High-Temperature Gibbs States are Unentangled and Efficiently Preparable Ainesh Bakshi, Allen Liu, Ankur Moitra, Ewin Tang

 

High-Temperature Gibbs States are Unentangled and Efficiently Preparable

Ainesh Bakshi, Allen Liu, Ankur Moitra, Ewin Tang

https://arxiv.org/abs/2403.16850

The Bloch Sphere (simply explained)

 

math for quantum computing

 

math for quantum computing

terra quantum info

 

Reuben Brasher

https://github.com/rbattq

https://github.com/terra-quantum-public/benchmarking/tree/main/QPU%20notebooks

quantum Fourier transformation and comparison with discrete Fourier transformation

 explain quantum Fourier transformation and comparison with discrete Fourier transformation.

Oct 24, part 1. Deutsch Jozsa algorith review

|11> and |11> cannot be entangled states

 

No, the state \(|11\rangle \otimes |11\rangle\) is not an entangled state; it's actually a separable or product state. This means that it can be written as a tensor product of the individual states of each qubit, and the state of each qubit can be described independently of the other. 

In a truly entangled state, like the Bell states, it becomes impossible to write the joint state as a simple tensor product of individual qubit states. This results in the condition where measuring one qubit will immediately give you information about the other, regardless of the distance between them. 

In the state \(|11\rangle \otimes |11\rangle\), each qubit is already in a well-defined state of its own and measuring one doesn't provide any information about the other. This is unlike entangled states where the whole point is that the qubits are not in well-defined individual states but are correlated in such a way that the state of one depends on the state of the other.

To summarize, \(|11\rangle \otimes |11\rangle\) is not an entangled state, and the state of each qubit can be described independently of the others.

ket and bra symbol in quantum computing

quantum computing for computer scientist, microsoft research

 

quantum computing education

 

https://www.qubitbyqubit.org/

quantum computer and neural networks

 
Quantum processor swapped in for a neural network
Quantum processor used to model weather based on sparse data.

https://arstechnica.com/science/2021/12/quantum-processor-swapped-in-for-a-neural-network/

quantum reading notes, QAOA

superposition is a linear combination of states

quantum gates are matrices

Hadamard gate creates superposition. 

H on |0> gives to sqrt(2)( |0> + |1> ), whereas H on |1> gives sqrt(2) ( |0> - |1> ) 

Controlled NOT gate is on two qubit systems: 

Quantum Approximate Optimization Algorithm (QAOA) can solve Max-Cut of graphs, an NP-complete problem. 

For n vertices and m edges, the vertices can be either k(i) = +1 or -1. A cut can be defined as k(i)xk(j)= -1. 

The n-vertices can implemented as n qubits. The 2^n assignments for the vertices will correspond to the 2^n dimenstional Hilbert space generated by n qubits. So, if <i,j> is a cut, the related qubit will land onto different bases. 

QIN: In the above implementation, each vertice is allowed either 1 or 0. So, expand this for my network aging model, I may be able to expand the vertice to sub-vertices, which allows for 1 or 0 separately. Can I? 

Reference: 

Quantgates training materials

Hadamard gate

 Hadamard gate puts a quantum bit (qubit) into superposition. 

Hamiltonia operator

 https://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics)

It refers to the total energy of a system (both kinetic and potential). Its energy spectrum or sets of energy eigenvalues is a set of possible outcomes of measurements. This is the foundation of quantum theory. 

quantum sequence alignment

 Quantum pattern recognition for local sequence alignment

https://ieeexplore.ieee.org/document/8269076 

https://github.com/spencerking/QiskitSummerJam-LocalSequenceAlignment 

amsantanubanerjee/quantum_sequence_alignment

 

QuASeR -- Quantum Accelerated De Novo DNA Sequence Reconstruction

https://arxiv.org/abs/2004.05078

https://github.com/QE-Lab/QuASeR

https://github.com/prince-ph0en1x/QuASeR

quantum speed up on alignment or alignment sequence analysis

 

alignment is a score matrix, so matrix method might speed the best alignment? 

https://www.youtube.com/watch?v=p2hZL38tqAs

quantum solution on the maximum unique match might be a good starting point. 

https://en.wikipedia.org/wiki/Sequence_alignment#Maximal_unique_match

alignment - free sequence 

https://bioinformaticsreview.com/20170704/role-of-information-theory-chaos-theory-and-linear-algebra-and-statistics-in-the-development-of-alignment-free-sequence-analysis/

Square of Ajacency matrice give estimation of path

Quantum Walk and Graph search. 

Qin: sequence alignment can be conerted all-2-all adjacent matrix. So, sequence alignment then might become a quantum walk and graph search problem. 

super position == linear combination

 super position == linear combination

linear combination of vectors in the hilbert space

PROGRAMMING QUANTUM COMPUTERS: A PRIMER WITH IBM Q AND D-WAVE EXERCISES

 PROGRAMMING QUANTUM COMPUTERS:  A PRIMER WITH IBM Q AND D-WAVE EXERCISES

https://sites.google.com/ncsu.edu/qc-tutorial/

quantum alignment, shor's algorithm

 

convert Shor's algorithm:

https://qiskit.org/textbook/ch-algorithms/shor.html

Shor's algorihm uses some kind of transformation for prime number factorization, and use a good guess, to my intuitive understanding.