G_{s_2 s_1}(\vb{r}_2, t_2; \vb{r}_1, t_1) @@ -75,9 +72,7 @@ which we assume to be instantaneous, i.e. time-independent hence it starts and ends at the same time, and no arrow is drawn: - - - +{% include image.html file="boson.png" width="60%" alt="Boson/interaction line diagram" %} $$\begin{aligned} = \frac{1}{i \hbar} W_{s_2 s_1}(\vb{r}_2, t_2; \vb{r}_1, t_1) @@ -99,9 +94,7 @@ $$\begin{aligned} One-body (time-dependent) operators $$\hat{V}$$ in $$\hat{H}_1$$ are instead represented by a special vertex: - - - +{% include image.html file="impurity.png" width="35%" alt="One-body perturbation (e.g. impurity) diagram" %} $$\begin{aligned} = \frac{1}{i \hbar} V_s(\vb{r}, t) @@ -148,6 +141,7 @@ so that a particle with a given spin propagates from vertex to vertex without getting flipped. + ## Fourier space If the system is time-independent and spatially uniform, @@ -177,9 +171,7 @@ Working in Fourier space allows us to simplify calculations. Consider the following diagram and the resulting expression, where $$\tilde{\vb{r}} = (\vb{r}, t)$$, and $$\tilde{\vb{k}} = (\vb{k}, \omega)$$: - - - +{% include image.html file="example.png" width="40%" alt="Example: fermion-fermion interaction" %} $$\begin{aligned} &= (i \hbar)^3 \sum_{s s'} \!\!\iint \dd{\tilde{\vb{r}}} \dd{\tilde{\vb{r}}'} @@ -274,6 +266,7 @@ then conservation removes all internal variables, so no integrals would be needed. + ## Imaginary time Feynman diagrams are also useful when working with diff --git a/source/know/concept/feynman-diagram/interaction.png b/source/know/concept/feynman-diagram/interaction.png deleted file mode 100644 index 3c2d093..0000000 Binary files a/source/know/concept/feynman-diagram/interaction.png and /dev/null differ diff --git a/source/know/concept/feynman-diagram/perturbation.png b/source/know/concept/feynman-diagram/perturbation.png deleted file mode 100644 index 2e8fbf6..0000000 Binary files a/source/know/concept/feynman-diagram/perturbation.png and /dev/null differ diff --git a/source/know/concept/metacentric-height/index.md b/source/know/concept/metacentric-height/index.md index 3d0c9a5..3d81d44 100644 --- a/source/know/concept/metacentric-height/index.md +++ b/source/know/concept/metacentric-height/index.md @@ -26,9 +26,7 @@ does not coincide with the origin in general, as is illustrated in the following sketch of our choice of coordinate system: - - - +{% include image.html file="sketch-full.png" width="75%" alt="Boat's coordinate system" %} Here, $$B$$ is the **center of buoyancy**, equal to the center of mass of the volume of water displaced by the boat diff --git a/source/know/concept/metacentric-height/sketch-full.png b/source/know/concept/metacentric-height/sketch-full.png new file mode 100644 index 0000000..f76350b Binary files /dev/null and b/source/know/concept/metacentric-height/sketch-full.png differ diff --git a/source/know/concept/metacentric-height/sketch-half.avif b/source/know/concept/metacentric-height/sketch-half.avif new file mode 100644 index 0000000..e6be2dc Binary files /dev/null and b/source/know/concept/metacentric-height/sketch-half.avif differ diff --git a/source/know/concept/metacentric-height/sketch-half.jpg b/source/know/concept/metacentric-height/sketch-half.jpg new file mode 100644 index 0000000..066bc93 Binary files /dev/null and b/source/know/concept/metacentric-height/sketch-half.jpg differ diff --git a/source/know/concept/metacentric-height/sketch-half.png b/source/know/concept/metacentric-height/sketch-half.png new file mode 100644 index 0000000..6835bbc Binary files /dev/null and b/source/know/concept/metacentric-height/sketch-half.png differ diff --git a/source/know/concept/metacentric-height/sketch-half.webp