Quantum Gibbs Sampling: Thermal States on a Computer
Quantum Gibbs sampling prepares thermal states of quantum systems. How it differs from classical sampling and its uses in simulation and machine learning.
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Quantum Multivariate Polynomial Interpolation
How quantum methods might speed up interpolation of multivariate polynomials, the circuits involved and possible uses in cryptography and machine learning.
Boson Sampling: The Photonic Route to Quantum Advantage
Boson sampling sends photons through a network of beam splitters. Why its output is hard to simulate classically and what the experiments have shown.
The Quantum Adiabatic Algorithm, Explained
The quantum adiabatic algorithm slowly evolves a simple Hamiltonian into one encoding a problem. The adiabatic theorem, annealing and hardware limits.
Quantum Algorithms for Diophantine Equations
What quantum algorithms can and cannot do for Diophantine equations, with the roles of Shor’s, Grover’s and HHL algorithms and variational methods.
Quantum Order-Finding: The Core of Shor’s Algorithm
Order finding is the quantum core of Shor’s algorithm. How phase estimation and the quantum Fourier transform find the period of modular exponentiation.
Quantum Algorithms for Solving Pell’s Equation
How quantum algorithms solve Pell’s equation, a number theory problem linked to cryptography, using period finding and the quantum Fourier transform.
Quantum Machine Learning Algorithms, Compared
Quantum machine learning algorithms compared: how they encode data, where speedups are claimed, and the practical and theoretical challenges they face.
The Hidden Subgroup Problem and Why It Matters
The hidden subgroup problem unifies Simon’s and Shor’s algorithms. Its formulation, the role of the quantum Fourier transform and open research questions.
Quantum Phase Kickback: The Trick Behind Many Speedups
Phase kickback moves a phase from a target qubit to a control qubit. Why this simple effect underlies Deutsch-Jozsa, phase estimation and Shor’s algorithm.
The Quantum Random Walk Algorithm, Explained
How quantum random walks work: the coin operator, interference, implementation on quantum hardware, search algorithms and experiments.
Quantum Principal Component Analysis (QPCA)
Quantum principal component analysis finds the main directions in data using phase estimation. How it compares with classical PCA and its caveats.