A Journey From Quantum Physics To Quantum Computers

By Arif Shahriar on 2024-07-15 00:52:46

Agenda:

1. Quantum mechanics.

2. The idea behind the quantum computer.

3. Quantum Computer.

4. Classical gates and Quantum gates.

5. Quantum Programming.

6. Overall structure of a quantum computer.

7. Application of Quantum computer.

8. Problems with quantum computers:

1. Quantum Mechanics:

LIGHT

The humble object is responsible for the birth of the most important theory “Quantum mechanics”.

Everyone has heard about the double-slit is one of the most famous experiments in physics and one of the strangest experiments When Young first carried out the double-split experiment in 1801. He found that light behaved like a wave. 

As the light passes through the slits, each, in turn, becomes almost like a new source of light. On the far side of the divider, the light from each slit diffracts and overlaps with the light from the other slit, interfering with each other. As a result, a light and dark interference pattern will form in the wall like in the picture. It tells us that light is a wave and when two waves interfere with each other they will form constructive and destructive interference. From the time people start believing that, the light is a wave.

Now, let’s introduce a scientific device called an Electroscope is used to detect the presence of an electric charge on a body. The mechanism of the Electroscope can be found here, and looks like this below:

Later, another question arose among the scientists that, 

-- why red light can’t repair the electroscope defect?

-- Why blue light can repair the defect of the electroscope?

This is called the photoelectric effect. The mystery of the photoelectric effects was solved by Albert Einstein. He explains below, 

We can think of incident light as a stream of photons with an energy determined by the light frequency. When a photon hits the metal surface, the photon's energy is absorbed by an electron in

the metal. He also describes that UV / blue light needs more energy to make. About 100 times more energy than red light. Hence it has a higher frequency and it can omit electrons from metal surfaces. 

Einstein’s theory left physicists with a dizzying paradox. Because light might be a wave. Now it was proved that it is a particle too.

As we all know, every atom has elections and everything in the world is built with atoms. To know the reality of the nature. An experiment was carried out at Bell Laboratories in the 1920s which uncovered the unexpected about electrons. The experiment is presented in the below picture.

We discuss the double-slit experiment in the above. Rather than light, they used an electron gun with can throw electrons like a gun. In the left side image, if we throw electrons at ones or all at ones it will create an interference pattern as we get in the Young double-slit experiment. That proves that an electron is a wave because only a wave can form this kind of interference pattern. 

In the second picture, all the experiment settings were the same as the previous one except we placed a detector we could detect or navigate the path of electron. When throwing an electron one by one from the electron gun and when the detector is on a particle-like pattern appears on the screen. The electron goes through either the upper slit or lower slit and forms a pattern like this. 

In the third picture, when the detector is turned off, they get the same pattern as the first picture.

This is a strange situation because the same electron behaves like a particle (Second picture) and wave (First and Third picture) at the same time. When we place the detector, its presence is like a particle, and when the detector is off, its presence is like a wave. This characteristic is present in every sub-atomic particle on Earth and it’s known as wave-particle duality. When we observe sub atomic particle, it collapse. Hence, Reality is a wave function, it collapses to something when observed.

It can be better visualized using coin flipping scenario.

As it spins, it is both in the head and tails.	When flipping the coin stops, we can tell the outcome.

When a coin is in both states (head and tails) is called the superposition. When the coin stops flipping, the superposition state collapses and we can measure the outcome. 

Nills Borh effectively claims that one can never know where the electron is until we measure it. That means electrons are everywhere at once. Only by looking at them, we conjure their positions into existence.

There is a special characteristic between two quantum/electrons. Two quanta connect in such a way that one observation is similar to the other and it’s called Entanglement. If we destroy one superposition then the other superposition will also be destroyed and the result will be the same. As Einstein said, nothing can travel faster than light, so how do they communicate? He can’t reveal the truth. So he called it spooky at a distance. He wrote this in his research paper named EPR paradox. But Entanglement exists and it is proved by Alain Aspect, John Clauser, and Anton Zeilinger. For that, They achieved The Nobel Prize in Physics in 2022.

Fig: Entanglement

2. The idea behind the quantum computer:

If we want to simulate the real world/natural things, the classical computer fails. To simulate something perfectly, we need to go to a small portion of the material. But the complexity to simulate from there is very much complex. For example, 1 cup of coffee has 36mg caffeine—10^20 molecule. To represent 1 molecule's energy state and bonding between electrons we need 10^48 bit. IBM supercomputer SUMMIT can’t do this.

Richard Feynman was the first who introduce how to build quantum computers using quantum mechanics. The name of the research paper is: Simulating physics with computers. And lastly, in 1998 the first quantum computer was invented.

3. Quantum Computer:

Classical computer building blocks are a bit, and they can be either 0 or 1. In quantum computers they use Qubits. They are in always superposition between 0 and 1. That means it can be 0 and 1 at the same time. This can be visualized below picture:

Superposition is the ability of a quantum system to be in multiple states at the same time until it is measured. It can be 0 and 1 at the same time. The superposition is very much useful for building quantum computers. For example, If the classical computer has 3 bits then at a time we get 3 bits of information. But in quantum computers, we will get 2^3 information at the same time by using only 3 Qubits as they will be in superposition.

Let’s see an example, how fast a quantum computer calculates,

If we write a program to find the food for the maze in the above picture, the classical computer will investigate each path one by one and backtrack to find the correct path. It will investigate n number of paths and the time complexity will be big O(n). In a quantum computer, all the path exists in a superposition at a time and the correct result or path will be found using big O(1) time.

