Scribd
Upload
41 views1 page

3.2.B Problem Set

The document discusses functions on quantum computers, specifically how to apply the quantum function Uf to various quantum states. It provides examples of applying Uf to states with different input and output configurations, demonstrating the phase oracle formula. The results show how Uf transforms the input states based on the function's output values.

Uploaded by

eligotextus
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
41 views1 page

3.2.B Problem Set

The document discusses functions on quantum computers, specifically how to apply the quantum function Uf to various quantum states. It provides examples of applying Uf to states with different input and output configurations, demonstrating the phase oracle formula. The results show how Uf transforms the input states based on the function's output values.

Uploaded by

eligotextus
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 1

Introduction to Quantum Computing: quantumsoar.

com

3.2.B Functions on Quantum Computers

The notation f : {0, 1}n → {0, 1}m means the function f takes in a bit string of length
n and returns a bit string of length m.
 
1
1. Apply Uf to the state |ψ⟩ = 3 |001⟩|0⟩ + |010⟩|0⟩ + |111⟩|0⟩ , where the function
√

f : {0, 1}3 → {0, 1}. Let the first register of qubits be the input to the function and second
register be the output register.
 
1
2. Apply Uf to the state |ψ⟩ = 3 |001⟩|−⟩ + |010⟩|−⟩ + |111⟩|−⟩ , where the function
√

f : {0, 1}3 → {0, 1}. Let the first register of qubits be the input to the function and second
register be the output register. Recall the phase oracle formula: Uf |x⟩|−⟩ = (−1)f (x) |x⟩|−⟩

Answers
 
1. Uf |ψ⟩ = Uf √13 |001⟩|0⟩ + |010⟩|0⟩ + |111⟩|0⟩
 
1
= √
3
Uf |001⟩|0⟩ + Uf |010⟩|0⟩ + Uf |111⟩|0⟩
 
1
= √
3
|001⟩|f (001)⟩ + |010⟩|f (010)⟩ + |111⟩|f (111)⟩
 
1
2. Uf |ψ⟩ = Uf √3 |001⟩|−⟩ + |010⟩|−⟩ + |111⟩|−⟩
 
1
= √
3
Uf |001⟩|−⟩ + Uf |010⟩|−⟩ + Uf |111⟩|−⟩
 
1 f (001) f (010) f (111)
= √
3
(−1) |001⟩|−⟩ + (−1) |010⟩|−⟩ + (−1) |111⟩|−⟩

You might also like