# How quantum computing works An exploration of the fundamentals of quantum computing, from qubits and entanglement to Shor and Grover, quantum noise, and error correction. ## [Quantum information basics](https://web3-lab.annaburd.me/how-quantum-computing-works/quantum-information-basics/) From classical bits to qubits: state vectors and Dirac notation, measurement, compound systems, quantum circuits, and entanglement, with teleportation, superdense coding and the CHSH game. 1. [01 Classical information](https://web3-lab.annaburd.me/how-quantum-computing-works/quantum-information-basics/#classical-information) 2. [02 Quantum information](https://web3-lab.annaburd.me/how-quantum-computing-works/quantum-information-basics/#quantum-information) 3. [03 Multiple systems: classical](https://web3-lab.annaburd.me/how-quantum-computing-works/quantum-information-basics/#multiple-systems-classical) 4. [04 Multiple systems: quantum](https://web3-lab.annaburd.me/how-quantum-computing-works/quantum-information-basics/#multiple-systems-quantum) 5. [05 Quantum circuits](https://web3-lab.annaburd.me/how-quantum-computing-works/quantum-information-basics/#quantum-circuits) 6. [06 Quantum states and measurements](https://web3-lab.annaburd.me/how-quantum-computing-works/quantum-information-basics/#quantum-states-measurements) 7. [07 Limitations of quantum measurements](https://web3-lab.annaburd.me/how-quantum-computing-works/quantum-information-basics/#limitations-quantum-measurements) 8. [08 Entanglement](https://web3-lab.annaburd.me/how-quantum-computing-works/quantum-information-basics/#entanglement) ## [Quantum algorithms](https://web3-lab.annaburd.me/how-quantum-computing-works/quantum-algorithms/) What a quantum computer does better: query problems from Deutsch to Simon, the cost of classical arithmetic, phase estimation and Shor's factoring, and Grover's search. 1. [09 Query-model algorithms](https://web3-lab.annaburd.me/how-quantum-computing-works/quantum-algorithms/#quantum-algorithms) 2. [10 The cost of classical algorithms](https://web3-lab.annaburd.me/how-quantum-computing-works/quantum-algorithms/#classical-problems) 3. [11 Classical circuits as quantum circuits](https://web3-lab.annaburd.me/how-quantum-computing-works/quantum-algorithms/#classical-circuits-quantum) 4. [12 Phase estimation and factoring](https://web3-lab.annaburd.me/how-quantum-computing-works/quantum-algorithms/#phase-estimation) 5. [13 Grover's algorithm](https://web3-lab.annaburd.me/how-quantum-computing-works/quantum-algorithms/#grover) ## [Quantum states and channels](https://web3-lab.annaburd.me/how-quantum-computing-works/general-quantum-information/) Density matrices for mixed states, quantum channels and their representations, general measurements, purifications and fidelity. 1. [14 Density matrices](https://web3-lab.annaburd.me/how-quantum-computing-works/general-quantum-information/#density-matrices) 2. [15 Quantum channels](https://web3-lab.annaburd.me/how-quantum-computing-works/general-quantum-information/#quantum-channels) 3. [16 Channel representations](https://web3-lab.annaburd.me/how-quantum-computing-works/general-quantum-information/#channel-representations) 4. [17 General measurements](https://web3-lab.annaburd.me/how-quantum-computing-works/general-quantum-information/#general-measurements) 5. [18 State discrimination and tomography](https://web3-lab.annaburd.me/how-quantum-computing-works/general-quantum-information/#state-discrimination-tomography) 6. [19 Purifications](https://web3-lab.annaburd.me/how-quantum-computing-works/general-quantum-information/#purifications-fidelity) 7. [20 Fidelity](https://web3-lab.annaburd.me/how-quantum-computing-works/general-quantum-information/#fidelity-chapter) ## [Foundations of quantum error correction](https://web3-lab.annaburd.me/how-quantum-computing-works/quantum-error-correction/) How a noisy quantum computer can still compute: error-correcting codes, stabilizers, CSS, toric, surface and color codes, and fault tolerance up to the threshold theorem. 1. [21 Quantum error correction](https://web3-lab.annaburd.me/how-quantum-computing-works/quantum-error-correction/#quantum-error-correction) 2. [22 The stabilizer formalism](https://web3-lab.annaburd.me/how-quantum-computing-works/quantum-error-correction/#stabilizer-formalism) 3. [23 Quantum code constructions](https://web3-lab.annaburd.me/how-quantum-computing-works/quantum-error-correction/#code-constructions) 4. [24 Fault-tolerant quantum computing](https://web3-lab.annaburd.me/how-quantum-computing-works/quantum-error-correction/#fault-tolerance)