Editing Glossary
The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.
Latest revision | Your text | ||
Line 47: | Line 47: | ||
*'''Pauli Gates(U):''' Single Qubit Gates I (Identity), X, Y, Z. All the gates in this set follow <math>U^2=I</math> | *'''Pauli Gates(U):''' Single Qubit Gates I (Identity), X, Y, Z. All the gates in this set follow <math>U^2=I</math> | ||
*'''Clifford Gates(C):''' Pauli Gates, Phase Gate, C-NOT. This set of gates can be simulated on classical computer. All the gates in this set follow CU=U'C, where U and U' are two different Pauli gates depending on C | *'''Clifford Gates(C):''' Pauli Gates, Phase Gate, C-NOT. This set of gates can be simulated on classical computer. All the gates in this set follow CU=U'C, where U and U' are two different Pauli gates depending on C | ||
*'''Universal Set of gates:''' This set consists of all Clifford gates and one Non-Clifford gate (T gate). If a model can realise Universal Set of gates, it can imlement any quantum computation efficiently. T gates follow <math>UT=P^aU'T</math>, where P is the phase gate and U, U' are any two Pauli gates depending on | *'''Universal Set of gates:''' This set consists of all Clifford gates and one Non-Clifford gate (T gate). If a model can realise Universal Set of gates, it can imlement any quantum computation efficiently. T gates follow <math>UT=P^aU'T</math>, where P is the phase gate and U, U' are any two Pauli gates depending on C. Parameter <math>a\epsilon{0,1}</math> is obtained from U, such that <math>P^0=I</math>, <math>P^1=P</math>.</br> | ||
To summarize, if <math>C^1=</math>P, <math>C^2=</math>C, <math>C^3=</math>T, then <math>C^{k}=\{U:UQU=C^{k-1}|Q\ | To summarize, if <math>C^1=</math>P, <math>C^2=</math>C, <math>C^3=</math>T, then <math>C^{k}=\{U:UQU=C^{k-1}|Q\epsilon C^1\}</math> | ||
===Magic States=== | ===Magic States=== | ||
Line 223: | Line 223: | ||
[[File:SWAP_test_figure.png |center|thumb|500px|Figure 9: Gate Teleporation for Multiple Single Qubit Gates]]</div> | [[File:SWAP_test_figure.png |center|thumb|500px|Figure 9: Gate Teleporation for Multiple Single Qubit Gates]]</div> | ||
Quantum SWAP test helps to compare two quantum states <math>|\psi\rangle</math> and <math>|\psi'\rangle</math>. An ancilla qubit is prepared here in the state <math>\frac{|0\rangle + |1\rangle}{2}</math> and a controlled swap test is performed on two states <math>|\psi\rangle</math> and <math>|\psi'\rangle</math>. | |||
If <math>|\psi\rangle</math> = <math>|\psi'\rangle</math>, then the ancilla qubit, after performing a Hadamard operation, yields <math>|0\rangle</math> when measurement is applied in computational basis. The SWAP test passes here. | If <math>|\psi\rangle</math> = <math>|\psi'\rangle</math>, then the ancilla qubit, after performing a Hadamard operation, yields <math>|0\rangle</math> when measurement is applied in computational basis. The SWAP test passes here. | ||
Line 229: | Line 229: | ||
If <math>|\psi\langle|\psi'\rangle \leq \delta</math>, then the ancilla qubit, after performing a Hadamard Gate and upon measurement, passes the test with probability <math>\frac{1+\delta^2}{2}</math> | If <math>|\psi\langle|\psi'\rangle \leq \delta</math>, then the ancilla qubit, after performing a Hadamard Gate and upon measurement, passes the test with probability <math>\frac{1+\delta^2}{2}</math> | ||
and fails the test with probability <math>\frac{1-\delta^2}{2}</math>. Hence, the SWAP test always passes for the same inputs and sometimes fails if they are different. By repeating the SWAP test, its efficiency can be amplified. | and fails the test with probability <math>\frac{1-\delta^2}{2}</math>. Hence, the SWAP test always passes for the same inputs and sometimes fails if they are different. By repeating the SWAP test, its efficiency can be amplified. | ||
===Quantum Capable Homomorphic Encryption=== | ===Quantum Capable Homomorphic Encryption=== | ||
*'''Homomorphic Encryption'''<br/>A homomorphic encryption scheme HE is a scheme to carry out classical computation from the Server while hiding the inputs, outputs and computation. It can be divided into following four stages. | *'''Homomorphic Encryption'''<br/>A homomorphic encryption scheme HE is a scheme to carry out classical computation from the Server while hiding the inputs, outputs and computation. It can be divided into following four stages. | ||
Line 244: | Line 243: | ||
==References== | ==References== | ||
<div style='text-align: right;'>''*contributed by Shraddha Singh''</div> | <div style='text-align: right;'>''*contributed by Shraddha Singh''</div> |