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Many companies are working on quantum computers.

Quantum Computing

What is Quantum Computer?

They operate in fundamentally distinct ways.

A qubit is more complicated.

quantum-computing-superposition.drawio

This superposition state is a combination state of 0 and 1.

So, thats the effect of superposition explained; now well move on to entanglement.

Entanglement

In classical computers, the bits are entirely independent of each other.

Entanglement.drawio-2-1

The state of one bit is not influenced by the state of any of the other bits.

For example, lets look at two qubits which are each in different superposition states but arent entangled yet.

Either 00, 01, 10, or 11.

qubits

And this is true no matter how many qubits you have.

Youll also note that for one qubit you have a probability distribution over 2 states.

With two qubits, you have a probability distribution spread across four states.

Interference.drawio

In general, a quantum computer of n qubits can be in a combination of 2^n states.

So Id say this is the core difference between classical computers and quantum computers.

But you may wonder how being in this superposition state can be useful in a computer.

factorization.drawio

Well for that we need the final component: Interference.

Wavefunctions are the fundamental mathematical description of everything in quantum mechanics.

Lets take a look at them.

Shors-Algorithm.drawio

It is a lot more difficult.

And there is no efficient classical algorithm for finding the factors of large numbers.

To answer these questions we need to take a little detour into the world of quantum complexity theory.

Complexity-theory.drawio-1

The classification is determined by the increasing level of difficulty in solving the problem as it becomes larger.

And these are the problems that quantum computers will be better than classical computers at solving.

Is it twice as hard?

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And what is the trend as you add more and more digits?

This is called its complexity or scaling, and for factorization, it is exponential.

Anything with the N in the exponent is exponentially hard.

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But we should be careful here to verify we dont mischaracterize classical computers.

People think it is very unlikely, but it is not ruled out.

you’ve got the option to even simulate a quantum computer on a classical computer and vice versa.

Screenshot-2023-10-23-121633

But simulating quantum systems with as few particles is difficult even on the worlds most powerful supercomputers.

you might learn about quantum chemistry simulation in depth.

This has the potential to significantly expedite processes and result in substantial time and cost savings.

Screenshot-2023-10-25-121415

But these are the kinds of problems quantum computers would be well suited to.

They put these gates in a specific order to create a quantum algorithm.

In the end, measure the qubits to get the answer needed.

Physical-Implementations

Adiabatic quantum computing works by framing problems so that the quantum systems lowest energy state represents the solution.

These quasi-particles are predicted to be more stable due to their physical separation from each other.

Quantum computing is changing quickly, and picking the right approach is vital for future success.

Applications-of-Quantum-Computers

This is likely to be the same for quantum computers.

Subsequently, I addressed the challenges and practical implementation issues associated with quantum computing.

Finally, we examined the wide range of potential applications for quantum computers.