Chapter 6 Flashcards
1
Q
How can you represent a number between 0 and 1 with m bits?
A
theta = y / 2 ^ m
where y is an integer between 0 and (2^m) - 1
2
Q
How do you take the exponential of a matrix?
A
- Diagonalise the exponential
e_A = U(dagger) e^lamda U
3
Q
What is a diagonal Pauli string?
A
Pauli string make of only identity and Z.
4
Q
How do you diagonalise the X operator?
A
HXH = Z
5
Q
How do you diagonalise the Y operator?
A
(SH)dagger Y (SH) = Z
6
Q
How do you turn a string of Z operations to a single Z operation?
A
Cascasing CNOT gates.
The qubit which is the control of the CNOT has it’s Z operator replaced by Identity.
7
Q
How do you implement the time-evolution operator e^(−ictP) where P is a single Pauli string?
A
- Find a unitary circuit which diagonalizes the operator on each qubit of the Pauli string, by
transforming it into a string of Z and 1 operators on each qubit - To perform the exponentiation of the product of Z operators, sequentially reduce Z ⊗ Z
to Z ⊗ 1 via CNOT gates - Apply a rotation around the Z-axis of the remaining qubit, with angle ϕ = 2ct
- Undo the unitary action applied to transform the operator by applying the conjugate transpose
8
Q
What does BQP stand for?
A
Bounded-time quantum polynomial