Quantum Computing gate matricies

Click For Summary
SUMMARY

The discussion focuses on calculating matrices for consecutive quantum gates, specifically the Hadamard gate followed by a CNOT gate. The correct approach involves using matrix multiplication rather than addition, as the matrices represent operations on quantum states. The Hadamard gate (H) and the identity matrix (I) are combined using the tensor product to form the initial state, which is then processed through the CNOT gate. The final output state is obtained by applying the CNOT gate to the result of the Hadamard operation.

PREREQUISITES
  • Understanding of quantum states and notation, specifically |q0⟩ and |q1⟩.
  • Familiarity with quantum gates, particularly the Hadamard (H) and CNOT gates.
  • Knowledge of matrix operations, including tensor products and matrix multiplication.
  • Basic principles of quantum computing and circuit design.
NEXT STEPS
  • Study the tensor product of matrices in quantum mechanics.
  • Learn about the CNOT gate and its role in quantum circuits.
  • Explore the concept of quantum gate sequences and their matrix representations.
  • Review quantum state transformations and how they relate to gate operations.
USEFUL FOR

Students and professionals in quantum computing, particularly those studying quantum circuits and gate operations. This discussion is beneficial for anyone looking to deepen their understanding of matrix calculations in quantum mechanics.

Fixxxer125
Messages
40
Reaction score
0
Hi there
I am working through a quantum gate section of my course and I am a bit puzzled on how to calculate a matrix for consecutive quantum gates. I understand how to generate a matrix for

|q0⟩--------[H]-------
|q1⟩------------------
Which is simply the tensor product of the hadamard and identity matrix. However I am unsure what to do if the circuit is modified to be have a CNOT gate after the hadamard gate with the top qubit as the control and the bottom as a target. i have tried adding the matricies but this doesn't seem to work. Thanks for your time
 
Physics news on Phys.org
You should do matrix multiplication(keeping in mind the order) not addition.

The matrices represent operations (hence operators) done on the state. So if we take the input state as |in>, have state after the above circuit is (H x I)|in>, which is then the input to CNOT gate. So finally you get |out>=CNOT((H x I)|in>) which is equivalent to matrix multiplication of CNOT with H x I and |in>
 
Thanks for your help!
 

Similar threads

Undergrad Calculating qubit purity/entanglement in a quantum computer
  • · Replies 0 ·
Replies
0
Views
2K
Undergrad Discover Beginner-Friendly Books on Quantum Information and Computation | Q&A
  • · Replies 8 ·
Replies
8
Views
6K
High School Help with math in a quantum circuit
  • · Replies 6 ·
Replies
6
Views
2K
High School Quantum computer vs supercomputer performance
  • · Replies 8 ·
Replies
8
Views
3K
High School Quantum Computing for Beginners: Understanding Double Hadamard Gates
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Help Understanding a Quantum Circuit Identity
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Equivalence of these quantum circuits
  • · Replies 3 ·
Replies
3
Views
2K
Graduate How to measure the first qubit in two qubit system? QC
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Representing Quantum Gates in Tensor Product Space
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Are all quantum computers feedforward networks?
  • · Replies 14 ·
Replies
14
Views
3K