From 0c0ff8093ff292f22b1bc95ddd666fd411867c8d Mon Sep 17 00:00:00 2001 From: quantumjim Date: Mon, 11 Nov 2024 21:45:06 +0100 Subject: [PATCH] cleanup --- exercises/Exercise3.ipynb | 6 ++-- .../Exercise4.ipynb | 26 ++++++++++++++---- exercises_qec_2018/Answers4.pdf | Bin 302261 -> 0 bytes exercises_qec_2018/Answers9.pdf | Bin 180012 -> 0 bytes exercises_qec_2018/Exercise9.pdf | Bin 112413 -> 0 bytes 5 files changed, 24 insertions(+), 8 deletions(-) rename exercises_2022/Exercise10.ipynb => exercises/Exercise4.ipynb (77%) delete mode 100644 exercises_qec_2018/Answers4.pdf delete mode 100644 exercises_qec_2018/Answers9.pdf delete mode 100644 exercises_qec_2018/Exercise9.pdf diff --git a/exercises/Exercise3.ipynb b/exercises/Exercise3.ipynb index 83f52f1..904e49d 100644 --- a/exercises/Exercise3.ipynb +++ b/exercises/Exercise3.ipynb @@ -15,11 +15,11 @@ "source": [ "## 1\n", "\n", - "Given an abitrary single qubit state $a|0\\rangle +b|1\\rangle$:\n", + "Given an arbitrary single qubit state $a|0\\rangle +b|1\\rangle$:\n", "\n", - "(a) Write down the correponding density matrix.\n", + "(a) Write down the corresponding density matrix.\n", "\n", - "(b) Write down the density matrix representing the effect of applying an $X$ with probability $q_x$, $Y$ with probability $q_y$ and $Z$ with probability $q_z$.\n", + "(b) Write down the density matrix representing the effect of applying an $X$ with probability $q_x$, $Y$ with probability $q_y$, $Z$ with probability $q_z$ (and doing nothing with probability $1-q_x-q_y-q_z$).\n", "\n", "(c) Write down the density matrix for representing the effect of replacing the state with $I/2$ with probability $p$.\n", "\n", diff --git a/exercises_2022/Exercise10.ipynb b/exercises/Exercise4.ipynb similarity index 77% rename from exercises_2022/Exercise10.ipynb rename to exercises/Exercise4.ipynb index 8818cc0..a507a94 100644 --- a/exercises_2022/Exercise10.ipynb +++ b/exercises/Exercise4.ipynb @@ -7,7 +7,7 @@ "id": "pmm5uV8cQQN6" }, "source": [ - "# Exercise 10" + "# Exercise 4" ] }, { @@ -74,11 +74,27 @@ ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": {}, - "outputs": [], - "source": [] + "source": [ + "## 3. The Toric Code\n", + "\n", + "The surface code is defined on a plane with rough and smooth boundary conditions.\n", + "But we could instead wrap the $L \\times L$ square lattice around a torus and have periodic\n", + "boundary conditions. Then the code would be translationally invariant, and all $A_s$\n", + "and $B_p$ stabilizers would be four qubit operators.\n", + "\n", + "* (a) The parameter $L$ counts the number of plaquettes along each direction. Show that\n", + "$n = 2L^2$, where $n$ is the number of qubits.\n", + "* (b) Show that the number of plaquette operators is $L^2$, but that the number of independent plaquette operators is $L^2-1$. Show the same thing for the vertex operators.\n", + "* (c) How many logical qubits, $k$, can be stored in the stabilizer space?\n", + "* (d) Define logical $X$ and $Z$ operators for these logical qubits. Note that these are not\n", + "uniquely defined. However, as with any stabilizer code, you will know that your logical\n", + "operators are a valid choice if they satisfy the following conditions.\n", + " 1. Logical Pauli operators must commute with all stabilizers.\n", + " 2. Logical Pauli operators for the same logical qubit anticommute: $\\left[ X_j, Z_j \\right] = 0$.\n", + " 3. Logical Pauli operators for different logical qubits commute: $\\{ X_j, Z_j \\} = 0$." + ] } ], "metadata": { diff --git a/exercises_qec_2018/Answers4.pdf b/exercises_qec_2018/Answers4.pdf deleted file mode 100644 index f94d9020aa59504f90a6a3f65603191d46f63ee2..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 302261 zcmV)CK*GNzP((&8F)lR4?5av(28Y+-a|L}g=dWMv9IJ_>Vma%Ev{3V57sy~(a6Jrf+Z=TqD#xGqk`;u8ok z;Ej4IXdyrYVDwp7UikH0nGuo6(-MAs`0t6XVsXrgIs8AR{@DNi=l}TmKmN=0^FRLI za{XLCcWpmwx1ay{-+umkxqjQc_VaW7-ffL(PyfgN@cx=V|KI!a|M~v+f0zICpI_km z`LCs3KmXU;zln+ZRg6W{WR#c;ekVTj{{HiBm&-QKRrl>1X<@5 zzng52-{*bks=u|>_rd(_%l-bm+kSty-|O9-4$KY!Gy4K{wc^O=0Iuaf>v)de^>?m( z;RW7~&JDoU?cUGtzIVxw+uu|P=KDtl zGMYWo>?;5+`^fX2!P^^Yzw7Z7uld`rS^)H2U!-%S?;JjF3+wF$`t^=^ z8*s$~^&P-{@Ap9K=i90K`Cap9;QjYjx3ACJt8Tq~2ef@X)Jp)~?fb$L?WxCPBrxBZ zE)H}bdcFE@>(4*Pex9S*dcDoOo90C3@B5*0`<{OH7Jl0@IZd!PmbLl<&r%!n-6e+j zDkQLey%oOmc5dIkq=26G_~P!NX0|PrEy%O8EBC&9ne&mibIZSQy!8&iCpQ{?SG>lj 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