b/source/know/concept/metacentric-height/sketch-half.webp new file mode 100644 index 0000000..70af91d Binary files /dev/null and b/source/know/concept/metacentric-height/sketch-half.webp differ diff --git a/source/know/concept/metacentric-height/sketch.jpg b/source/know/concept/metacentric-height/sketch.jpg deleted file mode 100644 index 6a0544b..0000000 Binary files a/source/know/concept/metacentric-height/sketch.jpg and /dev/null differ diff --git a/source/know/concept/modulational-instability/index.md b/source/know/concept/modulational-instability/index.md index a01293c..e29b2d5 100644 --- a/source/know/concept/modulational-instability/index.md +++ b/source/know/concept/modulational-instability/index.md @@ -172,9 +172,7 @@ $$\begin{aligned} = \sqrt{P_0} \sech\!\Big(\frac{t}{T_0}\Big) \end{aligned}$$ - - - +{% include image.html file="simulation-full.png" width="100%" alt="Modulational instability simulation results" %} Where $$L_\mathrm{NL} = 1/(\gamma P_0)$$ is the characteristic length of nonlinear effects. 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To demonstrate this, spectrograms of the same simulation @@ -53,9 +51,7 @@ After OWB, a train of small waves falls off the edges, which eventually melt together, leading to a trapezoid shape in the $$t$$-domain. Dispersive broadening then continues normally: - - - +{% include image.html file="spectrograms-full.png" width="100%" alt="Spectrograms of pulse shape evolution" %} We call the distance at which the wave breaks $$L_\mathrm{WB}$$, and would like to analytically predict it. @@ -183,9 +179,7 @@ $$\begin{aligned} This prediction for $$L_\mathrm{WB}$$ appears to agree well with the OWB observed in the simulation: - - - +{% include image.html file="simulation-full.png" width="100%" alt="Optical wave breaking simulation results" %} Because all spectral broadening up to $$L_\mathrm{WB}$$ is caused by SPM, whose frequency behaviour is known, it is in fact possible to draw diff --git a/source/know/concept/optical-wave-breaking/pheno-break-inst-small.jpg b/source/know/concept/optical-wave-breaking/pheno-break-inst-small.jpg deleted file mode 100644 index f7568e6..0000000 Binary files a/source/know/concept/optical-wave-breaking/pheno-break-inst-small.jpg and /dev/null differ diff --git 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b/source/know/concept/optical-wave-breaking/spectrograms-half.png differ diff --git a/source/know/concept/optical-wave-breaking/spectrograms-half.webp b/source/know/concept/optical-wave-breaking/spectrograms-half.webp new file mode 100644 index 0000000..b0c3fad Binary files /dev/null and b/source/know/concept/optical-wave-breaking/spectrograms-half.webp differ diff --git a/source/know/concept/quantum-fourier-transform/index.md b/source/know/concept/quantum-fourier-transform/index.md index 113367c..1c68ad0 100644 --- a/source/know/concept/quantum-fourier-transform/index.md +++ b/source/know/concept/quantum-fourier-transform/index.md @@ -172,17 +172,13 @@ The quantum circuit to execute the mentioned steps is illustrated below, excluding the swapping part to get the right order. Here, $$R_m$$ means $$R_\phi$$ with $$\phi = 2 \pi / 2^m$$: - - - +{% include image.html file="qft-circuit-noswap.png" width="100%" alt="QFT circuit, without final swap" %} Again, note how the inputs $$\Ket{x_j}$$ and outputs $$\Ket{k_j}$$ are in the opposite order. The complete circuit, including the swapping at the end, therefore looks like this: - - - +{% include image.html file="qft-circuit-swap.png" width="85%" alt="QFT circuit, including final swap" %} For each of the $$n$$ qubits, $$\mathcal{O}(n)$$ gates are applied, so overall the QFT algorithm is $$\mathcal{O}(n^2)$$. diff --git a/source/know/concept/quantum-fourier-transform/qft-circuit-noswap.avif