Quantum Computing Institute

Fundamentals

What is a qubit?

A classical bit is 0 or 1. A qubit is a quantum system that can be in a superposition of |0> and |1> simultaneously: |psi> = alpha|0> + beta|1>, where |alpha|^2 + |beta|^2 = 1. When measured, it collapses to |0> with probability |alpha|^2 or |1> with probability |beta|^2.

Key Concepts

• Superposition — a qubit exists in multiple states simultaneously until measured
• Entanglement — two qubits become correlated; measuring one instantly determines the other
• Interference — quantum amplitudes can add (constructive) or cancel (destructive)
• Decoherence — quantum states are fragile; interaction with environment destroys superposition
• No-cloning theorem — you cannot copy an unknown quantum state
• Quantum gates — unitary operations that transform qubit states (analogous to classical logic gates)

Quantum vs Classical

• N classical bits = one state out of 2^N. N qubits = superposition of ALL 2^N states simultaneously.
• Quantum parallelism: a single operation acts on all 2^N states at once
• But: you can only extract limited information through measurement
• Quantum advantage requires clever algorithms that amplify correct answers

Free Courses

Textbooks

• Nielsen & Chuang — "Quantum Computation and Quantum Information." THE textbook. Covers everything from linear algebra to quantum error correction.
• Scott Aaronson: Quantum Computing Since Democritus — Accessible, witty overview connecting QC to complexity theory and philosophy.
• Hidary: Quantum Computing: An Applied Approach — Practical, code-heavy approach with Qiskit examples.
• Strassler: Quantum Field Theory — For those wanting deeper physics foundations.
• Preskill: Quantum Computing in the NISQ era and beyond — Seminal paper on near-term quantum computing. Free on arXiv.

Key Research Papers

Open-Source Tools

Quantum Hardware Providers

Algorithm Reference

Near-term (NISQ) Algorithms

• VQE — Variational Quantum Eigensolver. Find ground state energy of molecules. Hybrid quantum-classical.
• QAOA — Quantum Approximate Optimization. Solve combinatorial problems (MaxCut, TSP).
• Quantum ML — Quantum kernel methods, quantum neural networks, quantum feature maps.
• Quantum simulation — Simulate quantum systems (materials, chemistry) that are hard classically.

Fault-Tolerant Algorithms (future hardware)

• Shor's algorithm — Factor large integers in polynomial time. Breaks RSA encryption.
• Grover's algorithm — Search unsorted database in O(sqrt(N)). Quadratic speedup.
• Quantum Phase Estimation — Estimate eigenvalues. Building block for Shor and HHL.
• HHL algorithm — Solve linear systems exponentially faster (with caveats).
• Quantum walks — Graph traversal with quantum speedup. Used in element distinctness.
• QFT — Quantum Fourier Transform. Core of Shor's and QPE. Exponentially faster than FFT.

Quantum Error Correction

• Surface codes — Most promising error correction code. Threshold ~1% error rate.
• Steane code — [[7,1,3]] code. Encodes 1 logical qubit in 7 physical qubits.
• Bacon-Shor code — Subsystem code with simpler syndrome measurement.
• Color codes — Transversal gates, topological protection.

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