1) Encoding into higher dimensional space In QEC, one needs to encode information into a higher dimensional Hilbert space, which can be a system of multiple qubits (like conventional repetition codes, Shor's code, Steane's code,...) or a d-level sy..
[7,1] Steane code is an ubiquitous example of Calderbank-Shor-Steane (CSS) class of quantum error correction codes. Steane code was constructed from classical [7,4,3] Hamming code whose parity-check matrix takes the following form \begin{equation..
As discussed in the QFT note, given a frequency φ(0≤φ<1) that satisfies k≡2nφ∈N, the matrix representation of the following vector is the kth-column of DFT matrix \[ \ket{\widetilde{\varphi}} = \frac{1}{2^{n/2}} \s..
Quick summary: Except a special class of quantum states where quantum Fourier transform can exponentially speedup, in general it is not faster than classical Fourier transform. Definition of classical Fourier transform A discrete Fourier transform (DFT) of a 2n-length vector $x= \left( x_0, x_1, \ldots, x_{2^n..
Honeycomb lattices Honeycomb lattice (or hexagonal lattice) is realized by graphene. The lattice consists of two carbon atoms (hereafter we call them A and B sites) per unit cell. The lattice vectors can be written as →a1=a2(3,√3),→a2=a2(3,−√3), where a denotes carbon-carbon distance. The corresponding reciprocal lattice vector..
Physics Corner 2022. 7. 17. 11:37
1) Encoding into higher dimensional space In QEC, one needs to encode information into a higher dimensional Hilbert space, which can be a system of multiple qubits (like conventional repetition codes, Shor's code, Steane's code,...) or a d-level sy..
Physics Corner 2022. 7. 17. 10:59
[7,1] Steane code is an ubiquitous example of Calderbank-Shor-Steane (CSS) class of quantum error correction codes. Steane code was constructed from classical [7,4,3] Hamming code whose parity-check matrix takes the following form \begin{equation..
Physics Corner 2022. 7. 17. 10:23
As discussed in the QFT note, given a frequency φ(0≤φ<1) that satisfies k≡2nφ∈N, the matrix representation of the following vector is the kth-column of DFT matrix \[ \ket{\widetilde{\varphi}} = \frac{1}{2^{n/2}} \s..
Physics Corner 2022. 7. 16. 22:46
Quick summary: Except a special class of quantum states where quantum Fourier transform can exponentially speedup, in general it is not faster than classical Fourier transform. Definition of classical Fourier transform A discrete Fourier transform (DFT) of a 2n-length vector $x= \left( x_0, x_1, \ldots, x_{2^n..
Physics Corner 2022. 7. 16. 17:13
Honeycomb lattices Honeycomb lattice (or hexagonal lattice) is realized by graphene. The lattice consists of two carbon atoms (hereafter we call them A and B sites) per unit cell. The lattice vectors can be written as →a1=a2(3,√3),→a2=a2(3,−√3), where a denotes carbon-carbon distance. The corresponding reciprocal lattice vector..