b/source/know/concept/quantum-fourier-transform/qft-circuit-noswap.avif new file mode 100644 index 0000000..bee92cd Binary files /dev/null and b/source/know/concept/quantum-fourier-transform/qft-circuit-noswap.avif differ diff --git a/source/know/concept/quantum-fourier-transform/qft-circuit-swap.avif b/source/know/concept/quantum-fourier-transform/qft-circuit-swap.avif new file mode 100644 index 0000000..6f41319 Binary files /dev/null and b/source/know/concept/quantum-fourier-transform/qft-circuit-swap.avif differ diff --git a/source/know/concept/quantum-gate/cnot.avif b/source/know/concept/quantum-gate/cnot.avif new file mode 100644 index 0000000..75e36ae Binary files /dev/null and b/source/know/concept/quantum-gate/cnot.avif differ diff --git a/source/know/concept/quantum-gate/cu.avif b/source/know/concept/quantum-gate/cu.avif new file mode 100644 index 0000000..e58c66a Binary files /dev/null and b/source/know/concept/quantum-gate/cu.avif differ diff --git a/source/know/concept/quantum-gate/index.md b/source/know/concept/quantum-gate/index.md index 8c251be..e8ff579 100644 --- a/source/know/concept/quantum-gate/index.md +++ b/source/know/concept/quantum-gate/index.md @@ -14,6 +14,7 @@ the number of possible quantum gates is uncountably infinite, so we only consider the most important examples here. + ## One-qubit gates As an example, consider the following must general single-qubit state $$\Ket{\psi}$$: @@ -165,6 +166,7 @@ This is the definition of universality: any state can be approximated. + ## Two-qubit gates As an example, let us consider @@ -202,9 +204,7 @@ but not always in the basis of $$\Ket{0}_1$$, $$\Ket{1}_1$$, $$\Ket{0}_2$$ and $ With that said, the first two-qubit gate is $$\mathrm{SWAP}$$, which simply swaps $$\Ket{\psi_1}$$ and $$\Ket{\psi_2}$$: - - - +{% include image.html file="swap.png" width="22%" alt="SWAP gate diagram" %} $$\begin{aligned} \boxed{ @@ -231,9 +231,7 @@ $$\begin{aligned} Next, there is the **controlled NOT gate** $$\mathrm{CNOT}$$, which "flips" (applies $$X$$ to) $$\Ket{\psi_2}$$ if $$\Ket{\psi_1}$$ is true: - - - +{% include image.html file="cnot.png" width="22%" alt="CNOT gate diagram" %} $$\begin{aligned} \boxed{ @@ -258,9 +256,7 @@ More generally, from every one-qubit gate $$U$$, we can define a two-qubit **controlled U gate** $$\mathrm{CU}$$, which applies $$U$$ to $$\Ket{\psi_2}$$ if $$\Ket{\psi_1}$$ is true: - - - +{% include image.html file="cu.png" width="22%" alt="CU gate diagram" %} $$\begin{aligned} \boxed{ diff --git a/source/know/concept/quantum-gate/swap.avif b/source/know/concept/quantum-gate/swap.avif new file mode 100644 index 0000000..a70c43c Binary files /dev/null and b/source/know/concept/quantum-gate/swap.avif differ diff --git a/source/know/concept/random-phase-approximation/dyson.avif b/source/know/concept/random-phase-approximation/dyson.avif new file mode 100644 index 0000000..dc80856 Binary files /dev/null and b/source/know/concept/random-phase-approximation/dyson.avif differ diff --git a/source/know/concept/random-phase-approximation/index.md b/source/know/concept/random-phase-approximation/index.md index 0f53136..698e1e7 100644 --- a/source/know/concept/random-phase-approximation/index.md +++ b/source/know/concept/random-phase-approximation/index.md @@ -71,23 +71,17 @@ leaving only the single most divergent one at each order $$n$$, i.e. the ones where all $$n$$ interaction lines carry the same momentum and energy: - - - +{% include image.html file="self-energy.png" width="92%" alt="RPA self-energy definition" %} Where we have defined the **screened interaction** $$W^\mathrm{RPA}$$, denoted by a double wavy line: - - - +{% include image.html