\end{equation} &= I+\left(-i\Delta t\right)\left|x\right\rangle\left\langle x\right|+\frac{\left(-i\Delta t\right)^2}{2}\left|x\right\rangle\left\langle x\right|+\frac{\left(-i\Delta t\right)^3}{6}\left|x\right\rangle\left\langle x\right|+\cdots \\ &= \left(\mathrm{e}^{-i\Delta t}\left|x\right\rangle\left\langle x\right|+\left|y\right\rangle\left\langle y\right|\right)\left|y\right\rangle\left|0\right\rangle \\ Guillaume Aubrun (Lyon 1), Andre Chailloux (Inria Paris), Omar Fawzi (ENS Lyon) This course will give the student the basics of quantum information science, as well as some selected research topics in particular on quantum algorithms and on the mathematics of quantum states. \left|\psi_5\right\rangle &= \left(\sum_j\left\langle j\middle|y\right\rangle\left|j\right\rangle-\frac{1}{\sqrt{N}}\sum_j\left\langle j\middle|y\right\rangle\sum_k\left|k\right\rangle\right)\left|0\right\rangle+\frac{\mathrm{e}^{-i\Delta t}}{\sqrt{N}}\sum_j\left\langle j\middle|y\right\rangle\sum_k\left|k\right\rangle\left|0\right\rangle \\ \left|\psi_2\right\rangle &= \left(\sum_j\left\langle j\middle|y\right\rangle H^{\otimes n}\left|j\right\rangle-\frac{1}{\sqrt{N}}\sum_j\left\langle j\middle|y\right\rangle\left|0\right\rangle\right)\left|0\right\rangle+\frac{1}{\sqrt{N}}\sum_j\left\langle j\middle|y\right\rangle\left|0\right\rangle\left|1\right\rangle \\ $$, $$ &= I+\left[\sum_{j=1}^{\infty}\frac{\left(-i\Delta t\right)^j}{j! There is no guarantee that these solutions are correct. If nothing happens, download Xcode and try again. \begin{align} }\right]\left|x\right\rangle\left\langle x\right| \\ Entanglement, teleportation and the possibility of using the non-local behavior of quantum mechanics to factor integers in random polynomial time have also added to … Quantum Information and Computation General information. $$, $$ The quantum computer is the Philosopher's Stone of our century, and Nielsen and Chuang is our basic book of incantations. $$, $$ &= \left(I-\left|\psi\right\rangle\left\langle\psi\right|+\mathrm{e}^{-i\Delta t}\left|\psi\right\rangle\left\langle\psi\right|\right)\left|y\right\rangle\left|0\right\rangle Quantum Computation and Quantum Information is a textbook about quantum information science written by Michael Nielsen and Isaac Chuang, regarded as a standard text on the subject. $$, $$ You can always update your selection by clicking Cookie Preferences at the bottom of the page. \end{align} &= -\left(a_1a_2\left|00\right\rangle-a_1b_2\left|01\right\rangle-b_1a_2\left|10\right\rangle-b_1b_2\left|11\right\rangle\right) \\ &= \left(\sum_j\left\langle j\middle|y\right\rangle H^{\otimes n}\left|j\right\rangle-\frac{1}{\sqrt{N}}\sum_j\left\langle j\middle|y\right\rangle\left|0\right\rangle\right)\left|0\right\rangle+\frac{1}{\sqrt{N}}\sum_j\left\langle j\middle|y\right\rangle\left|0\right\rangle\left|0\right\rangle \\ &= \left(\sum_{j}\left|j\right\rangle\left\langle j\right|\right)\left|y\right\rangle\left|0\right\rangle \\ Clearly, $G$ corresponds to the $\theta$-rotation in $\left|\alpha\right\rangle-\left|\beta\right\rangle$ plane because $O$ is the $-\theta$ rotation followed by $2\theta$ rotation. &= \frac{2}{N}\sum_{x=0}^{N-1}\sum_k\alpha_k\left|x\right\rangle-\sum_k\alpha_k\left|k\right\rangle \\ they're used to log you in. &= \left(\sum_{j=0}^{N-1}\left|j\right\rangle\left\langle j\right|-\frac{1}{\sqrt{N}}\sum_{k=0}^{N-1}\left|k\right\rangle\frac{1}{\sqrt{N}}\sum_{j=0}^{N-1}\left\langle j\right|\right)\left|y\right\rangle\left|0\right\rangle+\frac{\mathrm{e}^{-i\Delta t}}{\sqrt{N}}\sum_{k=0}^{N-1}\left|k\right\rangle\frac{1}{\sqrt{N}}\sum_{j=0}^{N-1}\left\langle j\right|\left|y\right\rangle\left|0\right\rangle \\ So it is especially useful for students who want to become acquainted with quantum information and computation. The register qubit is transformed into $\left|\beta\right\rangle$, which is the linear combination of the solutions. \left|\psi_4\right\rangle &= \left(\sum_j\left\langle j\middle|y\right\rangle H^{\otimes n}\left|j\right\rangle-\frac{1}{\sqrt{N}}\sum_j\left\langle j\middle|y\right\rangle\left|0\right\rangle\right)\left|0\right\rangle+\mathrm{e}^{-i\Delta t}\frac{1}{\sqrt{N}}\sum_j\left\langle j\middle|y\right\rangle\left|0\right\rangle\left|0\right\rangle \\ \begin{align} \left|\psi_5\right\rangle &= a_1\left|0\right\rangle\left(-a_2\left|0\right\rangle+b_2\left|1\right\rangle\right)+b_1\left|1\right\rangle\left(a_2\left|0\right\rangle+b_2\left|1\right\rangle\right) \\ & & & \ddots & \\ You signed in with another tab or window. \left|\psi_3\right\rangle &= \frac{b_1}{\sqrt{2}}\left|0\right\rangle\left(\left(a_2+b_2\right)\left|0\right\rangle+\left(b_2-a_2\right)\left|1\right\rangle\right)+\frac{a_1}{\sqrt{2}}\left|1\right\rangle\left(\left(b_2-a_2\right)\left|0\right\rangle+\left(a_2+b_2\right)\left|1\right\rangle\right) \\ --Zentralblatt MATH. \left|\psi_0\right\rangle &= \left(a_1\left|0\right\rangle+b_1\left|1\right\rangle\right)\left(a_2\left|0\right\rangle+b_2\left|1\right\rangle\right) \\ Solution for Quantum Computation and Quantum Information by Nielsen and Chuang. This is unofficial solution manual for "Quantum Computation and Quantum Information: 10th Anniversary Edition" (ISBN-13: 978-1107002173) by Nielsen and Chuang. &= I+\left(-i\Delta t\right)\left|\psi\right\rangle\left\langle\psi\right| + \frac{\left(-i\Delta t\right)^2}{2}\left|\psi\right\rangle\left\langle\psi\right|+\frac{\left(-i\Delta t\right)^3}{6}\left|\psi\right\rangle\left\langle\psi\right|+\cdots \\ Solution for Quantum Computation and Quantum Information. If nothing happens, download GitHub Desktop and try again. We use optional third-party analytics cookies to understand how you use GitHub.com so we can build better products. get the PDF. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. &= -\left(2\left|00\right\rangle - I\right)\left|\phi_1\phi_2\right\rangle Learn more. We use optional third-party analytics cookies to understand how you use GitHub.com so we can build better products. \left|\psi_2\right\rangle &= \mathrm{e}^{-i\Delta t}\left\langle x\middle|y\right\rangle \left|x\right\rangle\left|1\right\rangle + \left\langle y\middle|y\right\rangle\left|y\right\rangle\left|0\right\rangle \\ We use essential cookies to perform essential website functions, e.g. $$ 2\left|0\right\rangle\left\langle0\right|-I &= 2\left|0\right\rangle\left\langle0\right|-\sum_{j=0}^{2^n-1}\left|j\right\rangle\left\langle j\right| \\