Doxa

Friday, December 6, 2024

Q_1.3

Qiskit 1.3 is out, as of December 4, 2024. Meant to make things more secure and

a lot faster by switching to the Rust language for transpiling.

The annoucement:

https://www.ibm.com/quantum/blog/qiskit-1-3-release-summary

The Rust language, online:

Data Types - The Rust Programming Language

Rust is considered Easy Peasy. Ha!! It's still programming 😏

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Meanwhile, looking forward to the week-end...

The RUNNING MAN:

The 5 basic moves:

1- Running Man

2- Polly PocKet

3- Kickbacks

4- Charleston

5- T-Step

33333. Kickbacks 4.

Thursday, December 5, 2024

Max_Fun

Why keep all the fun to myself. I asked Copilot for a harder max-cut problem

to work on, just to make sure I am getting the notion right. Below:

mathematics; could I see a difficult max-cut problem?

Sure! Here's an example of a moathemare challenging Max-Cut problem:

Problem Description

Consider a graph with 8 vertices and 14 edges. The vertices are labeled from 0 to 7, and the edges are as follows:

(0, 1), (0, 2), (0, 3), (1, 2), (1, 4), (2, 5), (3, 6), (4, 5), (4, 7), (5, 6), (5, 7), (6, 7), (1, 6), (2, 7)

Objective

Partition the vertices into two sets, S and T, such that the number of edges between the sets is maximized.

Solution Approach

Graph Representation: Visualize the graph with the given vertices and edges.

Initial Partition: Start with an initial random partition of the vertices into two sets.

terative Improvement: Use an algorithm like the Kernighan-Lin algorithm to iteratively improve the partition by swapping vertices between the sets to increase the number of edges crossing the partition.

Maximize the Cut: Continue the process until no further improvement can be made.

Example Solution

After applying the algorithm, one possible partition could be:

Set S: {0, 1, 4, 5}

Set T: {2, 3, 6, 7}

In this partition, the edges crossing the partition are:

(0, 2), (0, 3), (1, 2), (1, 6), (2, 5), (3, 6), (4, 7), (5, 6), (5, 7), (2, 7)

This results in a maximum cut with 10 edges crossing the partition.

* * *

To accomplish step 1, ie getting a visual representation of the problem, ended

up asking Meta for python code to do this. I needed to install networkx (with conda)

and did so.

That's it so far. I do know the Kernighan-Lin algorithm is available

in the package...

* * *

https://www.getmerlin.in/chat/share/a68c3bf5-6883-4bae-be20-35134511291a

* * *

Finally, settled on ChatGPT code:

Wednesday, December 4, 2024

NP_Hard

COPILOT:

Mathematics; what is a maxcut problem?

The Max-Cut problem is a classic problem in graph theory and combinatorial optimization. It involves finding a way to partition the vertices of a graph into two complementary sets such that the number of edges between the two sets is as large as possible.

In simpler terms, imagine you have a network of nodes connected by edges. The goal is to divide these nodes into two groups in such a way that the number of connections (edges) between the two groups is maximized. This problem is known to be NP-complete, meaning it is computationally challenging to solve exactly for large graphs.

The Max-Cut problem has practical applications in various fields, including physics, where it can be used to model certain types of spin systems, and in circuit design, where it helps in minimizing the number of connections between different layers of a circuit.

Isn't it fascinating how such abstract mathematical problems can have real-world applications?

Explain the Max-Cut problem to me in layman's terms, and why it is important?

Sure! Imagine you have a group of friends, and you want to split them into two teams for a game. The goal is to make sure that as many friends as possible are on different teams. Each friendship is like a connection, or an "edge," between two friends, or "nodes." The Max-Cut problem is about finding the best way to split the group so that the number of connections between the two teams is as large as possible.

