Quantum¶

Making quantum leaps in understanding.

I'm John Azariah — a lifelong student interested in mathematics, physics, and quantum computing, bringing three decades of software engineering and functional programming to get a better understanding of what makes the universe tick.

This is the quantum computing companion to my main blog, which covers functional programming, software engineering, and language design.

Series¶

Linear Algebra for Fun and Profit¶

The linear algebra behind quantum computing and machine learning. Each post builds from first principles with a single running example you can check by hand.

How to Raise e to a Matrix (and Why You'd Want To) — the matrix exponential solves the Schrödinger equation, and the result is a rotation rather than a stretch.
Where Eigenvalues Pay Rent — three industries, three matrices, three ways the same linear algebra pays rent.
The Eigensolver Zoo — every eigensolver is a function of the operator; this post surveys the classical half.
What a Difference i Makes — insert a factor of i and stretch becomes rotation. The quantum eigensolvers.

The Quantum Bottleneck¶

In The Quantum Bottleneck, I begin with problems that already cost industries real money, then follow each one down to the mathematical obstruction and the circuit proposed to address it. Every post has a runnable notebook and a reality check against the classical methods and hardware limits that remain.

The $50M Delivery Route — UPS can save up to $50 million a year by removing one mile from each driver's daily route. We use a three-node MaxCut problem to inspect the complete QAOA loop before putting the trucks back in.
The Trapdoor — Shor's algorithm does not search for factors. A compiled phase-estimation example exposes a period, then ordinary number theory turns that period into 3 and 5.
The $2B Molecule — A two-qubit H2 example keeps the complete VQE measurement loop visible without pretending to be a drug-discovery platform.
The Feature Explosion — A quantum overlap kernel and a classical radial-basis-function kernel tie at 11/12 on the same small dataset. The negative result is the useful result.
The Convergence Wall — Classical Monte Carlo prices the option; a compiled quantum circuit shows the phase-readout mechanism behind amplitude estimation, with the unbuilt oracles left visible.
The Scheduling Nightmare — Two binary decisions are enough to inspect the QUBO-to-Ising-to-QAOA pipeline and see how faithfully a circuit can optimise the wrong model.
The Materials Maze — A two-site Hubbard benchmark is followed by a deliberately visible handoff from classical diagonalisation into compiled quantum phase estimation.
The Catalyst Bottleneck — Quantum embedding gives the quantum solver a bounded job inside a larger catalyst-screening workflow, rather than asking one device to solve the whole material.
Series overview and companion notebooks — the full eight-part path and its runnable notebooks.
Circuit Bench — thirteen circuit notes with diagrams, OpenQASM, expected output, and gate-by-gate explanations.

The complete eight-part series is now live.

From Saturday to Co-Author¶

How a functional programmer went from "what is QAOA?" on a Saturday morning to co-author on a quantum computing paper, eight weeks later. Written in Julia and grounded in functional programming.