Contents

## Is there a proof for P NP?

1: **It is impossible to prove that P =NP in the deterministic or time inde- pendent framework of Mathematics**.

## Is P versus NP problem solved?

Although one-way functions have never been formally proven to exist, most mathematicians believe that they do, and a proof of their existence would be a much stronger statement than P ≠ NP. Thus **it is unlikely that natural proofs alone can resolve P = NP**.

## How do you prove a problem is NP problem?

To prove that problem A is NP-hard, **reduce a known NP-hard problem to A**. In other words, to prove that your problem is hard, you need to describe an ecient algorithm to solve a dierent problem, which you already know is hard, using an hypothetical ecient algorithm for your problem as a black-box subroutine.

## Is P NP solvable?

**P is the set of all decision problems that are efficiently solvable**. P is a subset of NP. P is the set of all decision problems that are efficiently solvable and is a subset of NP. Basic Arithmetic is solvable in Polynomial-time, thus belongs to P.

## Can NP problems be solved in polynomial time?

NP stands for Non-deterministic Polynomial time. This means that **the problem can be solved in Polynomial time using a Non-deterministic Turing machine** (like a regular Turing machine but also including a non-deterministic “choice” function).

## What was the first problem proved to be NP-complete?

**SAT (Boolean satisfiability problem)** is the first NP-Complete problem proved by Cook (See CLRS book for proof). It is always useful to know about NP-Completeness even for engineers.

## How do you solve NP-complete problems?

**NP-Completeness**

- Use a heuristic. If you can’t quickly solve the problem with a good worst case time, maybe you can come up with a method for solving a reasonable fraction of the common cases.
- Solve the problem approximately instead of exactly. …
- Use an exponential time solution anyway. …
- Choose a better abstraction.

## How many steps are required to prove that a decision problem is NP-complete *?

How many steps are required to prove that a decision problem is NP complete? Explanation: **First, the problem should be NP.** **Next, it should be proved that every problem in NP is reducible to the problem in question in polynomial time**.

## Can NP-hard problems be solved?

NP-Hard problems(say X) **can be solved if and only if there is a NP-Complete problem(say Y) that can be reducible into X in polynomial time**. NP-Complete problems can be solved by a non-deterministic Algorithm/Turing Machine in polynomial time.

## Are NP-hard problems solvable?

**No, if a problem is NP-complete then it is not solvable in polynomial time unless P=NP**, which has not been proven yet. Furthermore, if there were any NP-hard problem which would be solvable in polynomial time then (by reduction) it could be used to solve any other problem in NP, thus implying P=NP.

## Can quantum computers solve NP problems?

Contrary to myth, **quantum computers are not known to be able to solve efficiently the very hard class called NP-complete problems**.

## Will quantum computers solve everything?

The current —and rather harsh—truth is that **there aren’t really any real-world problems only solvable with a quantum computer**. At least not right now. Anything we currently care about can most likely be solved on a classical computer if you give it a few million or billion years (and plenty of power).

## What problems has quantum computing solved?

A quantum computer just solved a decades-old problem **three million times faster than a classical computer**. Using a method called quantum annealing, D-Wave’s researchers demonstrated that a quantum computational advantage could be achieved over classical means.

## Is Google a quantum computer?

In 2019, Google announced that its **Sycamore quantum computer** had completed a task in 200 seconds that would take a conventional computer 10,000 years.

## Is Quantum AI possible?

**Quantum computing can be used for the rapid training of machine learning models and to create optimized algorithms**. An optimized and stable AI provided by quantum computing can complete years of analysis in a short time and lead to advances in technology.

## Who invented quantum computing?

Quantum computers were proposed in the 1980s by **Richard Feynman and Yuri Manin**. The intuition behind quantum computing stemmed from what was often seen as one of the greatest embarrassments of physics: remarkable scientific progress faced with an inability to model even simple systems.

## How big is a time crystal?

We find that time crystals can be created with sizes in the range **s ≈ 20–100** and that such big time crystals are easier to realize experimentally than a period-doubling (s=2) time crystal because they require either a larger drop height or a smaller number of bounces on the mirror.

## How big is Google’s quantum computer?

An example: A simple quantum computer is **about the size of a room**, featuring a cryostat that maintains the quantum processor at a super-cold temperature of about 10 milliKelvin – making the cryostat one of the coldest places in the known universe.

## How fast is a quantum computer?

Quantum computing is a new generation of technology that involves a type of computer **158 million times faster than the most sophisticated supercomputer we have in the world today**. It is a device so powerful that it could do in four minutes what it would take a traditional supercomputer 10,000 years to accomplish.

## What are Google’s time crystals?

A team of researchers including ones from Stanford and Google have created and observed **a new phase of matter**, popularly known as a time crystal. There is a huge global effort to engineer a computer capable of harnessing the power of quantum physics to carry out computations of unprecedented complexity.

## Can we reverse time?

**Yes, you really can turn back time—with a catch**. A new paper suggests that time can actually flow forward and backward. Microscopic systems can naturally evolve toward lower entropy, meaning they could return to a prior state. Humans don’t perceive these micro phenomenons at the quantum level.

## What are quantum crystals?

A quantum crystal is **one in which the zero point motion of an atom about its equilibrium position is a large fraction of the near neighbor distance**. Both short range correlations and long range correlations (phonons) are of importance and must be treated with care in the description of quantum crystals.