an insight into quantum tunneling with Harry Potter

Image: ©Quanta Magazine: used for representational purposes only.

Have you ever wondered how Harry Potter passed or phased through the brick wall of Platform 9¾? Or have you imagined how The Flash, Vision, and Kitty Pryde phased through stuff? Well, today we are going to discuss all of these weird phenomena via Quantum Physics, more explicitly Quantum Tunneling. Speaking of Harry Potter’s tunneling, for non-Potterheads, here is a cool introduction from the Harry Potter wiki:

King’s Cross Station is considered one of the main train stations to serve London, England. Students of Hogwarts School of Witchcraft and Wizardry take the…

This is the third installment in our QPE series and revolves around a very interesting approach towards phase estimation. Some prerequisites for this article are phase kickback and basic phase estimation algorithm. Also, if the reader has followed the series up until now, they should be able to understand and appreciate the Iterative Quantum Phase Estimation (IQPE) Algorithm. Let’s get started then.

Motivation behind IQPE

Let us backtrack a little bit and see our basic QPE circuit, which we talked about in our last post.

QFT⁻¹ for three qubits. Since q2 contains the least significant bit of the phase, a swap gate is applied at the end for a better visual interpretation.

In the last post of our series, we explored some of the required mathematics to tackle phase estimation. We learned phase kickbacks and phase encodings. This post revolves around the last piece of our puzzle (QPE), i.e., the Quantum Fourier Transform followed by the combination of all the mathematics into the QPE algorithm and why do we even care about it in the first place. Let’s get started then.

Classical Fourier transform, similar to its quantum counterpart. Image by AAVOS International.

Quantum Fourier Transform

Sounds a bit scary.

Anyway, let’s remember where we left off in the previous post. …

If you haven’t read our previous article about NumPy, make sure to check it out before reading this article.

Yeah, NumPy can be useful, but it’s definitely not your only library if you’re doing quantum computing. NumPy is predominantly a math library, but as we know, quantum computing is an intersection of math, physics, computer science and many more fields, so using a plain math library is insufficient.

Qiskit logo. All rights to IBM

Qiskit, on the other hand, is an open source library by IBM that is high level and quite comprehensive. Qiskit allows you to build, run, simulate quantum circuits with a wide variety…

Quantum key distribution (QKD), very closely related to quantum cryptography, is a secure communication method that implements a cryptographic protocol involving components of quantum mechanics. Before discussing quantum cryptography, let’s talk a bit about the basics of classical cryptography.

Simple classical cypher. Pandar Mayur CC BY-SA 4.0, via Wikimedia Commons

Classical Cryptography

Cryptography is a method of storing and transmitting data in a particular form so that only those for whom it is intended can read and process it. Classical cryptography has two major branches: secret or symmetric key cryptography and public or asymmetric key distribution.

Secret Key Cryptography

In secret-key cryptography, two parties encrypt and decrypt their messages using the same shared key. Here the…

Image: © Quanta Magazine : Image used for representational purposes only.

In the year 1964, John Stewart Bell, a physicist, published an article titled ‘On the Einstein-Podolsky-Rosen Experiment’, citing an apparent paradox discovered by three greats of Institute of Advanced Study, Princeton, namely Albert Einstein, Nathan Rosen, and Boris Podolsky.

The paradox, known as the ‘EPR Paradox’, rejected the uncertainties of quantum mechanics. So, what was this Paradox and how did Bell’s theorem solve this problem?

The EPR Paradox

Today, the quantum community is focusing on generating bigger, fault-tolerant devices. Say that we did achieve it. How are we going to harness them with just a few quantum algorithms up our sleeves? We need to discover new algorithms, this is what this post is about.

A quantum computer

Quantum computing is an entirely different domain of computation. It builds upon the strange properties of quantum systems to get a computational speedup in specific problems, beyond what is capable with present-day classical computers. This has been proven in principle but it hasn’t been realized experimentally, as of now. Quantum computers are in their ‘vacuum tube’ era and reaching up to the capabilities of classical systems will take more time.

Today’s NISQ (noisy intermediate-scale quantum) computers face some major issues of scalability, non-availability of algorithms, and error correction. …

Mathematics for QPE

This is the first post in a new series on Quantum Phase Estimation algorithms. The series aims to dive into a very important subroutine in quantum computation: the QPE algorithm. In the first two posts, we will look at the basics of the QPE algorithm — what it is, why is it needed and some mathematics required to fully understand it. These posts assume that the reader is familiar with the linear algebra required for quantum computing. You may look at our Linear Algebra series to brush up on such concepts. Let us get started then!

Intuition behind QPE

Let’s start with an…

Last but not least, we have the most recent major advances in quantum computing, with the Variational Quantum Eigensolver. This algorithm is a realization of physicist Richard Feynman’s dream of simulating large and complex molecules. As with our journey in the IBM Quantum Challenge, we are on our fourth day of the challenge, with two full days to get a place on the leaderboard.

Feynman diagrams, one of Richard Feynman's most significant contributions, only behind theorizing the quantum computer.

Now with Quantum Error Correction and Transmon Qubits completed, we have one more exercise more to go. VQE was one of those things, along QML, that I’ve been meaning to dive into for so long. And…

In part 1, we managed to solve the first two exercises. We did this quickly and had momentum going. Now, let’s get into the solutions for the next two exercises: quantum error correction and transmon qubits.

5 qubit computer by IBM, you can see the individual qubits

1995: Quantum error correction

After a rather easy time with the first two exercises, I arrived at quantum error correction. A few weeks ago, I had attended a couple of lectures on surface code, so I felt confident when I saw that was the theme of this challenge.

The purpose of quantum error correction is to detect and correct errors introduced during the execution of a circuit. Overall…

Quantum Untangled

Untangling the mysteries that surround quantum computing.

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