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Quantum Computing

Qubits on the Bloch sphere, quantum gates, superposition and entanglement — visualised. From the fundamentals of quantum mechanics to Grover's search and quantum cryptography.

This category explains how quantum computers store and process information using qubits instead of classical bits. By exploring each interactive Quantum Computing model you will learn how superposition lets a qubit hold many values at once, how entanglement links qubits into correlated systems, and how unitary gates such as Hadamard, CNOT and the Pauli operators transform quantum states. The simulations walk you from the geometry of the Bloch sphere through to landmark algorithms — Grover's quadratic search speed-up and Shor's polynomial-time factoring — so you build genuine intuition before touching real hardware. Understanding these ideas matters because quantum computing is reshaping cryptography, drug discovery, materials science and optimisation, making it one of the most consequential technologies of the coming decade.

3 simulations Schrödinger · Hilbert space QFT · Gates · Bloch sphere

Category Simulations

Open a simulation — it runs right in your browser

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★★★ Advanced New
Shor's Algorithm
Quantum factoring: find the period r of aˣ mod N via QFT, then gcd(a^(r/2)±1, N) reveals the factors. Watch the QFT peaks at multiples of Q/r and the classical post-processing.
Shor's Algorithm QFT Factoring Canvas 2D
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New ★★★ Advanced
Schrödinger Equation
Time-dependent Schrödinger equation in 1D. Gaussian wave packet tunnelling through a potential barrier. Visualise probability density |ψ|² and phase.
Wave Function Tunnelling Canvas 2D
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New ★★☆ Moderate
Double-Slit Experiment
Send photons one at a time and watch the interference pattern build up. Toggle the "which-path" detector and see the quantum-to-classical transition in real time.
Wave-Particle Duality Interference Canvas 2D
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New ★★★ Advanced
Hydrogen Atom Orbitals
3D probability density clouds for any (n, l, m) quantum number combination. Rendered via spherical harmonics on the GPU. Compare s, p, d and f orbitals.
Three.js Spherical Harmonics Quantum Numbers
New ★★☆ Moderate
Qubit & Bloch Sphere
Single qubit on the Bloch sphere. Apply Pauli X/Y/Z, Hadamard and phase gates interactively and watch the state vector rotate.
Three.js Qubit Gates
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New ★★☆ Moderate
Quantum Entanglement
Two-qubit Bell states. Visualise correlations, run Bell inequality tests and explore what entanglement does (and doesn't) allow.
Canvas 2D Bell States EPR CHSH
Grover's Search Algorithm
Step through Grover's amplitude amplification on a 4-qubit register. See why quantum search is O(√N) vs classical O(N).
Canvas 2D Amplitude Amplification Oracle O(√N)

Learning Resources

Deep dives into quantum computing concepts

About Quantum Computing Simulations

Qubits, gates, superposition, and quantum algorithms — interactively

Quantum computing simulations model the behaviour of quantum circuits built from qubits and unitary gates. Gate-circuit simulators track the 2ⁿ-dimensional complex state vector of n qubits as Hadamard, CNOT, Toffoli, and phase gates are applied, visualising amplitude and phase on Bloch spheres. Algorithm simulations show Grover's search algorithm achieving √N query complexity and Deutsch-Jozsa returning the global parity of a black-box function in one query.

Quantum error correction simulations demonstrate how the three-qubit bit-flip code and Shor's nine-qubit code detect and correct decoherence errors. These models are computationally exact for small qubit counts and run entirely in the browser using JavaScript complex-number arithmetic. They are ideal for developing an operational understanding of quantum speedup, entanglement, and measurement before working with real quantum hardware APIs.

Quantum computing simulations run on classical hardware by tracking the full 2ⁿ-dimensional state vector — which is why simulating more than ~30 qubits becomes infeasible classically. Real quantum computers from IBM, Google, and IonQ achieve quantum advantage by maintaining physical qubit coherence. These simulations let you build intuition for quantum circuits, interference, and algorithmic speedup without requiring a dilution refrigerator.

Key Concepts

Topics and algorithms you'll explore in this category

QubitSuperposition of |0⟩ and |1⟩ states on the Bloch sphere
Quantum GatesHadamard, CNOT, Pauli gates as unitary matrices
EntanglementBell states and non-local correlations
Grover's AlgorithmO(√N) unstructured database search
Shor's AlgorithmPolynomial-time integer factorisation
Bloch SphereGeometric representation of a single qubit state

Frequently Asked Questions

Common questions about this simulation category

What is quantum superposition?
A qubit can exist in a linear combination α|0⟩ + β|1⟩ of both basis states simultaneously, where |α|² + |β|² = 1. Measurement collapses the superposition to |0⟩ with probability |α|² or |1⟩ with probability |β|². This is not the same as classical probability — interference between α and β is possible.
How does Grover's algorithm speed up search?
Grover's algorithm uses amplitude amplification: the phase oracle marks the solution state, and the diffusion operator inverts amplitudes around their average. After O(√N) iterations, the solution state's amplitude is amplified to near-certainty, giving a quadratic speedup over classical O(N) search.
What is quantum entanglement?
Entanglement is a correlation between qubits that cannot be explained by classical probability. A Bell state |Φ+⟩ = (|00⟩ + |11⟩)/√2 has perfectly correlated measurement outcomes regardless of the distance between qubits — the basis of quantum cryptography and teleportation protocols.

Other Categories

Every interactive Quantum Computing model on this page runs free in your browser, turning abstract theory into something you can see and manipulate. Use a Quantum Computing simulation to test how gates rotate a qubit, how measurement collapses superposition, or how Grover's oracle amplifies the correct answer. Whether you are a student, an educator or a developer preparing to learn Quantum Computing online, these visual tools build the intuition needed for real-world applications such as breaking and designing cryptographic systems, simulating molecules for drug discovery, and solving large-scale optimisation problems.