In more technical terms, the Max-Cut problem involves dividing the nodes of a graph into two sets in such a way that the number of edges between the sets is maximized. This problem is important because it has applications in various fields, such as:

Physics: Modeling certain types of spin systems.
Circuit Design: Minimizing the number of connections between different layers of a circuit.
Network Design: Optimizing the layout of networks to improve efficiency and reduce costs.

By solving the Max-Cut problem, we can make better decisions in these areas, leading to more efficient and effective designs and systems. Isn't it fascinating how a simple idea of splitting friends into teams can have such wide-ranging applications?

Computer Science; what are Np_ problems?

In computer science, NP problems are a class of problems known as nondeterministic polynomial time problems. These are decision problems for which a given solution can be verified as correct or incorrect in polynomial time by a deterministic Turing machine. In simpler terms, if you have a potential solution to an NP problem, you can check whether it's correct relatively quickly.

Here's a bit more detail:

NP (Nondeterministic Polynomial time): This class includes problems for which a solution can be verified in polynomial time. However, finding the solution might not be as quick.
P (Polynomial time): These are problems that can be both solved and verified in polynomial time.
NP-complete: These are the hardest problems in NP. If you can find a polynomial-time solution for any NP-complete problem, you can solve all NP problems in polynomial time.
NP-hard: These problems are at least as hard as the hardest problems in NP, but they don't necessarily have to be in NP (i.e., their solutions might not be verifiable in polynomial time).

An example of an NP problem is the traveling salesman problem: given a list of cities and the distances between them, find the shortest possible route that visits each city exactly once and returns to the origin city. Verifying a given route is quick, but finding the optimal route is computationally challenging.

source: Maximum cut problem

MERLIN(ChatGPT3.5)

COPILOT:

Sure! Let's break down the Max-Cut problem and its solution from the image you uploaded.

Understanding the Problem

The Max-Cut problem involves dividing the vertices of a graph into two sets, S and T, such that the number of edges between the two sets is maximized. In the graph provided, there are 6 vertices and 8 edges.

Solution Explanation

Graph Description: The graph has 6 vertices (0, 1, 2, 3, 4, 5) and 8 edges connecting them.

Partitioning: The vertices are divided into two sets:

Set S: {0, 1, 4, 5}

Set T: {2, 3}

Maximizing the Cut: The goal is to maximize the number of edges that cross between sets S and T. In this solution, all 8 edges cross between the two sets, meaning every edge has one endpoint in S and one in T.

Result: The maximum cut for this graph is 8, as all 8 edges are between the two sets, with no edges internal to either set.

Why This Solution Works

No Internal Edges: There are no edges within set S or set T, ensuring that all edges contribute to the cut.

Maximizing Edges: By placing vertices 2 and 3 in set T and the rest in set S, the solution ensures that every edge in the graph crosses the partition, achieving the maximum possible cut.

This approach effectively maximizes the number of edges between the two sets, which is the objective of the Max-Cut problem.

* * *

Got it! By putting from the central nodes in one set, one catches everything else. So

why is this such a problem!?

* * *

IBM quantum Learning offers a tutorial on solving a Max-Cut problemon a quantum

computer. I will be looking at this next...

Tuesday, December 3, 2024

Syria

From Le Monde's French language edition:

Timing_it

Physics; what is the smallest unit of time physicists work with?

Physicists often work with incredibly small units of time, but one of the smallest is the Planck time. The Planck time is approximately $5.39 \times 10^{-44}$ seconds. It's the time it takes for light to travel one Planck length, which is the smallest measurable length in the universe. This unit is named after Max Planck, the father of quantum theory. It's so small that it's beyond the reach of current technology to measure directly, but it plays a crucial role in theoretical physics, especially in the realms of quantum mechanics and general relativity.

Isn't it fascinating how the universe operates on such mind-bogglingly tiny scales?

What is the unit of time in which a satellite broadcasts to earth?

Satellites typically broadcast data to Earth in units of milliseconds or microseconds. These small time intervals are crucial for ensuring precise and accurate communication, especially for applications like GPS, weather monitoring, and data transmission. The exact unit can vary depending on the specific satellite and its mission requirements.