4. Quantum vs Classical gates:

Everyone is familiar with with classical gates. Here I present some Quantum gates,

Pauli X The Pauli X gate is exactly the classical NOT gate. It reverts 0 to 1 and 1 to 0.
Pauli Y The Pauli Y gate is an interesting machine - we get the same result as the Pauli X gate, but instead of moving through real space we move through imaginary space instead.
Pauli Z The Pauli Z gate changes the state of our qubit along the plane formed by the vectors represented by our two states. This means that no change will occur if we're fully in one state or the other - only if we're somewhere between the two.
Hadamard Gate The Hadamard gate imposes a uniform superposition on our system. This gate is very important because often we need to scramble our initial state before we can start computation. The Hadamard gate does this for us in a predictable way.
The Controlled Not Gate This gate is also called the "CX" or the "controlled X" gate. You can guess what this means - it performs the same operation as the Pauli x gate but is controlled by another qubit. We pass in two bits - a control bit and a target bit. If the control bit is 1, the target bit will flip states. If the control bit is 0, nothing happens. The control bit is never affected by this gate.
How to Generate Entanglement between two or more qubits: Using two qubits to generate an entanglement state, also called Bell state, with a Hadamard gate and a CNOT gate. You can use the link to simulate circuit design using quantum gates.

5. Quantum Programming.

There are several Quantum programming languages as listed below:

• Q# Programming language

• Qiskit

• Cirq

• Quipper

• Forest and PyQuil

Qiskit:

Qiskit is an open-source quantum computing framework developed by IBM. It allows developers to write quantum algorithms using Python. Qiskit provides tools for creating and manipulating quantum programs and running them on prototype quantum devices on IBM Q Experience or simulators on a local computer. For more about qiskit, you can visit the link.

Here it simulates a basic quantum circuit, observes the resulting quantum states, and visualizes the circuit.

from qiskit import QuantumCircuit, transpile
from qiskit_aer import AerSimulator
from qiskit.visualization import plot_histogram

## Setup the simulator
simulator = AerSimulator()

## Create the quantum circuit
circuit = QuantumCircuit(2, 2)

## Apply quantum gates
circuit.h(0)
circuit.cx(0, 1)


## Measure the qubits
circuit.measure([0, 1], [0, 1])

## Transpile the circuit
compiled_circuit = transpile(circuit, simulator)

## Run the simulation
job = simulator.run(compiled_circuit, shots=1000)
result = job.result()
counts = result.get_counts(compiled_circuit)

## Print the result
print("\nTotal count for 00 and 11 are:", counts)

##Draw the circuit
circuit.draw("mpl")

Result: When measured, the qubits are expected to collapse to either ∣00⟩ or ∣11⟩ with equal probability (approximately 50% each), assuming an ideal noise-free environment.

Here is the code:

QuantumCircuit: can be thought of as the instructions of the quantum system. It holds all your quantum operations.

AerSimulator: is the Aer high-performance circuit simulator.

6. Overall structure of a quantum computer.

Fig: The flow of submitting a job from a classical computer to a quantum computer, executing the job, and returning quantum measurement results to the classical computer.
Fig: The core portion of a quantum computer:

7. Application of Quantum computer

A. Encryption: Today’s most popular encryption algorithm is RSA algorithms. Almost all the data transactions happened today using this algorithm. Let’s understand the algorithm:

Key generation process: AxB=C Here A and B are prime numbers of 313 digits each. C is the prime factor   We use C = public key and A, B = private key. To break or get the private key from the public key, the supercomputer needs 16 million years to break. But It is super easy to break the encryption by using the quantum computer because of the powerful nature of qubits. By using only several qubits it can generate the private keys from the public key.

To make data transactions in a more secure way several new encryption algorithms have been proposed among them bb84 is the most popular that can’t be broken by quantum computers.

Fig: The working procedure of the bb84 encryption algorithm

B. Drug discovery: It can accelerate the discovery of new drugs. It can also help to diagnose the disease early. Biogen has already started to discover and tackle diseases like Alzheimer’s and Parkinson's disease.

C. Climate modeling: The use of quantum computing in climate modeling and weather forecasting could significantly improve the accuracy of predictions. By taking into account more variables and processing data faster, quantum computing could allow for more detailed climate models and more accurate weather forecasts. IBM already using environmental sustainability.

D. Supply chain optimization: Optimal routing to the delivery vehicle. Volkswagen uses quantum computers to optimize the route of its electrical vehicle shuttle service in real time.

E. Machine learning or deep learning: Quantum machine learning is the integration of quantum algorithms within machine learning programs. Complex datasets and complex model calculations can be very fast.

8. Problems with quantum computers:

• The quantum system is extremely sensitive to the external environment, so it should be safely isolated.

• It is hard to achieve a decoherence time that is more than the algorithm running time.

• Error correction (requires more qubits!).

• Physical implementation of computations.

• New quantum algorithms to solve more problems.

• Entangled states for data transfer.

• Running time increases exponentially with matrix size.

Additional Resources

Quantum Algorithms and Applications

• Deutsch–Jozsa algorithm

• Bernstein–Vazirani algorithm

• Simon's algorithm

• Quantum phase estimation algorithm

• Grover's algorithm

• Shor’s Algorithm

• Quantum Fourier Transform

Youtube video:

1. https://www.youtube.com/@travisgritter3497/playlists

2. https://youtu.be/F_Riqjdh2oM

3. https://www.youtube.com/results?search_query=quantum+computer+ayushkaari

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