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

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2
Q

How do you take the exponential of a matrix?

A
  1. Diagonalise the exponential
    e_A = U(dagger) e^lamda U
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3
Q

What is a diagonal Pauli string?

A

Pauli string make of only identity and Z.

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4
Q

How do you diagonalise the X operator?

A

HXH = Z

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5
Q

How do you diagonalise the Y operator?

A

(SH)dagger Y (SH) = Z

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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.

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7
Q

How do you implement the time-evolution operator e^(−ictP) where P is a single Pauli string?

A
  1. 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
  2. To perform the exponentiation of the product of Z operators, sequentially reduce Z ⊗ Z
    to Z ⊗ 1 via CNOT gates
  3. Apply a rotation around the Z-axis of the remaining qubit, with angle ϕ = 2ct
  4. Undo the unitary action applied to transform the operator by applying the conjugate transpose
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8
Q

What does BQP stand for?

A

Bounded-time quantum polynomial

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