Is there a particular satellite or type of data transmission you're curious about?

What is a microsecond?

A microsecond is a unit of time equal to one millionth of a second, or $10^{-6}$ seconds. To put it in perspective, a microsecond is to a second what a second is to about 11.6 days. It's a very short period of time, often used in fields like telecommunications, computing, and physics where precise timing is crucial.

For example, in computing, microseconds are used to measure the time it takes for data to be processed or transmitted. In telecommunications, they can be used to measure the delay in signal transmission.

Isn't it amazing how even such tiny fractions of time can have such significant impacts in technology and science?

What is a femtosecond and how is it used?

A femtosecond is a unit of time equal to one quadrillionth of a second, or $10^{-15}$ seconds. To put it in perspective, a femtosecond is to a second what a second is to about 31.7 million years. It's an incredibly short period of time, often used in fields like physics and chemistry where extremely fast processes need to be measured.

Femtoseconds are particularly important in the study of ultrafast phenomena, such as the movement of electrons in atoms and molecules. For example, femtosecond lasers are used to observe and control chemical reactions at the atomic level, allowing scientists to see how bonds form and break in real-time. This has applications in fields like material science, biology, and even medicine.

Isn't it fascinating how we can measure and manipulate such incredibly brief moments in time?

What is the unit of time used in warfare, where drones are intercepted and downed?

In modern warfare, especially with the use of drones, the unit of time often used is milliseconds. This is because the interception and downing of drones require extremely precise and rapid responses. For example, air defense systems need to detect, track, and engage drones within milliseconds to be effective.

The speed and agility of drones, combined with the need for real-time decision-making, make milliseconds a critical unit of time in these scenarios. It's fascinating how technology has evolved to operate on such incredibly short timescales in the context of warfare.

Isn't it intriguing how advancements in technology have transformed the dynamics of modern conflict?

Drone Technology Is Transforming Warfare in Real Time - Centre for International Governance Innovation

Monday, December 2, 2024

Cruising

Quantum computing; what is trotterized time evolution?

Trotterized time evolution is a technique used in quantum computing to simulate the time evolution of quantum systems. It involves breaking down the exponential of a Hamiltonian (which describes the energy of the system) into a sequence of simpler operations that can be implemented on a quantum computer. This method is based on the Trotter-Suzuki decomposition, which approximates the time evolution operator by a product of exponentials of simpler operators.

In essence, Trotterization allows us to simulate complex quantum dynamics by dividing the time evolution into small steps, each of which can be handled by the quantum computer. This approach is particularly useful for simulating quantum spin systems and other many-body quantum systems.

* * *

Tell me about Trotter-Suzuki decomposition.

* * *

In layman's terms, what are Lie groups?

Lie groups are mathematical structures that combine the properties of groups and smooth manifolds. In simpler terms, they are sets of elements that can be multiplied together and inverted, just like numbers, but they also have a smooth structure that allows for calculus to be done on them.

Here's a more relatable analogy:

Groups: Imagine a group as a set of objects with a rule for combining them. For example, the set of whole numbers with addition is a group because you can add any two whole numbers to get another whole number, and every number has an "inverse" (its negative) that brings you back to zero.

Smooth Manifolds: Think of a smooth manifold as a shape that can be stretched and bent smoothly without tearing or gluing. For example, the surface of a sphere is a smooth manifold because you can move around on it smoothly.

Lie Groups: Now, combine these two ideas. A Lie group is a set of elements that you can combine (like a group) and that also has a smooth structure (like a manifold). This means you can do calculus on Lie groups, which is very useful in physics and engineering.

Lie groups are used to describe symmetries in various physical systems, such as the rotations of a sphere or the symmetries of molecules. They play a crucial role in many areas of mathematics and theoretical physics.

* * *

Can you give me an example problem or application?

Sure! Let's consider an example problem involving Lie groups in the context of physics, specifically in the study of rotations.