The Anti-Infinity Parade

A QLDPC decoder

Abdullah Khalid — Wed, 28 Jun 2023 00:00:00 +0500

In an error-correction code, once the syndromes have been measured, the next step is to infer the error that has occurred on the physical qubits. This is a decoding algorithm to be run on a classical computer. Today, I want to explore a particular decoding algorithm (Delfosse et al. 2021 …

Logical Operations for the Steane Code

Abdullah Khalid — Tue, 01 Nov 2022 00:00:00 +0500

Today, I want to discuss how to obtain a universal set of gates for the Steane code.

Previously, we discussed Gottesman's method for constructing the encoded $\bar{X}$ and $\bar{Z}$ logical operations for stabilizer codes.

import stac
cd = stac.CommonCodes.generate_code …

Algorithms for code concatenation

Abdullah Khalid — Sun, 30 Oct 2022 00:00:00 +0500

My goal is to compute fault-tolerance thresholds for stabililzer codes. To this end, we need to understand how to concatenate quantum codes. Briefly, code concatenation is when a state is encoded first by one code, then the encoded qubits again by same or another code. The resultant qubits may be …

Fault-tolerant syndrome measurements

Abdullah Khalid — Wed, 26 Oct 2022 00:00:00 +0500

Last time we studied a non-fault-tolerant version of syndrome measurements. Today, let's study a method that is fault-tolerant (FT), i.e. a single error in a block does not create more than one errors in the same or any other block.

Problem with the non-FT measurement circuit and a basic …

Syndrome Measurements

Abdullah Khalid — Fri, 21 Oct 2022 00:00:00 +0500

The critical part of any error correcting code is error-detection. For the stabilizer codes in general, error-detection is done by measuring each of the $m=n-k$ stabilizer generators on the state. An error-free state is a $+1$ eigenstate of all stabilizer generators …

Decoding Circuits

Abdullah Khalid — Thu, 13 Oct 2022 00:00:00 +0500

Decoding is not an important part of error correction when quantum error correction is employed to protect against noise during the execution of quantum algorithms. We do all operations - logical operations, error correction and measurement of the output of the computation - on the encoded states themselves. Therefore, decoding is not …

Encoding circuits for stabilizer codes and the Steane code

Abdullah Khalid — Sat, 08 Oct 2022 00:00:00 +0500

Yesterday we introduced the Steane code. One thing we did was mathematically construct the logical basis states for Steane code. A natural question to ask is, how does one create that state using a quantum circuit?

Gottesman's method to construct logical zero state of stabilizer codes

There is a very …

An introduction to the Steane code

Abdullah Khalid — Thu, 06 Oct 2022 00:00:00 +0500

The Steane code is a simple quantum error correction code, that nevertheless has a number of interesting properties.

The Steane code encodes the state of one logical qubit into the state of 7 physical qubits, in a way that any one qubit error can be corrected.
By concatenating the code …

Designing a chip with TinyTapeout

Abdullah Khalid — Wed, 31 Aug 2022 00:00:00 +0500

I have always wanted to fully understand the process of designing and manufacturing computer chips. This weekend I dipped my feet in the water with the TinyTapeout project.

First some context. Efabless as part of their Open Shuttle Program, sponsored by Google and Skywater, is trying to encourage innovation in …

Reality and maps of reality

Abdullah Khalid — Fri, 29 Oct 2021 00:00:00 +0500

I am teaching a course on Modern Physics this semester. When I was a student, this course and Chemistry 101 really bothered me. My perception of science was that it consisted of theories with broad domains of applicability, and there was little or no overlap or conflicts between different theories …

The XOR Fourier and quantum algorithms

Abdullah Khalid — Wed, 17 Mar 2021 00:00:00 +0500

I am teaching a course in quantum computing this semester, and the hardest part is building some intuition on why quantum algorithms work. Right now, we are discussing the most basic of quantum algorithms, the Deutsch-Jozsa and the Bernstein-Vazirani algorithms. The popular textbooks on quantum computing don't do justice to …

Impossibility proofs

Abdullah Khalid — Fri, 04 Dec 2020 00:00:00 +0500

Patrick Honner over at Quanta Magazine has an essay on what impossibility proofs in mathematics can teach us. He brings up a number of beneficial effects of exploring such proofs, described here with my interpretation.

At some point in our mathematical training, we start encountering problems that simply don't have …

Quantum Mechanics in Your Face

Abdullah Khalid — Sun, 29 Nov 2020 00:00:00 +0500

Recently, a 1994 lecture by Sidney Coleman was transcribed and put on arXiv. The whole lecture is filled with wisdom, and clarity of thought regarding the conceptual framework of quantum mechanics. One particular point really struck me as something to permanently keep in my mind, and here described from my …

Qworld, QPakistan and the QBronze workshops

Abdullah Khalid — Sun, 22 Nov 2020 00:00:00 +0500

I recently have had the pleasure of joining QWorld, an initiative to spread knowledge and skills related to quantum technologies across the world.

This started with the hardworking Jibran Rashid putting in the effort to get a group of Pakistani academics to start QPakistan, as one of the QCousins within …

The difference between classical and quantum

Abdullah Khalid — Sat, 14 Nov 2020 00:00:00 +0500

Once you imagine physics through the lens of information theory, you can answer some fundamental questions in completely different ways. One of the oft asked questions by physicists, where you can get an interesting answer, is as follows: is a given system classical or quantum mechanical in nature?

The information-theoretic …

The difference between Physics and Chemistry

Abdullah Khalid — Tue, 10 Nov 2020 00:00:00 +0500

In a hallway discussion at the University, somebody claimed that atomic and molecular Chemistry is just Physics because the laws that govern the former are those well-studied by the latter. I have often held similar views, but when somebody else poses the same same, it is easier to be assess …

Scientific experts and authority

Abdullah Khalid — Fri, 08 May 2020 00:00:00 +0500

Somebody posted on Hacker News the Baloney Detection Kit by Carl Sagan. Wonderful reading, as is the full book, Demon Haunted World: Science as the Candle in the Dark.

One person, perhaps trolling, asked

'Arguments from authority carry little weight — "authorities" have made mistakes in the past. They will do …

Bell's theorem for temporal order

Abdullah Khalid — Sun, 02 Feb 2020 00:00:00 +0500

To figure a unification of quantum theory and gravity, the physics community has recently started pursuing a new direction. The core idea of this direction is rather simple. Suppose, an object with mass is placed in a quantum superposition of two location, then presumably the gravitational interaction of this object …