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Notes

Research notes

The notes are the building blocks of this notebook: each one takes a single concept, claim, or investor question and works through it from the science up. They are organized below by topic, the same four clusters as the research map, with the newest notes pinned on top. If you are new, begin with a “start here” note and follow its links.

New in the notebook

July 28, 2026 Foundations

What Is a Quantum Observable?

The state describes the system; the observable defines what is measured; a measurement gives one outcome; many measurements estimate an expectation value. Four ideas that are related without being interchangeable. Why a Pauli-Z measurement of the plus state averages to zero although no single run ever returns zero, how a bitstring becomes an eigenvalue sample, how a Hamiltonian is decomposed into Pauli terms, and the questions worth asking of any reported quantum result.

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July 6, 2026 Foundations

Quantum Phase Estimation: The Trick That Turns Physics Into a Number

Reading a molecule's energy off a quantum computer by hiding it in a phase and reading it back out. The textbook inverse-QFT method and why it is too deep for today's hardware, the leaner single-qubit version that trades qubits for thousands of measurements, and the first error-corrected demonstration: molecular hydrogen's ground-state energy on a Quantinuum trapped-ion machine.

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June 28, 2026 Hardware

The Majorana Qubit: A Bit Hidden Where Noise Cannot Reach

Microsoft's bet: a qubit that stores one bit of information across two Majorana zero modes at opposite ends of a wire, so no local noise can read the whole of it. How topological protection works, why quasiparticle poisoning is the enemy, why the modes' very existence is still contested, and why it is the qubit hardest to build but, in theory, easiest to scale.

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Foundations

The Qubit

start here

Both answers at once, and hard to hold: the basic unit of quantum information.

Superposition

The particle that interferes with itself, and why that is a resource.

Measurement

The price of looking: reading a qubit ends its quantum behavior.

Entanglement

The bond Einstein bet against, with correlations nothing classical can match.

Quantum Gates

A solved idea, an unsolved machine: how qubits are steered.

The GHZ State

start here

All together, or not at all: entanglement’s gold standard.

Qubits: the Overview

The qubit families compared, and why this is a winner-takes-most bet on physics.

Hardware

The Physical Qubit

start here

The fragile raw material every quantum machine is built from.

Coherence Time

The clock every qubit races before its information fades.

Error Correction

The Logical Qubit

Safety in numbers: many fragile qubits acting as one dependable one.

Benchmarks

Gate Fidelity

The probability an operation did what it claimed.