Models of Quantum Computation, Compared
The main models of quantum computation compared: circuits, adiabatic, measurement-based and topological, with their hardware and limits.
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Quantum Interactive Proofs: Power and Protocols
Quantum interactive proofs let a verifier check a prover by exchanging quantum messages. The roles, security and the result QIP equals PSPACE.
Quantum Information Theory: Entropy and Channels
Quantum information theory: qubits, von Neumann entropy, entanglement, channels and their applications in cryptography and computing.
Quantum Non-Local Games and What They Prove
Non-local games such as CHSH and the magic square game show that entangled players can beat classical ones. What they prove and how they are used.
Quantum Channel Theory: Modelling Noise Properly
Quantum channels describe how noise acts on quantum states. Types of channels, error correction, capacity, teleportation and simulation.
Quantum Inapproximability: Limits on Approximation
Quantum inapproximability studies problems that quantum computers cannot even approximate efficiently, and its links to the quantum PCP conjecture.
Quantum Cryptography: What It Protects and How
What quantum cryptography protects and how: QKD, entanglement-based protocols, known hacking attacks and the transition to quantum-safe methods.
Quantum Key Distribution: How BB84 Works
How the BB84 protocol distributes a secret key using photon polarization and detects eavesdroppers, and the challenges of real QKD systems.
Quantum Reduction Techniques Between Problems
Reductions show that solving one problem would solve another. How reductions are used in quantum complexity theory and algorithm design.
Quantum Complexity Theory: The Classes That Matter
The complexity classes that matter for quantum computing, including BQP and QMA, the oracle model, and what is known about their power.
The Threshold Theorem: When Correction Wins
The threshold theorem shows that error correction beats error accumulation below a certain physical error rate. Codes, estimates and experiments.
Topological Quantum Computing: Braids as Gates
Topological quantum computing would perform gates by braiding anyons. The theory, error resistance, challenges and state of the experiments.