two qubit base vectors

 

20240710 UTC quantum circuit

https://www.youtube.com/playlist?list=PLo62Vf9IYqhosCIlWLtV15hb3rUUwAcpX

* IBM, right click to see icon info, gate, NOT, CNOT. Drag and drop on gate. editing the code. 

* explain Hadamard gate

* explain Q-sphere

* explain CNOT

q0 + Hadamard + CNOT = Entangled two-qubit state

https://youtu.be/wCAZWlcS-3I?si=EXaBNr7Wp6_fyuEH

super-position versus entaglement

https://youtu.be/0fGyJbqdCfY?si=3COYTQqolrFZfvIV

https://youtu.be/mObvTSakK5Y?si=3-GUqqwS7nhf3HRx

interference

https://youtu.be/evm38AMeJyk?si=S63eIX9Uu2aSSKk5

1. introduction to IBM quantum circuit. Go over the icon for information. Quits. Q-sphere. 

Entanglement example:

 

https://quantum.ibm.com/composer/files/new

https://github.com/hongqin/quantum_sandbox

 review Bloch sphere definition, using IBM Quantum Composer to interactively explore the states, quantum state definition, 

one qubit. Tip: manually edit the script for fast editing. 

two qubit

Q-sphere view

https://learning.quantum-computing.ibm.com/tutorial/composer-user-guide#q-sphere-view 

Midterm review? 

basic circuit

 https://qiskit.org/documentation/tutorials/circuits/01_circuit_basics.html

qiskit primitives

 

https://qiskit.org/ecosystem/ibm-runtime/primitives.html

Sampler: Generates quasi-probability distribution from input circuits.

Estimator: Calculates expectation values from input circuits and observables.

https://learning.quantum-computing.ibm.com/tutorial/working-with-the-qiskit-runtime-sampler-primitive#primitives

quantum phase estimation

 

Shor's algorithm

 

Explain why the period is related to factoring.

The connection between finding the period of a function and factoring large numbers is a clever insight that forms the basis of Shor's Algorithm. Here's how they are related.

More details on the example of factoring 15:

How do we choose a?

Shor's algorithm in details: 

Quantum Fourier transform

References

https://en.wikipedia.org/wiki/Shor%27s_algorithm

TODO Oct ?? draft quantum computing, teleporting

Quantum teleporting?  

https://www.youtube.com/watch?v=6fixVgtt2wg

Grover's algorithm

 

search a number

https://youtu.be/pYD6bvKLI_c?feature=shared

https://lab.quantum-computing.ibm.com/user/5f848abaff5562001ae12c12/lab/tree/1.%20motivation-why-quantum-computing.ipynb

https://lab.quantum-computing.ibm.com/user/5f848abaff5562001ae12c12/lab/tree/2.%20elements-of-quantum-programming.ipynb

Apply Grover's algorithm to break RSA key. 

Because we do not know the factors of the RSA key, how do we define the Oracle when applying Gover's algorithm?

Oct 24 , Part 2, assignment, H,H,Cx, not entangled

 Explain the following code mathematically. Is the final state entangled or not?

OPENQASM 2.0; include "qelib1.inc"; qreg q[2]; creg c[1]; h q[0]; h q[1]; cx q[0], q[1];

Oct 19, deutsch-jozsa-algorithm

charge iPad and ipen

Show that Deutsch-Jozsa extend the deutsch problem

 https://learning.quantum-computing.ibm.com/course/fundamentals-of-quantum-algorithms/quantum-query-algorithms#the-deutsch-jozsa-algorithm

The Deutsch-Josza algorithm is a quantum computing algorithm that solves a specific problem much faster than classical computers. Imagine you have a black box (also called an "oracle") with a function inside it. This function takes a binary input (like 0 or 1) and gives a binary output (again, 0 or 1). You're told that the function is either "constant" (always gives the same output, either all 0s or all 1s) or "balanced" (gives an equal number of 0s and 1s).

In a classical computer, you might have to check multiple inputs to figure out whether the function is constant or balanced. But the Deutsch-Josza algorithm can tell you this in just one step! It uses the principles of quantum mechanics, like superposition and interference, to do this quickly.

Phase esimation

 

Oct 10, lecture, Query algorithm, Deutschs algorithm

Explain classical computing problem and query model of computing. 

Query model: entire input is not provided, but in a form of "function"

bitwise exclusive OR 

https://learning.quantum-computing.ibm.com/course/fundamentals-of-quantum-algorithms/quantum-query-algorithms#deutschs-algorithm

https://lab.quantum-computing.ibm.com/user/5f848abaff5562001ae12c12/lab/tree/deutsch_algorith.ipynb

announcement: asynchronous lecture on Thu. 

Oct 5, lect, part 2, H, H is not entangled.

 

OPENQASM 2.0;

include "qelib1.inc";

qreg q[2];

creg c[1];

h q[0];

h q[1];

Oct 5, lecture, part 1, CNOT + H gate

 

Explain step by step of the following, with mathematical formula. Is the final state entangled or not? OPENQASM 2.0; include "qelib1.inc"; qreg q[2]; creg c[1]; cx q[0], q[1]; h q[0];