Quantum Boltzmann Machines and Their Training
Quantum Boltzmann machines extend Boltzmann machines with quantum terms. How they are trained, possible uses and current challenges.
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Quantum Gibbs States: Preparation and Complexity
Quantum Gibbs states describe quantum systems in thermal equilibrium. How hard they are to prepare and study, and their uses.
The Cost of Quantum State Tomography
Full quantum state tomography needs a number of measurements that grows exponentially with qubits. The cost, the methods and the alternatives.
Quantum State Distinguishability and Trace Distance
How distinguishable two quantum states are is measured by the trace distance and fidelity. Why it matters for measurement, protocols and codes.
The BB84 Protocol: The First QKD Scheme
BB84, proposed by Bennett and Brassard in 1984, was the first QKD protocol. How it encodes bits in photons and detects eavesdropping.
Quantum Oracle Query Complexity and Its Bounds
Oracle query complexity counts the queries a quantum algorithm needs. Bounds, amplitude amplification, speedups and practical limitations.
Quantum Computational Geometry and Its Algorithms
Quantum algorithms for computational geometry problems such as convex hulls and point location, and where speedups are possible.
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.
Solving Polynomial Equations on Quantum Hardware
How quantum algorithms approach polynomial equations and polynomial optimization, and what speedups are plausible.
Quantum Simulation: Using Qubits to Model Physics
Quantum simulation uses qubits to model other quantum systems. The basic approach and its uses in materials science and chemistry.
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.