Chapter 1: Introduction to Quantum Computing

If you’re engaging with this text, you’re likely on a personal computer (PC). This device may take the form of a smartphone, tablet, or laptop, but they all operate on the same basic principles.

A personal computer relies on bits to perform its functions. You can envision bits as binary switches. Each bit can either be 0 (off) or 1 (on). When the bit is in the 1 state, the switch is activated, illuminating the light bulb; if it’s in the 0 state, the switch is off, and the bulb remains dark.

Understanding Bits

It’s crucial to note that the bits in a PC function independently. Activating the lights in one room does not impact the lights in another.

Chapter 2: What is a Quantum Computer?

You might not be using a quantum computer (QC) to read this article. Quantum computers operate on a fundamentally different architecture compared to standard devices.

#### Exploring Qubits

Instead of conventional bits, quantum computers utilize qubits. Imagine a qubit as a sphere where the direction of an arrow indicates its value.

The remarkable aspect of qubits is their ability to exist in a state of superposition. Unlike bits, which have a definitive state, the precise value of a qubit remains unknown until it is measured.

The Concept of Superposition

Recall the thought experiment known as Schrödinger’s cat? In this scenario, a cat is placed in a sealed box with a mechanism that has a 50% chance of releasing poison. Until we open the box, we cannot determine if the cat is alive or dead.

This principle parallels how qubits function. Until we measure them, we cannot ascertain whether they are in the 0 or 1 state; instead, we can only express their state in terms of probabilities.

In the image above, the probability of the qubit being either 0 or 1 is 50%. If the arrow leans towards 0, the likelihood of measuring 0 increases.

Entanglement in Quantum Computing

In classical computing, bits are independent of one another. For instance, turning on the kitchen lights does not affect the living room lights.

However, in quantum computing, qubits are intertwined, meaning the state of one qubit influences the states of the others.

Chapter 3: The Role of Interference

This interdependence raises a question: how can computations occur when the states are unknown before measurement? The answer lies in interference. Each qubit is represented by a wave function, and the overall wavefunction results from the interference of all qubits.

Interference occurs when multiple wave functions combine. This can result in constructive or destructive interference.

Quantum algorithms exploit this interference to enhance the likelihood of identifying the correct answer during measurement.

Comparing PC and QC

After exploring the distinctions between bits and qubits, one may wonder about the advantages of quantum computers. To illustrate this, consider an example of attempting to crack a password with a conventional PC versus a quantum computer.

Example Scenario

Let’s say you are trying to guess a password consisting of two binary digits. The possible combinations would be:

• 00
• 01
• 10
• 11

When attempting to guess, it might take several tries. For instance, if the password is 10, you could go through the combinations as follows:

• 00 - WRONG
• 01 - WRONG
• 10 - CORRECT

In this case, it took three attempts to find the correct password. However, with a quantum computer, employing Grover’s algorithm allows you to find the answer in a single try.

The video titled "Quantum Computers, explained with MKBHD" provides a detailed overview of quantum computing principles and their implications.

Computational Complexity

One of the significant challenges in current computing is the computational expense associated with various operations. For our example, if we consider three bits instead:

• 2 bits: 2^2 = 4
• 3 bits: 2^3 = 8
• 4 bits: 2^4 = 16
• 5 bits: 2^5 = 32
• 6 bits: 2^6 = 64

The complexity grows exponentially as the number of bits increases.

By utilizing quantum computing, we can significantly reduce the computational complexity for specific problems. For instance, Grover’s algorithm operates with a complexity of 2^(N/2).

The video "Quantum Computers, Explained With Quantum Physics" delves into the intricacies of quantum algorithms and their advantages.

Conclusion

Quantum computers are fundamentally different from standard PCs. They utilize qubits, which can exist in superposition and are entangled, enabling a new era of computational possibilities. This innovative architecture paves the way for algorithms that can potentially minimize the time complexity of various problems, revolutionizing the field of computing.