The Hidden Subgroup Problem: Groups That Yield
For which groups the hidden subgroup problem can be solved efficiently on a quantum computer, and why the non-abelian cases remain hard.
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Tagged: Superposition
333 articles
Solving Polynomial Equations on Quantum Hardware
How quantum algorithms approach polynomial equations and polynomial optimization, and what speedups are plausible.
Quantum Algorithms: How They Get Their Speedup
Where quantum speedups come from: superposition, interference and entanglement, illustrated with Shor’s and Grover’s algorithms.
Quantum Class Separations: Where Quantum Wins
Where quantum and classical complexity classes are known or believed to differ, from oracle separations to the complexity zoo.
Models of Quantum Computation, Compared
The main models of quantum computation compared: circuits, adiabatic, measurement-based and topological, with their hardware and limits.
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 Reduction Techniques Between Problems
Reductions show that solving one problem would solve another. How reductions are used in quantum complexity theory and algorithm design.
