What is a qubit?
I wanted to understand quantum computing properly, which for me means building the thing rather than driving a framework that does the linear algebra in the basement and hands back an answer.
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Quantum Computing from Scratch
Building a NumPy quantum simulator from a single qubit to Shor's algorithm, density matrices, noise, and error correction. Nothing asserted that the code cannot show.
The Whole Machine Is an Array
This series builds quantum computing from nothing but NumPy: a qubit is a length-two complex array, a gate is a small matrix, and everything mysterious (superposition, entanglement, interference, measurement) is something you can watch happen inside the array rather than take on faith.
The arc runs in three movements. Posts 0 through 3 build the pure-state machinery and cash it in on Grover’s search. Posts 4 through 6 build the quantum Fourier transform, phase estimation, and Shor’s algorithm, the payoff of the pure-state picture. Posts 7 through 12 rebuild the engine to scale, then give up the pure-state picture itself: density matrices, noise and decoherence, error correction, the consolidated engine in full, and a closing essay on what the Born rule does and does not mean.
The Code
Every post executes its own code. The library behind the series, qfs, lives
at queelius/quantum-from-scratch
with a test suite that includes differential checks against Qiskit. The
consolidated engine, reproduced verbatim in post 11, is about fifty lines.
Posts in this Series
Showing 13 of 13 posts
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Many qubits, and entanglement
In post 0 a qubit was a unit vector in $\mathbb{C}^2$, and everything about it fit in a length-two array.
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Circuits and interference
So far the qubits have mostly sat still.
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Grover's search
Deutsch-Jozsa and Bernstein-Vazirani solved artificial promise problems.
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The Quantum Fourier Transform
The last three posts built circuits whose payoff was a single global fact read out by interference.
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Phase estimation
The last post built the Quantum Fourier Transform and promised it was a readout instrument.
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Shor's algorithm
This is the one everyone has heard of: the algorithm that factors integers in polynomial time and, if a big enough quantum computer is ever built, breaks RSA.
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Scaling the simulator
This post does not add a quantum idea.
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Mixed states and the density matrix
Every state in this series so far has been a single vector with definite amplitudes.
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Noise and decoherence
Last post ended with a warning: the off-diagonal coherences of a density matrix are the fragile part, and a real qubit loses them on its own.
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Quantum error correction
Last post was the bad news: a real qubit leaks its coherence into the environment and forgets what it was doing.
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The engine, in full
Across the series I kept saying the simulator was small: a qubit is an array, a gate is a matrix, the whole thing is a few hundred lines.
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Epilogue: measure and meaning
The very first useful thing our simulator did, back in post 0, was turn a vector of amplitudes into a vector of probabilities.