file="interaction.png" width="95%" alt="RPA screened interaction definition" %} Rearranging the above sequence of diagrams quickly leads to the following [Dyson equation](/know/concept/dyson-equation/): - - - +{% include image.html file="dyson.png" width="55%" alt="Dyson equation for screened interaction" %} In Fourier space, this equation's linear shape means it is algebraic, so we can write it out: @@ -104,9 +98,7 @@ with an internal wavevector $$\vb{q}$$, fermionic frequency $$i \omega_m^F$$, an Abbreviating $$\tilde{\vb{k}} \equiv (\vb{k}, i \omega_n^B)$$ and $$\tilde{\vb{q}} \equiv (\vb{q}, i \omega_n^F)$$: - - - +{% include image.html file="pairbubble.png" width="45%" alt="Internal variables of pair-bubble diagram" %} We isolate the Dyson equation for $$W^\mathrm{RPA}$$, which reveals its physical interpretation as a *screened* interaction: diff --git a/source/know/concept/random-phase-approximation/interaction.avif b/source/know/concept/random-phase-approximation/interaction.avif new file mode 100644 index 0000000..f3f6cbe Binary files /dev/null and b/source/know/concept/random-phase-approximation/interaction.avif differ diff --git a/source/know/concept/random-phase-approximation/interaction.png b/source/know/concept/random-phase-approximation/interaction.png new file mode 100644 index 0000000..bb5ccdd Binary files /dev/null and b/source/know/concept/random-phase-approximation/interaction.png differ diff --git a/source/know/concept/random-phase-approximation/pairbubble.avif b/source/know/concept/random-phase-approximation/pairbubble.avif new file mode 100644 index 0000000..bca964e Binary files /dev/null and b/source/know/concept/random-phase-approximation/pairbubble.avif differ diff --git a/source/know/concept/random-phase-approximation/rpasigma.png b/source/know/concept/random-phase-approximation/rpasigma.png deleted file mode 100644 index fedc9f5..0000000 Binary files a/source/know/concept/random-phase-approximation/rpasigma.png and /dev/null differ diff --git a/source/know/concept/random-phase-approximation/screened.png b/source/know/concept/random-phase-approximation/screened.png deleted file mode 100644 index bb5ccdd..0000000 Binary files a/source/know/concept/random-phase-approximation/screened.png and /dev/null differ diff --git a/source/know/concept/random-phase-approximation/self-energy.avif b/source/know/concept/random-phase-approximation/self-energy.avif new file mode 100644 index 0000000..3ddfed7 Binary files /dev/null and b/source/know/concept/random-phase-approximation/self-energy.avif differ diff --git a/source/know/concept/random-phase-approximation/self-energy.png b/source/know/concept/random-phase-approximation/self-energy.png new file mode 100644 index 0000000..fedc9f5 Binary files /dev/null and b/source/know/concept/random-phase-approximation/self-energy.png differ diff --git a/source/know/concept/repetition-code/bit-flip-detect.avif b/source/know/concept/repetition-code/bit-flip-detect.avif new file mode 100644 index 0000000..83d509a Binary files /dev/null and b/source/know/concept/repetition-code/bit-flip-detect.avif differ diff --git a/source/know/concept/repetition-code/bit-flip-encode.avif b/source/know/concept/repetition-code/bit-flip-encode.avif new file mode 100644 index 0000000..37bc495 Binary files /dev/null and b/source/know/concept/repetition-code/bit-flip-encode.avif differ diff --git a/source/know/concept/repetition-code/index.md b/source/know/concept/repetition-code/index.md index 99ac630..678211e 100644 --- a/source/know/concept/repetition-code/index.md +++ b/source/know/concept/repetition-code/index.md @@ -27,6 +27,7 @@ albeit with some complications, as discussed below. + ## Bit flip code Suppose that we want to detect errors in @@ -76